TSTP Solution File: SYN440-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN440-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 23:55:24 EDT 2022
% Result : Unsatisfiable 3.58s 2.58s
% Output : Proof 3.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN440-1 : TPTP v8.1.0. Released v2.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n028.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 03:45:55 EDT 2022
% 0.12/0.34 % 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.
% 3.58/2.58 % SZS status Unsatisfiable
% 3.58/2.58 % SZS output start Proof
% 3.58/2.58 tff(c3_1_type, type, (
% 3.58/2.58 c3_1: $i > $o)).
% 3.58/2.58 tff(a606_type, type, (
% 3.58/2.58 a606: $i)).
% 3.58/2.58 tff(hskp5_type, type, (
% 3.58/2.58 hskp5: $o)).
% 3.58/2.58 tff(c0_1_type, type, (
% 3.58/2.58 c0_1: $i > $o)).
% 3.58/2.58 tff(a618_type, type, (
% 3.58/2.58 a618: $i)).
% 3.58/2.58 tff(a628_type, type, (
% 3.58/2.58 a628: $i)).
% 3.58/2.58 tff(c2_1_type, type, (
% 3.58/2.58 c2_1: $i > $o)).
% 3.58/2.58 tff(c1_1_type, type, (
% 3.58/2.58 c1_1: $i > $o)).
% 3.58/2.58 tff(ndr1_0_type, type, (
% 3.58/2.58 ndr1_0: $o)).
% 3.58/2.58 tff(hskp38_type, type, (
% 3.58/2.58 hskp38: $o)).
% 3.58/2.58 tff(hskp17_type, type, (
% 3.58/2.58 hskp17: $o)).
% 3.58/2.58 tff(a673_type, type, (
% 3.58/2.58 a673: $i)).
% 3.58/2.58 tff(a648_type, type, (
% 3.58/2.58 a648: $i)).
% 3.58/2.58 tff(hskp53_type, type, (
% 3.58/2.58 hskp53: $o)).
% 3.58/2.58 tff(hskp14_type, type, (
% 3.58/2.58 hskp14: $o)).
% 3.58/2.58 tff(a603_type, type, (
% 3.58/2.58 a603: $i)).
% 3.58/2.58 tff(hskp3_type, type, (
% 3.58/2.58 hskp3: $o)).
% 3.58/2.58 tff(hskp29_type, type, (
% 3.58/2.58 hskp29: $o)).
% 3.58/2.58 tff(hskp64_type, type, (
% 3.58/2.58 hskp64: $o)).
% 3.58/2.58 tff(a617_type, type, (
% 3.58/2.58 a617: $i)).
% 3.58/2.58 tff(a651_type, type, (
% 3.58/2.58 a651: $i)).
% 3.58/2.58 tff(hskp41_type, type, (
% 3.58/2.58 hskp41: $o)).
% 3.58/2.58 tff(a670_type, type, (
% 3.58/2.58 a670: $i)).
% 3.58/2.58 tff(hskp61_type, type, (
% 3.58/2.58 hskp61: $o)).
% 3.58/2.58 tff(hskp33_type, type, (
% 3.58/2.58 hskp33: $o)).
% 3.58/2.58 tff(hskp58_type, type, (
% 3.58/2.58 hskp58: $o)).
% 3.58/2.58 tff(a663_type, type, (
% 3.58/2.58 a663: $i)).
% 3.58/2.58 tff(hskp66_type, type, (
% 3.58/2.58 hskp66: $o)).
% 3.58/2.58 tff(hskp65_type, type, (
% 3.58/2.58 hskp65: $o)).
% 3.58/2.58 tff(a599_type, type, (
% 3.58/2.58 a599: $i)).
% 3.58/2.58 tff(hskp60_type, type, (
% 3.58/2.58 hskp60: $o)).
% 3.58/2.58 tff(a675_type, type, (
% 3.58/2.58 a675: $i)).
% 3.58/2.58 tff(hskp15_type, type, (
% 3.58/2.58 hskp15: $o)).
% 3.58/2.58 tff(a625_type, type, (
% 3.58/2.58 a625: $i)).
% 3.58/2.58 tff(a624_type, type, (
% 3.58/2.58 a624: $i)).
% 3.58/2.58 tff(a674_type, type, (
% 3.58/2.58 a674: $i)).
% 3.58/2.58 tff(a669_type, type, (
% 3.58/2.58 a669: $i)).
% 3.58/2.58 tff(hskp54_type, type, (
% 3.58/2.58 hskp54: $o)).
% 3.58/2.58 tff(hskp37_type, type, (
% 3.58/2.58 hskp37: $o)).
% 3.58/2.58 tff(a607_type, type, (
% 3.58/2.58 a607: $i)).
% 3.58/2.58 tff(hskp20_type, type, (
% 3.58/2.58 hskp20: $o)).
% 3.58/2.58 tff(a635_type, type, (
% 3.58/2.58 a635: $i)).
% 3.58/2.58 tff(a609_type, type, (
% 3.58/2.58 a609: $i)).
% 3.58/2.58 tff(hskp6_type, type, (
% 3.58/2.58 hskp6: $o)).
% 3.58/2.58 tff(a662_type, type, (
% 3.58/2.58 a662: $i)).
% 3.58/2.58 tff(hskp57_type, type, (
% 3.58/2.58 hskp57: $o)).
% 3.58/2.58 tff(hskp42_type, type, (
% 3.58/2.58 hskp42: $o)).
% 3.58/2.58 tff(a653_type, type, (
% 3.58/2.58 a653: $i)).
% 3.58/2.58 tff(hskp55_type, type, (
% 3.58/2.58 hskp55: $o)).
% 3.58/2.58 tff(a627_type, type, (
% 3.58/2.58 a627: $i)).
% 3.58/2.58 tff(hskp16_type, type, (
% 3.58/2.58 hskp16: $o)).
% 3.58/2.58 tff(hskp9_type, type, (
% 3.58/2.58 hskp9: $o)).
% 3.58/2.58 tff(a623_type, type, (
% 3.58/2.58 a623: $i)).
% 3.58/2.58 tff(hskp45_type, type, (
% 3.58/2.58 hskp45: $o)).
% 3.58/2.58 tff(a613_type, type, (
% 3.58/2.58 a613: $i)).
% 3.58/2.58 tff(a658_type, type, (
% 3.58/2.58 a658: $i)).
% 3.58/2.58 tff(hskp56_type, type, (
% 3.58/2.58 hskp56: $o)).
% 3.58/2.58 tff(a660_type, type, (
% 3.58/2.58 a660: $i)).
% 3.58/2.58 tff(a644_type, type, (
% 3.58/2.58 a644: $i)).
% 3.58/2.58 tff(hskp51_type, type, (
% 3.58/2.58 hskp51: $o)).
% 3.58/2.58 tff(hskp62_type, type, (
% 3.58/2.58 hskp62: $o)).
% 3.58/2.58 tff(a671_type, type, (
% 3.58/2.58 a671: $i)).
% 3.58/2.58 tff(a612_type, type, (
% 3.58/2.58 a612: $i)).
% 3.58/2.58 tff(hskp8_type, type, (
% 3.58/2.58 hskp8: $o)).
% 3.58/2.58 tff(a672_type, type, (
% 3.58/2.58 a672: $i)).
% 3.58/2.58 tff(hskp63_type, type, (
% 3.58/2.58 hskp63: $o)).
% 3.58/2.58 tff(a647_type, type, (
% 3.58/2.58 a647: $i)).
% 3.58/2.58 tff(hskp52_type, type, (
% 3.58/2.58 hskp52: $o)).
% 3.58/2.58 tff(hskp25_type, type, (
% 3.58/2.58 hskp25: $o)).
% 3.58/2.58 tff(a646_type, type, (
% 3.58/2.58 a646: $i)).
% 3.58/2.58 tff(a608_type, type, (
% 3.58/2.58 a608: $i)).
% 3.58/2.58 tff(a605_type, type, (
% 3.58/2.58 a605: $i)).
% 3.58/2.58 tff(hskp36_type, type, (
% 3.58/2.58 hskp36: $o)).
% 3.58/2.58 tff(1,assumption,(~c0_1(a628)), introduced(assumption)).
% 3.58/2.58 tff(2,plain,
% 3.58/2.58 (^[V: $i, U: $i] : refl((hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))),
% 3.58/2.58 inference(bind,[status(th)],[])).
% 3.58/2.58 tff(3,plain,
% 3.58/2.58 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 3.58/2.58 inference(quant_intro,[status(thm)],[2])).
% 3.58/2.58 tff(4,plain,
% 3.58/2.58 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(5,plain,
% 3.58/2.58 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c1_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)))), ((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), ((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))))), (((((~c3_1(U)) | (~c1_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)))), (((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V))), ((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V)))), (((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V))), (((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) | c1_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) | c1_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) | c1_1(V)) | c0_1(V)) | hskp38) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp38))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp38) <=> (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), (((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) | c1_1(V)) | c0_1(V)) | hskp38) <=> (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))))),
% 3.58/2.58 inference(bind,[status(th)],[])).
% 3.58/2.58 tff(6,plain,
% 3.58/2.58 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) | c1_1(V)) | c0_1(V)) | hskp38) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 3.58/2.58 inference(quant_intro,[status(thm)],[5])).
% 3.58/2.58 tff(7,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) | c1_1(V)) | c0_1(V)) | hskp38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause302')).
% 3.58/2.58 tff(8,plain,
% 3.58/2.58 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[7, 6])).
% 3.58/2.58 tff(9,plain,
% 3.58/2.58 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[8, 4])).
% 3.58/2.58 tff(10,plain,(
% 3.58/2.58 ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 3.58/2.58 inference(skolemize,[status(sab)],[9])).
% 3.58/2.58 tff(11,plain,
% 3.58/2.58 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[10, 3])).
% 3.58/2.58 tff(12,assumption,(~hskp17), introduced(assumption)).
% 3.58/2.58 tff(13,assumption,(~c2_1(a673)), introduced(assumption)).
% 3.58/2.58 tff(14,plain,
% 3.58/2.58 (^[V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 3.58/2.58 inference(bind,[status(th)],[])).
% 3.58/2.58 tff(15,plain,
% 3.58/2.58 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 3.58/2.58 inference(quant_intro,[status(thm)],[14])).
% 3.58/2.58 tff(16,plain,
% 3.58/2.58 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(17,plain,
% 3.58/2.58 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c1_1(V))) <=> ((~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 3.58/2.58 inference(bind,[status(th)],[])).
% 3.58/2.58 tff(18,plain,
% 3.58/2.58 (![V: $i, U: $i] : (((((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 3.58/2.58 inference(quant_intro,[status(thm)],[17])).
% 3.58/2.58 tff(19,axiom,(![V: $i, U: $i] : (((((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause301')).
% 3.58/2.58 tff(20,plain,
% 3.58/2.58 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[19, 18])).
% 3.58/2.58 tff(21,plain,
% 3.58/2.58 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[20, 16])).
% 3.58/2.58 tff(22,plain,(
% 3.58/2.58 ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 3.58/2.58 inference(skolemize,[status(sab)],[21])).
% 3.58/2.58 tff(23,plain,
% 3.58/2.58 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[22, 15])).
% 3.58/2.58 tff(24,assumption,(~hskp64), introduced(assumption)).
% 3.58/2.58 tff(25,plain,
% 3.58/2.58 (^[U: $i] : refl((hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 3.58/2.58 inference(bind,[status(th)],[])).
% 3.58/2.58 tff(26,plain,
% 3.58/2.58 (![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.58/2.58 inference(quant_intro,[status(thm)],[25])).
% 3.58/2.58 tff(27,plain,
% 3.58/2.58 (![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(28,plain,
% 3.58/2.58 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp53) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp53))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp53) <=> (hskp53 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp53) <=> (hskp53 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp53) | hskp17) <=> ((hskp53 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp17))), rewrite(((hskp53 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp17) <=> (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp53) | hskp17) <=> (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 3.58/2.58 inference(bind,[status(th)],[])).
% 3.58/2.58 tff(29,plain,
% 3.58/2.58 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp53) | hskp17) <=> ![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.58/2.58 inference(quant_intro,[status(thm)],[28])).
% 3.58/2.58 tff(30,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp53) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause285')).
% 3.58/2.58 tff(31,plain,
% 3.58/2.58 (![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[30, 29])).
% 3.58/2.58 tff(32,plain,
% 3.58/2.58 (![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[31, 27])).
% 3.58/2.58 tff(33,plain,(
% 3.58/2.58 ![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.58/2.58 inference(skolemize,[status(sab)],[32])).
% 3.58/2.58 tff(34,plain,
% 3.58/2.58 (![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[33, 26])).
% 3.58/2.58 tff(35,assumption,(~hskp53), introduced(assumption)).
% 3.58/2.58 tff(36,assumption,(hskp58), introduced(assumption)).
% 3.58/2.58 tff(37,plain,
% 3.58/2.58 (((~hskp58) | (~c1_1(a663))) <=> ((~hskp58) | (~c1_1(a663)))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(38,plain,
% 3.58/2.58 (((~c1_1(a663)) | (~hskp58)) <=> ((~hskp58) | (~c1_1(a663)))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(39,axiom,((~c1_1(a663)) | (~hskp58)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 3.58/2.58 tff(40,plain,
% 3.58/2.58 ((~hskp58) | (~c1_1(a663))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[39, 38])).
% 3.58/2.58 tff(41,plain,
% 3.58/2.58 ((~hskp58) | (~c1_1(a663))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[40, 37])).
% 3.58/2.58 tff(42,plain,
% 3.58/2.58 (~c1_1(a663)),
% 3.58/2.58 inference(unit_resolution,[status(thm)],[41, 36])).
% 3.58/2.58 tff(43,plain,
% 3.58/2.58 (((~hskp58) | (~c0_1(a663))) <=> ((~hskp58) | (~c0_1(a663)))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(44,plain,
% 3.58/2.58 (((~c0_1(a663)) | (~hskp58)) <=> ((~hskp58) | (~c0_1(a663)))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(45,axiom,((~c0_1(a663)) | (~hskp58)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 3.58/2.58 tff(46,plain,
% 3.58/2.58 ((~hskp58) | (~c0_1(a663))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[45, 44])).
% 3.58/2.58 tff(47,plain,
% 3.58/2.58 ((~hskp58) | (~c0_1(a663))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[46, 43])).
% 3.58/2.58 tff(48,plain,
% 3.58/2.58 (~c0_1(a663)),
% 3.58/2.58 inference(unit_resolution,[status(thm)],[47, 36])).
% 3.58/2.58 tff(49,plain,
% 3.58/2.58 (((~hskp58) | c3_1(a663)) <=> ((~hskp58) | c3_1(a663))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(50,axiom,((~hskp58) | c3_1(a663)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 3.58/2.58 tff(51,plain,
% 3.58/2.58 ((~hskp58) | c3_1(a663)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[50, 49])).
% 3.58/2.58 tff(52,plain,
% 3.58/2.58 ((~hskp58) | c3_1(a663)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[51, 49])).
% 3.58/2.58 tff(53,plain,
% 3.58/2.58 ((~hskp58) | c3_1(a663)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[52, 49])).
% 3.58/2.58 tff(54,plain,
% 3.58/2.58 ((~hskp58) | c3_1(a663)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[53, 49])).
% 3.58/2.58 tff(55,plain,
% 3.58/2.58 ((~hskp58) | c3_1(a663)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[54, 49])).
% 3.58/2.58 tff(56,plain,
% 3.58/2.58 ((~hskp58) | c3_1(a663)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[55, 49])).
% 3.58/2.58 tff(57,plain,
% 3.58/2.58 ((~hskp58) | c3_1(a663)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[56, 49])).
% 3.58/2.58 tff(58,plain,
% 3.58/2.58 ((~hskp58) | c3_1(a663)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[57, 49])).
% 3.58/2.58 tff(59,plain,
% 3.58/2.58 (c3_1(a663)),
% 3.58/2.58 inference(unit_resolution,[status(thm)],[58, 36])).
% 3.58/2.58 tff(60,assumption,(~ndr1_0), introduced(assumption)).
% 3.58/2.58 tff(61,plain,
% 3.58/2.58 ((ndr1_0 | (~hskp64)) <=> (ndr1_0 | (~hskp64))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(62,plain,
% 3.58/2.58 (((~hskp64) | ndr1_0) <=> (ndr1_0 | (~hskp64))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(63,axiom,((~hskp64) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 3.58/2.58 tff(64,plain,
% 3.58/2.58 (ndr1_0 | (~hskp64)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[63, 62])).
% 3.58/2.58 tff(65,plain,
% 3.58/2.58 (ndr1_0 | (~hskp64)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[64, 61])).
% 3.58/2.58 tff(66,plain,
% 3.58/2.58 (~hskp64),
% 3.58/2.58 inference(unit_resolution,[status(thm)],[65, 60])).
% 3.58/2.58 tff(67,plain,
% 3.58/2.58 (((~hskp66) | ndr1_0) <=> ((~hskp66) | ndr1_0)),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(68,axiom,((~hskp66) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 3.58/2.58 tff(69,plain,
% 3.58/2.58 ((~hskp66) | ndr1_0),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[68, 67])).
% 3.58/2.58 tff(70,plain,
% 3.58/2.58 ((~hskp66) | ndr1_0),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[69, 67])).
% 3.58/2.58 tff(71,plain,
% 3.58/2.58 ((~hskp66) | ndr1_0),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[70, 67])).
% 3.58/2.58 tff(72,plain,
% 3.58/2.58 ((~hskp66) | ndr1_0),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[71, 67])).
% 3.58/2.58 tff(73,plain,
% 3.58/2.58 ((~hskp66) | ndr1_0),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[72, 67])).
% 3.58/2.58 tff(74,plain,
% 3.58/2.58 ((~hskp66) | ndr1_0),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[73, 67])).
% 3.58/2.58 tff(75,plain,
% 3.58/2.58 ((~hskp66) | ndr1_0),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[74, 67])).
% 3.58/2.58 tff(76,plain,
% 3.58/2.58 ((~hskp66) | ndr1_0),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[75, 67])).
% 3.58/2.58 tff(77,plain,
% 3.58/2.58 (~hskp66),
% 3.58/2.58 inference(unit_resolution,[status(thm)],[76, 60])).
% 3.58/2.58 tff(78,plain,
% 3.58/2.58 ((ndr1_0 | (~hskp65)) <=> (ndr1_0 | (~hskp65))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(79,plain,
% 3.58/2.58 (((~hskp65) | ndr1_0) <=> (ndr1_0 | (~hskp65))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(80,axiom,((~hskp65) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 3.58/2.58 tff(81,plain,
% 3.58/2.58 (ndr1_0 | (~hskp65)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[80, 79])).
% 3.58/2.58 tff(82,plain,
% 3.58/2.58 (ndr1_0 | (~hskp65)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[81, 78])).
% 3.58/2.58 tff(83,plain,
% 3.58/2.58 (~hskp65),
% 3.58/2.58 inference(unit_resolution,[status(thm)],[82, 60])).
% 3.58/2.58 tff(84,plain,
% 3.58/2.58 ((hskp66 | hskp65 | hskp64) <=> (hskp66 | hskp65 | hskp64)),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(85,plain,
% 3.58/2.58 (((hskp64 | hskp65) | hskp66) <=> (hskp66 | hskp65 | hskp64)),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(86,axiom,((hskp64 | hskp65) | hskp66), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 3.58/2.58 tff(87,plain,
% 3.58/2.58 (hskp66 | hskp65 | hskp64),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[86, 85])).
% 3.58/2.58 tff(88,plain,
% 3.58/2.58 (hskp66 | hskp65 | hskp64),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[87, 84])).
% 3.58/2.58 tff(89,plain,
% 3.58/2.58 (hskp66 | hskp65 | hskp64),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[88, 84])).
% 3.58/2.58 tff(90,plain,
% 3.58/2.58 (hskp66 | hskp65 | hskp64),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[89, 84])).
% 3.58/2.58 tff(91,plain,
% 3.58/2.58 (hskp66 | hskp65 | hskp64),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[90, 84])).
% 3.58/2.58 tff(92,plain,
% 3.58/2.58 (hskp66 | hskp65 | hskp64),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[91, 84])).
% 3.58/2.58 tff(93,plain,
% 3.58/2.58 (hskp66 | hskp65 | hskp64),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[92, 84])).
% 3.58/2.58 tff(94,plain,
% 3.58/2.58 (hskp66 | hskp65 | hskp64),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[93, 84])).
% 3.58/2.58 tff(95,plain,
% 3.58/2.58 ($false),
% 3.58/2.58 inference(unit_resolution,[status(thm)],[94, 83, 77, 66])).
% 3.58/2.58 tff(96,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 3.58/2.58 tff(97,plain,
% 3.58/2.58 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c3_1(a663)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c3_1(a663)))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(98,plain,
% 3.58/2.58 ((hskp53 | hskp17 | (~ndr1_0) | c1_1(a663) | c0_1(a663) | (~c3_1(a663))) <=> (hskp53 | hskp17 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c3_1(a663)))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(99,plain,
% 3.58/2.58 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c3_1(a663))))),
% 3.58/2.58 inference(monotonicity,[status(thm)],[98])).
% 3.58/2.58 tff(100,plain,
% 3.58/2.58 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c3_1(a663)))),
% 3.58/2.58 inference(transitivity,[status(thm)],[99, 97])).
% 3.58/2.58 tff(101,plain,
% 3.58/2.58 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)))),
% 3.58/2.58 inference(quant_inst,[status(thm)],[])).
% 3.58/2.58 tff(102,plain,
% 3.58/2.58 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c3_1(a663))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[101, 100])).
% 3.58/2.58 tff(103,plain,
% 3.58/2.58 ($false),
% 3.58/2.58 inference(unit_resolution,[status(thm)],[102, 96, 35, 12, 59, 48, 42, 34])).
% 3.58/2.58 tff(104,plain,((~hskp58) | hskp53 | hskp17), inference(lemma,lemma(discharge,[]))).
% 3.58/2.58 tff(105,plain,
% 3.58/2.58 (~hskp58),
% 3.58/2.58 inference(unit_resolution,[status(thm)],[104, 35, 12])).
% 3.58/2.58 tff(106,assumption,(~hskp41), introduced(assumption)).
% 3.58/2.58 tff(107,plain,
% 3.58/2.58 (^[U: $i] : refl((hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 3.58/2.58 inference(bind,[status(th)],[])).
% 3.58/2.58 tff(108,plain,
% 3.58/2.58 (![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.58/2.58 inference(quant_intro,[status(thm)],[107])).
% 3.58/2.58 tff(109,plain,
% 3.58/2.58 (![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(110,plain,
% 3.58/2.58 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c0_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp58) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp58))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp58) <=> (hskp58 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp58) <=> (hskp58 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp58) | hskp41) <=> ((hskp58 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp41))), rewrite(((hskp58 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp41) <=> (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp58) | hskp41) <=> (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 3.58/2.58 inference(bind,[status(th)],[])).
% 3.58/2.58 tff(111,plain,
% 3.58/2.58 (![U: $i] : ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp58) | hskp41) <=> ![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.58/2.58 inference(quant_intro,[status(thm)],[110])).
% 3.58/2.58 tff(112,axiom,(![U: $i] : ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp58) | hskp41)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause295')).
% 3.58/2.58 tff(113,plain,
% 3.58/2.58 (![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[112, 111])).
% 3.58/2.58 tff(114,plain,
% 3.58/2.58 (![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[113, 109])).
% 3.58/2.58 tff(115,plain,(
% 3.58/2.58 ![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.58/2.58 inference(skolemize,[status(sab)],[114])).
% 3.58/2.58 tff(116,plain,
% 3.58/2.58 (![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[115, 108])).
% 3.58/2.58 tff(117,assumption,(hskp33), introduced(assumption)).
% 3.58/2.58 tff(118,plain,
% 3.58/2.58 (((~hskp33) | (~c2_1(a599))) <=> ((~hskp33) | (~c2_1(a599)))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(119,plain,
% 3.58/2.58 (((~c2_1(a599)) | (~hskp33)) <=> ((~hskp33) | (~c2_1(a599)))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(120,axiom,((~c2_1(a599)) | (~hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause210')).
% 3.58/2.58 tff(121,plain,
% 3.58/2.58 ((~hskp33) | (~c2_1(a599))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[120, 119])).
% 3.58/2.58 tff(122,plain,
% 3.58/2.58 ((~hskp33) | (~c2_1(a599))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[121, 118])).
% 3.58/2.58 tff(123,plain,
% 3.58/2.58 (~c2_1(a599)),
% 3.58/2.58 inference(unit_resolution,[status(thm)],[122, 117])).
% 3.58/2.58 tff(124,plain,
% 3.58/2.58 (((~hskp33) | c3_1(a599)) <=> ((~hskp33) | c3_1(a599))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(125,axiom,((~hskp33) | c3_1(a599)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 3.58/2.58 tff(126,plain,
% 3.58/2.58 ((~hskp33) | c3_1(a599)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[125, 124])).
% 3.58/2.58 tff(127,plain,
% 3.58/2.58 ((~hskp33) | c3_1(a599)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[126, 124])).
% 3.58/2.58 tff(128,plain,
% 3.58/2.58 ((~hskp33) | c3_1(a599)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[127, 124])).
% 3.58/2.58 tff(129,plain,
% 3.58/2.58 ((~hskp33) | c3_1(a599)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[128, 124])).
% 3.58/2.58 tff(130,plain,
% 3.58/2.58 ((~hskp33) | c3_1(a599)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[129, 124])).
% 3.58/2.58 tff(131,plain,
% 3.58/2.58 ((~hskp33) | c3_1(a599)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[130, 124])).
% 3.58/2.58 tff(132,plain,
% 3.58/2.58 ((~hskp33) | c3_1(a599)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[131, 124])).
% 3.58/2.58 tff(133,plain,
% 3.58/2.58 ((~hskp33) | c3_1(a599)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[132, 124])).
% 3.58/2.58 tff(134,plain,
% 3.58/2.58 (c3_1(a599)),
% 3.58/2.58 inference(unit_resolution,[status(thm)],[133, 117])).
% 3.58/2.58 tff(135,plain,
% 3.58/2.58 (((~hskp33) | c0_1(a599)) <=> ((~hskp33) | c0_1(a599))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(136,axiom,((~hskp33) | c0_1(a599)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 3.58/2.58 tff(137,plain,
% 3.58/2.58 ((~hskp33) | c0_1(a599)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[136, 135])).
% 3.58/2.58 tff(138,plain,
% 3.58/2.58 ((~hskp33) | c0_1(a599)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[137, 135])).
% 3.58/2.58 tff(139,plain,
% 3.58/2.58 ((~hskp33) | c0_1(a599)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[138, 135])).
% 3.58/2.58 tff(140,plain,
% 3.58/2.58 ((~hskp33) | c0_1(a599)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[139, 135])).
% 3.58/2.58 tff(141,plain,
% 3.58/2.58 ((~hskp33) | c0_1(a599)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[140, 135])).
% 3.58/2.58 tff(142,plain,
% 3.58/2.58 ((~hskp33) | c0_1(a599)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[141, 135])).
% 3.58/2.58 tff(143,plain,
% 3.58/2.58 ((~hskp33) | c0_1(a599)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[142, 135])).
% 3.58/2.58 tff(144,plain,
% 3.58/2.58 ((~hskp33) | c0_1(a599)),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[143, 135])).
% 3.58/2.58 tff(145,plain,
% 3.58/2.58 (c0_1(a599)),
% 3.58/2.58 inference(unit_resolution,[status(thm)],[144, 117])).
% 3.58/2.58 tff(146,assumption,(~hskp58), introduced(assumption)).
% 3.58/2.58 tff(147,plain,
% 3.58/2.58 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a599) | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a599) | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(148,plain,
% 3.58/2.58 ((hskp58 | hskp41 | (~ndr1_0) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599))) <=> (hskp58 | hskp41 | c2_1(a599) | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(149,plain,
% 3.58/2.58 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a599) | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599))))),
% 3.58/2.58 inference(monotonicity,[status(thm)],[148])).
% 3.58/2.58 tff(150,plain,
% 3.58/2.58 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a599) | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)))),
% 3.58/2.58 inference(transitivity,[status(thm)],[149, 147])).
% 3.58/2.58 tff(151,plain,
% 3.58/2.58 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))),
% 3.58/2.58 inference(quant_inst,[status(thm)],[])).
% 3.58/2.58 tff(152,plain,
% 3.58/2.58 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a599) | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[151, 150])).
% 3.58/2.58 tff(153,plain,
% 3.58/2.58 ($false),
% 3.58/2.58 inference(unit_resolution,[status(thm)],[152, 96, 146, 106, 145, 134, 123, 116])).
% 3.58/2.58 tff(154,plain,((~hskp33) | hskp58 | hskp41), inference(lemma,lemma(discharge,[]))).
% 3.58/2.58 tff(155,plain,
% 3.58/2.58 (~hskp33),
% 3.58/2.58 inference(unit_resolution,[status(thm)],[154, 106, 105])).
% 3.58/2.58 tff(156,assumption,(hskp15), introduced(assumption)).
% 3.58/2.58 tff(157,plain,
% 3.58/2.58 (((~hskp15) | (~c0_1(a625))) <=> ((~hskp15) | (~c0_1(a625)))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(158,plain,
% 3.58/2.58 (((~c0_1(a625)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a625)))),
% 3.58/2.58 inference(rewrite,[status(thm)],[])).
% 3.58/2.58 tff(159,axiom,((~c0_1(a625)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause247')).
% 3.58/2.58 tff(160,plain,
% 3.58/2.58 ((~hskp15) | (~c0_1(a625))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[159, 158])).
% 3.58/2.58 tff(161,plain,
% 3.58/2.58 ((~hskp15) | (~c0_1(a625))),
% 3.58/2.58 inference(modus_ponens,[status(thm)],[160, 157])).
% 3.58/2.58 tff(162,plain,
% 3.58/2.59 (~c0_1(a625)),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[161, 156])).
% 3.58/2.59 tff(163,plain,
% 3.58/2.59 (((~hskp15) | (~c1_1(a625))) <=> ((~hskp15) | (~c1_1(a625)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(164,plain,
% 3.58/2.59 (((~c1_1(a625)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a625)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(165,axiom,((~c1_1(a625)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause246')).
% 3.58/2.59 tff(166,plain,
% 3.58/2.59 ((~hskp15) | (~c1_1(a625))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[165, 164])).
% 3.58/2.59 tff(167,plain,
% 3.58/2.59 ((~hskp15) | (~c1_1(a625))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[166, 163])).
% 3.58/2.59 tff(168,plain,
% 3.58/2.59 (~c1_1(a625)),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[167, 156])).
% 3.58/2.59 tff(169,plain,
% 3.58/2.59 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(170,plain,
% 3.58/2.59 ((hskp53 | hskp17 | (~ndr1_0) | c1_1(a625) | c0_1(a625) | (~c3_1(a625))) <=> (hskp53 | hskp17 | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(171,plain,
% 3.58/2.59 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625))))),
% 3.58/2.59 inference(monotonicity,[status(thm)],[170])).
% 3.58/2.59 tff(172,plain,
% 3.58/2.59 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)))),
% 3.58/2.59 inference(transitivity,[status(thm)],[171, 169])).
% 3.58/2.59 tff(173,plain,
% 3.58/2.59 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))),
% 3.58/2.59 inference(quant_inst,[status(thm)],[])).
% 3.58/2.59 tff(174,plain,
% 3.58/2.59 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[173, 172])).
% 3.58/2.59 tff(175,plain,
% 3.58/2.59 (~c3_1(a625)),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[174, 96, 35, 12, 168, 162, 34])).
% 3.58/2.59 tff(176,plain,
% 3.58/2.59 (^[V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V)))),
% 3.58/2.59 inference(bind,[status(th)],[])).
% 3.58/2.59 tff(177,plain,
% 3.58/2.59 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.58/2.59 inference(quant_intro,[status(thm)],[176])).
% 3.58/2.59 tff(178,plain,
% 3.58/2.59 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(179,plain,
% 3.58/2.59 (^[V: $i, U: $i] : 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)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U)) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c0_1(V))), ((((~ndr1_0) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c0_1(V)))), (((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | c0_1(V)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | c0_1(V)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c0_1(V))), (((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c0_1(V)))), ((((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V))), ((((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V)))), (((((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) | c3_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))), (((((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) | c3_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V)))), ((((((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) | c3_1(V)) | c1_1(V)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))), ((((((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) | c3_1(V)) | c1_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))))),
% 3.58/2.59 inference(bind,[status(th)],[])).
% 3.58/2.59 tff(180,plain,
% 3.58/2.59 (![V: $i, U: $i] : (((((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) | c3_1(V)) | c1_1(V)) | c3_1(U)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.58/2.59 inference(quant_intro,[status(thm)],[179])).
% 3.58/2.59 tff(181,axiom,(![V: $i, U: $i] : (((((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) | c3_1(V)) | c1_1(V)) | c3_1(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause297')).
% 3.58/2.59 tff(182,plain,
% 3.58/2.59 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[181, 180])).
% 3.58/2.59 tff(183,plain,
% 3.58/2.59 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[182, 178])).
% 3.58/2.59 tff(184,plain,(
% 3.58/2.59 ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.58/2.59 inference(skolemize,[status(sab)],[183])).
% 3.58/2.59 tff(185,plain,
% 3.58/2.59 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[184, 177])).
% 3.58/2.59 tff(186,plain,
% 3.58/2.59 (((~hskp15) | (~c2_1(a625))) <=> ((~hskp15) | (~c2_1(a625)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(187,plain,
% 3.58/2.59 (((~c2_1(a625)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a625)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(188,axiom,((~c2_1(a625)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause245')).
% 3.58/2.59 tff(189,plain,
% 3.58/2.59 ((~hskp15) | (~c2_1(a625))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[188, 187])).
% 3.58/2.59 tff(190,plain,
% 3.58/2.59 ((~hskp15) | (~c2_1(a625))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[189, 186])).
% 3.58/2.59 tff(191,plain,
% 3.58/2.59 (~c2_1(a625)),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[190, 156])).
% 3.58/2.59 tff(192,plain,
% 3.58/2.59 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(193,plain,
% 3.58/2.59 (((~ndr1_0) | c3_1(a625) | c2_1(a625) | c0_1(a625) | c1_1(a625) | c3_1(a625) | c0_1(a625)) <=> (c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(194,plain,
% 3.58/2.59 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a625) | c2_1(a625) | c0_1(a625) | c1_1(a625) | c3_1(a625) | c0_1(a625))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625)))),
% 3.58/2.59 inference(monotonicity,[status(thm)],[193])).
% 3.58/2.59 tff(195,plain,
% 3.58/2.59 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a625) | c2_1(a625) | c0_1(a625) | c1_1(a625) | c3_1(a625) | c0_1(a625))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625))),
% 3.58/2.59 inference(transitivity,[status(thm)],[194, 192])).
% 3.58/2.59 tff(196,plain,
% 3.58/2.59 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a625) | c2_1(a625) | c0_1(a625) | c1_1(a625) | c3_1(a625) | c0_1(a625))),
% 3.58/2.59 inference(quant_inst,[status(thm)],[])).
% 3.58/2.59 tff(197,plain,
% 3.58/2.59 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[196, 195])).
% 3.58/2.59 tff(198,plain,
% 3.58/2.59 ($false),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[197, 96, 191, 168, 162, 185, 175])).
% 3.58/2.59 tff(199,plain,((~hskp15) | hskp53 | hskp17), inference(lemma,lemma(discharge,[]))).
% 3.58/2.59 tff(200,plain,
% 3.58/2.59 (~hskp15),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[199, 35, 12])).
% 3.58/2.59 tff(201,assumption,(hskp14), introduced(assumption)).
% 3.58/2.59 tff(202,plain,
% 3.58/2.59 (((~hskp14) | (~c2_1(a624))) <=> ((~hskp14) | (~c2_1(a624)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(203,plain,
% 3.58/2.59 (((~c2_1(a624)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a624)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(204,axiom,((~c2_1(a624)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause249')).
% 3.58/2.59 tff(205,plain,
% 3.58/2.59 ((~hskp14) | (~c2_1(a624))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[204, 203])).
% 3.58/2.59 tff(206,plain,
% 3.58/2.59 ((~hskp14) | (~c2_1(a624))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[205, 202])).
% 3.58/2.59 tff(207,plain,
% 3.58/2.59 (~c2_1(a624)),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[206, 201])).
% 3.58/2.59 tff(208,plain,
% 3.58/2.59 (((~hskp14) | c3_1(a624)) <=> ((~hskp14) | c3_1(a624))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(209,axiom,((~hskp14) | c3_1(a624)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 3.58/2.59 tff(210,plain,
% 3.58/2.59 ((~hskp14) | c3_1(a624)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[209, 208])).
% 3.58/2.59 tff(211,plain,
% 3.58/2.59 ((~hskp14) | c3_1(a624)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[210, 208])).
% 3.58/2.59 tff(212,plain,
% 3.58/2.59 ((~hskp14) | c3_1(a624)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[211, 208])).
% 3.58/2.59 tff(213,plain,
% 3.58/2.59 ((~hskp14) | c3_1(a624)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[212, 208])).
% 3.58/2.59 tff(214,plain,
% 3.58/2.59 ((~hskp14) | c3_1(a624)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[213, 208])).
% 3.58/2.59 tff(215,plain,
% 3.58/2.59 ((~hskp14) | c3_1(a624)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[214, 208])).
% 3.58/2.59 tff(216,plain,
% 3.58/2.59 ((~hskp14) | c3_1(a624)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[215, 208])).
% 3.58/2.59 tff(217,plain,
% 3.58/2.59 ((~hskp14) | c3_1(a624)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[216, 208])).
% 3.58/2.59 tff(218,plain,
% 3.58/2.59 (c3_1(a624)),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[217, 201])).
% 3.58/2.59 tff(219,plain,
% 3.58/2.59 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(220,plain,
% 3.58/2.59 ((hskp58 | hskp41 | (~ndr1_0) | c2_1(a624) | (~c3_1(a624)) | (~c0_1(a624))) <=> (hskp58 | hskp41 | c2_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(221,plain,
% 3.58/2.59 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a624) | (~c3_1(a624)) | (~c0_1(a624)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624))))),
% 3.58/2.59 inference(monotonicity,[status(thm)],[220])).
% 3.58/2.59 tff(222,plain,
% 3.58/2.59 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a624) | (~c3_1(a624)) | (~c0_1(a624)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)))),
% 3.58/2.59 inference(transitivity,[status(thm)],[221, 219])).
% 3.58/2.59 tff(223,plain,
% 3.58/2.59 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a624) | (~c3_1(a624)) | (~c0_1(a624)))),
% 3.58/2.59 inference(quant_inst,[status(thm)],[])).
% 3.58/2.59 tff(224,plain,
% 3.58/2.59 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[223, 222])).
% 3.58/2.59 tff(225,plain,
% 3.58/2.59 (~c0_1(a624)),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[224, 96, 105, 106, 218, 207, 116])).
% 3.58/2.59 tff(226,plain,
% 3.58/2.59 (((~hskp14) | (~c1_1(a624))) <=> ((~hskp14) | (~c1_1(a624)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(227,plain,
% 3.58/2.59 (((~c1_1(a624)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a624)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(228,axiom,((~c1_1(a624)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause248')).
% 3.58/2.59 tff(229,plain,
% 3.58/2.59 ((~hskp14) | (~c1_1(a624))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[228, 227])).
% 3.58/2.59 tff(230,plain,
% 3.58/2.59 ((~hskp14) | (~c1_1(a624))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[229, 226])).
% 3.58/2.59 tff(231,plain,
% 3.58/2.59 (~c1_1(a624)),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[230, 201])).
% 3.58/2.59 tff(232,plain,
% 3.58/2.59 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(233,plain,
% 3.58/2.59 ((hskp53 | hskp17 | (~ndr1_0) | c1_1(a624) | c0_1(a624) | (~c3_1(a624))) <=> (hskp53 | hskp17 | c1_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(234,plain,
% 3.58/2.59 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a624) | c0_1(a624) | (~c3_1(a624)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624))))),
% 3.58/2.59 inference(monotonicity,[status(thm)],[233])).
% 3.58/2.59 tff(235,plain,
% 3.58/2.59 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a624) | c0_1(a624) | (~c3_1(a624)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624)))),
% 3.58/2.59 inference(transitivity,[status(thm)],[234, 232])).
% 3.58/2.59 tff(236,plain,
% 3.58/2.59 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a624) | c0_1(a624) | (~c3_1(a624)))),
% 3.58/2.59 inference(quant_inst,[status(thm)],[])).
% 3.58/2.59 tff(237,plain,
% 3.58/2.59 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[236, 235])).
% 3.58/2.59 tff(238,plain,
% 3.58/2.59 ($false),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[237, 96, 35, 12, 218, 231, 34, 225])).
% 3.58/2.59 tff(239,plain,((~hskp14) | hskp53 | hskp17 | hskp41), inference(lemma,lemma(discharge,[]))).
% 3.58/2.59 tff(240,plain,
% 3.58/2.59 (~hskp14),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[239, 106, 12, 35])).
% 3.58/2.59 tff(241,plain,
% 3.58/2.59 (^[U: $i] : refl((hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))),
% 3.58/2.59 inference(bind,[status(th)],[])).
% 3.58/2.59 tff(242,plain,
% 3.58/2.59 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 3.58/2.59 inference(quant_intro,[status(thm)],[241])).
% 3.58/2.59 tff(243,plain,
% 3.58/2.59 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(244,plain,
% 3.58/2.59 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c0_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | 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)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp14))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp15) <=> ((hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp15))), rewrite(((hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp15) <=> (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp15) <=> (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))))),
% 3.58/2.59 inference(bind,[status(th)],[])).
% 3.58/2.59 tff(245,plain,
% 3.58/2.59 (![U: $i] : ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp15) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 3.58/2.59 inference(quant_intro,[status(thm)],[244])).
% 3.58/2.59 tff(246,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause293')).
% 3.58/2.59 tff(247,plain,
% 3.58/2.59 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[246, 245])).
% 3.58/2.59 tff(248,plain,
% 3.58/2.59 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[247, 243])).
% 3.58/2.59 tff(249,plain,(
% 3.58/2.59 ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 3.58/2.59 inference(skolemize,[status(sab)],[248])).
% 3.58/2.59 tff(250,plain,
% 3.58/2.59 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[249, 242])).
% 3.58/2.59 tff(251,assumption,(hskp65), introduced(assumption)).
% 3.58/2.59 tff(252,plain,
% 3.58/2.59 (((~hskp65) | (~c1_1(a674))) <=> ((~hskp65) | (~c1_1(a674)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(253,plain,
% 3.58/2.59 (((~c1_1(a674)) | (~hskp65)) <=> ((~hskp65) | (~c1_1(a674)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(254,axiom,((~c1_1(a674)) | (~hskp65)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 3.58/2.59 tff(255,plain,
% 3.58/2.59 ((~hskp65) | (~c1_1(a674))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[254, 253])).
% 3.58/2.59 tff(256,plain,
% 3.58/2.59 ((~hskp65) | (~c1_1(a674))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[255, 252])).
% 3.58/2.59 tff(257,plain,
% 3.58/2.59 (~c1_1(a674)),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[256, 251])).
% 3.58/2.59 tff(258,plain,
% 3.58/2.59 (((~hskp65) | c0_1(a674)) <=> ((~hskp65) | c0_1(a674))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(259,axiom,((~hskp65) | c0_1(a674)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 3.58/2.59 tff(260,plain,
% 3.58/2.59 ((~hskp65) | c0_1(a674)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[259, 258])).
% 3.58/2.59 tff(261,plain,
% 3.58/2.59 ((~hskp65) | c0_1(a674)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[260, 258])).
% 3.58/2.59 tff(262,plain,
% 3.58/2.59 ((~hskp65) | c0_1(a674)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[261, 258])).
% 3.58/2.59 tff(263,plain,
% 3.58/2.59 ((~hskp65) | c0_1(a674)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[262, 258])).
% 3.58/2.59 tff(264,plain,
% 3.58/2.59 ((~hskp65) | c0_1(a674)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[263, 258])).
% 3.58/2.59 tff(265,plain,
% 3.58/2.59 ((~hskp65) | c0_1(a674)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[264, 258])).
% 3.58/2.59 tff(266,plain,
% 3.58/2.59 ((~hskp65) | c0_1(a674)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[265, 258])).
% 3.58/2.59 tff(267,plain,
% 3.58/2.59 ((~hskp65) | c0_1(a674)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[266, 258])).
% 3.58/2.59 tff(268,plain,
% 3.58/2.59 (c0_1(a674)),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[267, 251])).
% 3.58/2.59 tff(269,plain,
% 3.58/2.59 (((~hskp65) | c2_1(a674)) <=> ((~hskp65) | c2_1(a674))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(270,axiom,((~hskp65) | c2_1(a674)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 3.58/2.59 tff(271,plain,
% 3.58/2.59 ((~hskp65) | c2_1(a674)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[270, 269])).
% 3.58/2.59 tff(272,plain,
% 3.58/2.59 ((~hskp65) | c2_1(a674)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[271, 269])).
% 3.58/2.59 tff(273,plain,
% 3.58/2.59 ((~hskp65) | c2_1(a674)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[272, 269])).
% 3.58/2.59 tff(274,plain,
% 3.58/2.59 ((~hskp65) | c2_1(a674)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[273, 269])).
% 3.58/2.59 tff(275,plain,
% 3.58/2.59 ((~hskp65) | c2_1(a674)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[274, 269])).
% 3.58/2.59 tff(276,plain,
% 3.58/2.59 ((~hskp65) | c2_1(a674)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[275, 269])).
% 3.58/2.59 tff(277,plain,
% 3.58/2.59 ((~hskp65) | c2_1(a674)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[276, 269])).
% 3.58/2.59 tff(278,plain,
% 3.58/2.59 ((~hskp65) | c2_1(a674)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[277, 269])).
% 3.58/2.59 tff(279,plain,
% 3.58/2.59 (c2_1(a674)),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[278, 251])).
% 3.58/2.59 tff(280,assumption,(~hskp14), introduced(assumption)).
% 3.58/2.59 tff(281,assumption,(~hskp15), introduced(assumption)).
% 3.58/2.59 tff(282,plain,
% 3.58/2.59 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | c1_1(a674) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a674) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(283,plain,
% 3.58/2.59 ((hskp15 | hskp14 | (~ndr1_0) | c1_1(a674) | (~c0_1(a674)) | (~c2_1(a674))) <=> (hskp15 | hskp14 | c1_1(a674) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(284,plain,
% 3.58/2.59 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a674) | (~c0_1(a674)) | (~c2_1(a674)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | c1_1(a674) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674))))),
% 3.58/2.59 inference(monotonicity,[status(thm)],[283])).
% 3.58/2.59 tff(285,plain,
% 3.58/2.59 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a674) | (~c0_1(a674)) | (~c2_1(a674)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a674) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)))),
% 3.58/2.59 inference(transitivity,[status(thm)],[284, 282])).
% 3.58/2.59 tff(286,plain,
% 3.58/2.59 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a674) | (~c0_1(a674)) | (~c2_1(a674)))),
% 3.58/2.59 inference(quant_inst,[status(thm)],[])).
% 3.58/2.59 tff(287,plain,
% 3.58/2.59 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a674) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[286, 285])).
% 3.58/2.59 tff(288,plain,
% 3.58/2.59 ($false),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[287, 96, 281, 280, 279, 268, 257, 250])).
% 3.58/2.59 tff(289,plain,((~hskp65) | hskp15 | hskp14), inference(lemma,lemma(discharge,[]))).
% 3.58/2.59 tff(290,plain,
% 3.58/2.59 (~hskp65),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[289, 240, 200])).
% 3.58/2.59 tff(291,plain,
% 3.58/2.59 (hskp66),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[94, 290, 24])).
% 3.58/2.59 tff(292,plain,
% 3.58/2.59 (((~hskp66) | (~c2_1(a675))) <=> ((~hskp66) | (~c2_1(a675)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(293,plain,
% 3.58/2.59 (((~c2_1(a675)) | (~hskp66)) <=> ((~hskp66) | (~c2_1(a675)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(294,axiom,((~c2_1(a675)) | (~hskp66)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 3.58/2.59 tff(295,plain,
% 3.58/2.59 ((~hskp66) | (~c2_1(a675))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[294, 293])).
% 3.58/2.59 tff(296,plain,
% 3.58/2.59 ((~hskp66) | (~c2_1(a675))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[295, 292])).
% 3.58/2.59 tff(297,plain,
% 3.58/2.59 (~c2_1(a675)),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[296, 291])).
% 3.58/2.59 tff(298,plain,
% 3.58/2.59 (((~hskp66) | c3_1(a675)) <=> ((~hskp66) | c3_1(a675))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(299,axiom,((~hskp66) | c3_1(a675)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 3.58/2.59 tff(300,plain,
% 3.58/2.59 ((~hskp66) | c3_1(a675)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[299, 298])).
% 3.58/2.59 tff(301,plain,
% 3.58/2.59 ((~hskp66) | c3_1(a675)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[300, 298])).
% 3.58/2.59 tff(302,plain,
% 3.58/2.59 ((~hskp66) | c3_1(a675)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[301, 298])).
% 3.58/2.59 tff(303,plain,
% 3.58/2.59 ((~hskp66) | c3_1(a675)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[302, 298])).
% 3.58/2.59 tff(304,plain,
% 3.58/2.59 ((~hskp66) | c3_1(a675)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[303, 298])).
% 3.58/2.59 tff(305,plain,
% 3.58/2.59 ((~hskp66) | c3_1(a675)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[304, 298])).
% 3.58/2.59 tff(306,plain,
% 3.58/2.59 ((~hskp66) | c3_1(a675)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[305, 298])).
% 3.58/2.59 tff(307,plain,
% 3.58/2.59 ((~hskp66) | c3_1(a675)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[306, 298])).
% 3.58/2.59 tff(308,plain,
% 3.58/2.59 (c3_1(a675)),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[307, 291])).
% 3.58/2.59 tff(309,plain,
% 3.58/2.59 (((~hskp66) | c1_1(a675)) <=> ((~hskp66) | c1_1(a675))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(310,axiom,((~hskp66) | c1_1(a675)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 3.58/2.59 tff(311,plain,
% 3.58/2.59 ((~hskp66) | c1_1(a675)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[310, 309])).
% 3.58/2.59 tff(312,plain,
% 3.58/2.59 ((~hskp66) | c1_1(a675)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[311, 309])).
% 3.58/2.59 tff(313,plain,
% 3.58/2.59 ((~hskp66) | c1_1(a675)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[312, 309])).
% 3.58/2.59 tff(314,plain,
% 3.58/2.59 ((~hskp66) | c1_1(a675)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[313, 309])).
% 3.58/2.59 tff(315,plain,
% 3.58/2.59 ((~hskp66) | c1_1(a675)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[314, 309])).
% 3.58/2.59 tff(316,plain,
% 3.58/2.59 ((~hskp66) | c1_1(a675)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[315, 309])).
% 3.58/2.59 tff(317,plain,
% 3.58/2.59 ((~hskp66) | c1_1(a675)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[316, 309])).
% 3.58/2.59 tff(318,plain,
% 3.58/2.59 ((~hskp66) | c1_1(a675)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[317, 309])).
% 3.58/2.59 tff(319,plain,
% 3.58/2.59 (c1_1(a675)),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[318, 291])).
% 3.58/2.59 tff(320,plain,
% 3.58/2.59 (^[V: $i, U: $i] : refl((hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 3.58/2.59 inference(bind,[status(th)],[])).
% 3.58/2.59 tff(321,plain,
% 3.58/2.59 (![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 3.58/2.59 inference(quant_intro,[status(thm)],[320])).
% 3.58/2.59 tff(322,plain,
% 3.58/2.59 (![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(323,plain,
% 3.58/2.59 (^[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))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | hskp41) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp41))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp41) <=> (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | hskp41) <=> (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 3.58/2.59 inference(bind,[status(th)],[])).
% 3.58/2.59 tff(324,plain,
% 3.58/2.59 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | hskp41) <=> ![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 3.58/2.59 inference(quant_intro,[status(thm)],[323])).
% 3.58/2.59 tff(325,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | hskp41)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause314')).
% 3.58/2.59 tff(326,plain,
% 3.58/2.59 (![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[325, 324])).
% 3.58/2.59 tff(327,plain,
% 3.58/2.59 (![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[326, 322])).
% 3.58/2.59 tff(328,plain,(
% 3.58/2.59 ![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 3.58/2.59 inference(skolemize,[status(sab)],[327])).
% 3.58/2.59 tff(329,plain,
% 3.58/2.59 (![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[328, 321])).
% 3.58/2.59 tff(330,assumption,(hskp60), introduced(assumption)).
% 3.58/2.59 tff(331,plain,
% 3.58/2.59 (((~hskp60) | (~c2_1(a669))) <=> ((~hskp60) | (~c2_1(a669)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(332,plain,
% 3.58/2.59 (((~c2_1(a669)) | (~hskp60)) <=> ((~hskp60) | (~c2_1(a669)))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(333,axiom,((~c2_1(a669)) | (~hskp60)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 3.58/2.59 tff(334,plain,
% 3.58/2.59 ((~hskp60) | (~c2_1(a669))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[333, 332])).
% 3.58/2.59 tff(335,plain,
% 3.58/2.59 ((~hskp60) | (~c2_1(a669))),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[334, 331])).
% 3.58/2.59 tff(336,plain,
% 3.58/2.59 (~c2_1(a669)),
% 3.58/2.59 inference(unit_resolution,[status(thm)],[335, 330])).
% 3.58/2.59 tff(337,assumption,(~c2_1(a675)), introduced(assumption)).
% 3.58/2.59 tff(338,plain,
% 3.58/2.59 (((~hskp60) | c1_1(a669)) <=> ((~hskp60) | c1_1(a669))),
% 3.58/2.59 inference(rewrite,[status(thm)],[])).
% 3.58/2.59 tff(339,axiom,((~hskp60) | c1_1(a669)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 3.58/2.59 tff(340,plain,
% 3.58/2.59 ((~hskp60) | c1_1(a669)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[339, 338])).
% 3.58/2.59 tff(341,plain,
% 3.58/2.59 ((~hskp60) | c1_1(a669)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[340, 338])).
% 3.58/2.59 tff(342,plain,
% 3.58/2.59 ((~hskp60) | c1_1(a669)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[341, 338])).
% 3.58/2.59 tff(343,plain,
% 3.58/2.59 ((~hskp60) | c1_1(a669)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[342, 338])).
% 3.58/2.59 tff(344,plain,
% 3.58/2.59 ((~hskp60) | c1_1(a669)),
% 3.58/2.59 inference(modus_ponens,[status(thm)],[343, 338])).
% 3.68/2.59 tff(345,plain,
% 3.68/2.59 ((~hskp60) | c1_1(a669)),
% 3.68/2.59 inference(modus_ponens,[status(thm)],[344, 338])).
% 3.68/2.59 tff(346,plain,
% 3.68/2.59 ((~hskp60) | c1_1(a669)),
% 3.68/2.59 inference(modus_ponens,[status(thm)],[345, 338])).
% 3.68/2.59 tff(347,plain,
% 3.68/2.59 ((~hskp60) | c1_1(a669)),
% 3.68/2.59 inference(modus_ponens,[status(thm)],[346, 338])).
% 3.68/2.59 tff(348,plain,
% 3.68/2.59 (c1_1(a669)),
% 3.68/2.59 inference(unit_resolution,[status(thm)],[347, 330])).
% 3.68/2.59 tff(349,plain,
% 3.68/2.59 (((~hskp60) | c0_1(a669)) <=> ((~hskp60) | c0_1(a669))),
% 3.68/2.59 inference(rewrite,[status(thm)],[])).
% 3.68/2.59 tff(350,axiom,((~hskp60) | c0_1(a669)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 3.68/2.59 tff(351,plain,
% 3.68/2.59 ((~hskp60) | c0_1(a669)),
% 3.68/2.59 inference(modus_ponens,[status(thm)],[350, 349])).
% 3.68/2.59 tff(352,plain,
% 3.68/2.59 ((~hskp60) | c0_1(a669)),
% 3.68/2.59 inference(modus_ponens,[status(thm)],[351, 349])).
% 3.68/2.59 tff(353,plain,
% 3.68/2.59 ((~hskp60) | c0_1(a669)),
% 3.68/2.59 inference(modus_ponens,[status(thm)],[352, 349])).
% 3.68/2.59 tff(354,plain,
% 3.68/2.59 ((~hskp60) | c0_1(a669)),
% 3.68/2.59 inference(modus_ponens,[status(thm)],[353, 349])).
% 3.68/2.59 tff(355,plain,
% 3.68/2.59 ((~hskp60) | c0_1(a669)),
% 3.68/2.59 inference(modus_ponens,[status(thm)],[354, 349])).
% 3.68/2.59 tff(356,plain,
% 3.68/2.59 ((~hskp60) | c0_1(a669)),
% 3.68/2.59 inference(modus_ponens,[status(thm)],[355, 349])).
% 3.68/2.59 tff(357,plain,
% 3.68/2.59 ((~hskp60) | c0_1(a669)),
% 3.68/2.59 inference(modus_ponens,[status(thm)],[356, 349])).
% 3.68/2.59 tff(358,plain,
% 3.68/2.59 ((~hskp60) | c0_1(a669)),
% 3.68/2.59 inference(modus_ponens,[status(thm)],[357, 349])).
% 3.68/2.59 tff(359,plain,
% 3.68/2.59 (c0_1(a669)),
% 3.68/2.59 inference(unit_resolution,[status(thm)],[358, 330])).
% 3.68/2.59 tff(360,assumption,(c3_1(a675)), introduced(assumption)).
% 3.68/2.59 tff(361,assumption,(c1_1(a675)), introduced(assumption)).
% 3.68/2.59 tff(362,plain,
% 3.68/2.59 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a675) | c2_1(a669) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a669)) | (~c1_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a675) | c2_1(a669) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a669)) | (~c1_1(a669)))),
% 3.68/2.59 inference(rewrite,[status(thm)],[])).
% 3.68/2.59 tff(363,plain,
% 3.68/2.59 ((hskp41 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669))) <=> (hskp41 | c2_1(a675) | c2_1(a669) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a669)) | (~c1_1(a669)))),
% 3.68/2.59 inference(rewrite,[status(thm)],[])).
% 3.68/2.59 tff(364,plain,
% 3.68/2.59 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a675) | c2_1(a669) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a669)) | (~c1_1(a669))))),
% 3.68/2.59 inference(monotonicity,[status(thm)],[363])).
% 3.68/2.59 tff(365,plain,
% 3.68/2.59 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a675) | c2_1(a669) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a669)) | (~c1_1(a669)))),
% 3.68/2.60 inference(transitivity,[status(thm)],[364, 362])).
% 3.68/2.60 tff(366,plain,
% 3.68/2.60 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))),
% 3.68/2.60 inference(quant_inst,[status(thm)],[])).
% 3.68/2.60 tff(367,plain,
% 3.68/2.60 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a675) | c2_1(a669) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a669)) | (~c1_1(a669))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[366, 365])).
% 3.68/2.60 tff(368,plain,
% 3.68/2.60 ($false),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[367, 96, 106, 361, 360, 359, 348, 337, 336, 329])).
% 3.68/2.60 tff(369,plain,((~hskp60) | hskp41 | (~c1_1(a675)) | (~c3_1(a675)) | c2_1(a675)), inference(lemma,lemma(discharge,[]))).
% 3.68/2.60 tff(370,plain,
% 3.68/2.60 (~hskp60),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[369, 106, 319, 308, 297])).
% 3.68/2.60 tff(371,plain,
% 3.68/2.60 ((hskp61 | hskp60 | hskp33) <=> (hskp61 | hskp60 | hskp33)),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(372,plain,
% 3.68/2.60 (((hskp33 | hskp60) | hskp61) <=> (hskp61 | hskp60 | hskp33)),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(373,axiom,((hskp33 | hskp60) | hskp61), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 3.68/2.60 tff(374,plain,
% 3.68/2.60 (hskp61 | hskp60 | hskp33),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[373, 372])).
% 3.68/2.60 tff(375,plain,
% 3.68/2.60 (hskp61 | hskp60 | hskp33),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[374, 371])).
% 3.68/2.60 tff(376,plain,
% 3.68/2.60 (hskp61 | hskp60 | hskp33),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[375, 371])).
% 3.68/2.60 tff(377,plain,
% 3.68/2.60 (hskp61 | hskp60 | hskp33),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[376, 371])).
% 3.68/2.60 tff(378,plain,
% 3.68/2.60 (hskp61 | hskp60 | hskp33),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[377, 371])).
% 3.68/2.60 tff(379,plain,
% 3.68/2.60 (hskp61 | hskp60 | hskp33),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[378, 371])).
% 3.68/2.60 tff(380,plain,
% 3.68/2.60 (hskp61 | hskp60 | hskp33),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[379, 371])).
% 3.68/2.60 tff(381,plain,
% 3.68/2.60 (hskp61 | hskp60 | hskp33),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[380, 371])).
% 3.68/2.60 tff(382,plain,
% 3.68/2.60 (hskp61),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[381, 370, 155])).
% 3.68/2.60 tff(383,plain,
% 3.68/2.60 (((~hskp61) | (~c0_1(a670))) <=> ((~hskp61) | (~c0_1(a670)))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(384,plain,
% 3.68/2.60 (((~c0_1(a670)) | (~hskp61)) <=> ((~hskp61) | (~c0_1(a670)))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(385,axiom,((~c0_1(a670)) | (~hskp61)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 3.68/2.60 tff(386,plain,
% 3.68/2.60 ((~hskp61) | (~c0_1(a670))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[385, 384])).
% 3.68/2.60 tff(387,plain,
% 3.68/2.60 ((~hskp61) | (~c0_1(a670))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[386, 383])).
% 3.68/2.60 tff(388,plain,
% 3.68/2.60 (~c0_1(a670)),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[387, 382])).
% 3.68/2.60 tff(389,plain,
% 3.68/2.60 (((~hskp61) | (~c1_1(a670))) <=> ((~hskp61) | (~c1_1(a670)))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(390,plain,
% 3.68/2.60 (((~c1_1(a670)) | (~hskp61)) <=> ((~hskp61) | (~c1_1(a670)))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(391,axiom,((~c1_1(a670)) | (~hskp61)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 3.68/2.60 tff(392,plain,
% 3.68/2.60 ((~hskp61) | (~c1_1(a670))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[391, 390])).
% 3.68/2.60 tff(393,plain,
% 3.68/2.60 ((~hskp61) | (~c1_1(a670))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[392, 389])).
% 3.68/2.60 tff(394,plain,
% 3.68/2.60 (~c1_1(a670)),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[393, 382])).
% 3.68/2.60 tff(395,plain,
% 3.68/2.60 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c3_1(a670)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c3_1(a670)))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(396,plain,
% 3.68/2.60 ((hskp53 | hskp17 | (~ndr1_0) | c1_1(a670) | c0_1(a670) | (~c3_1(a670))) <=> (hskp53 | hskp17 | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c3_1(a670)))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(397,plain,
% 3.68/2.60 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c3_1(a670))))),
% 3.68/2.60 inference(monotonicity,[status(thm)],[396])).
% 3.68/2.60 tff(398,plain,
% 3.68/2.60 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c3_1(a670)))),
% 3.68/2.60 inference(transitivity,[status(thm)],[397, 395])).
% 3.68/2.60 tff(399,plain,
% 3.68/2.60 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))),
% 3.68/2.60 inference(quant_inst,[status(thm)],[])).
% 3.68/2.60 tff(400,plain,
% 3.68/2.60 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c3_1(a670))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[399, 398])).
% 3.68/2.60 tff(401,plain,
% 3.68/2.60 (~c3_1(a670)),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[400, 96, 35, 12, 394, 388, 34])).
% 3.68/2.60 tff(402,plain,
% 3.68/2.60 (^[U: $i] : refl((hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))),
% 3.68/2.60 inference(bind,[status(th)],[])).
% 3.68/2.60 tff(403,plain,
% 3.68/2.60 (![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.68/2.60 inference(quant_intro,[status(thm)],[402])).
% 3.68/2.60 tff(404,plain,
% 3.68/2.60 (![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(405,plain,
% 3.68/2.60 (^[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)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp37) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp37))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp37) <=> (hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp37) <=> (hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp37) | hskp54) <=> ((hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp54))), rewrite(((hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp54) <=> (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp37) | hskp54) <=> (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))))),
% 3.68/2.60 inference(bind,[status(th)],[])).
% 3.68/2.60 tff(406,plain,
% 3.68/2.60 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp37) | hskp54) <=> ![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.68/2.60 inference(quant_intro,[status(thm)],[405])).
% 3.68/2.60 tff(407,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp37) | hskp54)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause286')).
% 3.68/2.60 tff(408,plain,
% 3.68/2.60 (![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[407, 406])).
% 3.68/2.60 tff(409,plain,
% 3.68/2.60 (![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[408, 404])).
% 3.68/2.60 tff(410,plain,(
% 3.68/2.60 ![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.68/2.60 inference(skolemize,[status(sab)],[409])).
% 3.68/2.60 tff(411,plain,
% 3.68/2.60 (![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[410, 403])).
% 3.68/2.60 tff(412,plain,
% 3.68/2.60 (((~hskp61) | c2_1(a670)) <=> ((~hskp61) | c2_1(a670))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(413,axiom,((~hskp61) | c2_1(a670)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 3.68/2.60 tff(414,plain,
% 3.68/2.60 ((~hskp61) | c2_1(a670)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[413, 412])).
% 3.68/2.60 tff(415,plain,
% 3.68/2.60 ((~hskp61) | c2_1(a670)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[414, 412])).
% 3.68/2.60 tff(416,plain,
% 3.68/2.60 ((~hskp61) | c2_1(a670)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[415, 412])).
% 3.68/2.60 tff(417,plain,
% 3.68/2.60 ((~hskp61) | c2_1(a670)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[416, 412])).
% 3.68/2.60 tff(418,plain,
% 3.68/2.60 ((~hskp61) | c2_1(a670)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[417, 412])).
% 3.68/2.60 tff(419,plain,
% 3.68/2.60 ((~hskp61) | c2_1(a670)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[418, 412])).
% 3.68/2.60 tff(420,plain,
% 3.68/2.60 ((~hskp61) | c2_1(a670)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[419, 412])).
% 3.68/2.60 tff(421,plain,
% 3.68/2.60 ((~hskp61) | c2_1(a670)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[420, 412])).
% 3.68/2.60 tff(422,plain,
% 3.68/2.60 (c2_1(a670)),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[421, 382])).
% 3.68/2.60 tff(423,assumption,(hskp37), introduced(assumption)).
% 3.68/2.60 tff(424,plain,
% 3.68/2.60 (((~hskp37) | (~c2_1(a607))) <=> ((~hskp37) | (~c2_1(a607)))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(425,plain,
% 3.68/2.60 (((~c2_1(a607)) | (~hskp37)) <=> ((~hskp37) | (~c2_1(a607)))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(426,axiom,((~c2_1(a607)) | (~hskp37)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause205')).
% 3.68/2.60 tff(427,plain,
% 3.68/2.60 ((~hskp37) | (~c2_1(a607))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[426, 425])).
% 3.68/2.60 tff(428,plain,
% 3.68/2.60 ((~hskp37) | (~c2_1(a607))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[427, 424])).
% 3.68/2.60 tff(429,plain,
% 3.68/2.60 (~c2_1(a607)),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[428, 423])).
% 3.68/2.60 tff(430,plain,
% 3.68/2.60 (((~hskp37) | c0_1(a607)) <=> ((~hskp37) | c0_1(a607))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(431,axiom,((~hskp37) | c0_1(a607)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 3.68/2.60 tff(432,plain,
% 3.68/2.60 ((~hskp37) | c0_1(a607)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[431, 430])).
% 3.68/2.60 tff(433,plain,
% 3.68/2.60 ((~hskp37) | c0_1(a607)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[432, 430])).
% 3.68/2.60 tff(434,plain,
% 3.68/2.60 ((~hskp37) | c0_1(a607)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[433, 430])).
% 3.68/2.60 tff(435,plain,
% 3.68/2.60 ((~hskp37) | c0_1(a607)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[434, 430])).
% 3.68/2.60 tff(436,plain,
% 3.68/2.60 ((~hskp37) | c0_1(a607)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[435, 430])).
% 3.68/2.60 tff(437,plain,
% 3.68/2.60 ((~hskp37) | c0_1(a607)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[436, 430])).
% 3.68/2.60 tff(438,plain,
% 3.68/2.60 ((~hskp37) | c0_1(a607)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[437, 430])).
% 3.68/2.60 tff(439,plain,
% 3.68/2.60 ((~hskp37) | c0_1(a607)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[438, 430])).
% 3.68/2.60 tff(440,plain,
% 3.68/2.60 (c0_1(a607)),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[439, 423])).
% 3.68/2.60 tff(441,plain,
% 3.68/2.60 (((~hskp37) | c1_1(a607)) <=> ((~hskp37) | c1_1(a607))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(442,axiom,((~hskp37) | c1_1(a607)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 3.68/2.60 tff(443,plain,
% 3.68/2.60 ((~hskp37) | c1_1(a607)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[442, 441])).
% 3.68/2.60 tff(444,plain,
% 3.68/2.60 ((~hskp37) | c1_1(a607)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[443, 441])).
% 3.68/2.60 tff(445,plain,
% 3.68/2.60 ((~hskp37) | c1_1(a607)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[444, 441])).
% 3.68/2.60 tff(446,plain,
% 3.68/2.60 ((~hskp37) | c1_1(a607)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[445, 441])).
% 3.68/2.60 tff(447,plain,
% 3.68/2.60 ((~hskp37) | c1_1(a607)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[446, 441])).
% 3.68/2.60 tff(448,plain,
% 3.68/2.60 ((~hskp37) | c1_1(a607)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[447, 441])).
% 3.68/2.60 tff(449,plain,
% 3.68/2.60 ((~hskp37) | c1_1(a607)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[448, 441])).
% 3.68/2.60 tff(450,plain,
% 3.68/2.60 ((~hskp37) | c1_1(a607)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[449, 441])).
% 3.68/2.60 tff(451,plain,
% 3.68/2.60 (c1_1(a607)),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[450, 423])).
% 3.68/2.60 tff(452,plain,
% 3.68/2.60 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a675) | c2_1(a607) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a607)) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a675) | c2_1(a607) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(453,plain,
% 3.68/2.60 ((hskp41 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp41 | c2_1(a675) | c2_1(a607) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(454,plain,
% 3.68/2.60 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a675) | c2_1(a607) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a607)) | (~c1_1(a607))))),
% 3.68/2.60 inference(monotonicity,[status(thm)],[453])).
% 3.68/2.60 tff(455,plain,
% 3.68/2.60 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a675) | c2_1(a607) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 3.68/2.60 inference(transitivity,[status(thm)],[454, 452])).
% 3.68/2.60 tff(456,plain,
% 3.68/2.60 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 3.68/2.60 inference(quant_inst,[status(thm)],[])).
% 3.68/2.60 tff(457,plain,
% 3.68/2.60 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a675) | c2_1(a607) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a607)) | (~c1_1(a607))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[456, 455])).
% 3.68/2.60 tff(458,plain,
% 3.68/2.60 ($false),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[457, 96, 106, 361, 360, 451, 440, 337, 429, 329])).
% 3.68/2.60 tff(459,plain,((~hskp37) | hskp41 | (~c1_1(a675)) | (~c3_1(a675)) | c2_1(a675)), inference(lemma,lemma(discharge,[]))).
% 3.68/2.60 tff(460,plain,
% 3.68/2.60 (~hskp37),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[459, 106, 319, 308, 297])).
% 3.68/2.60 tff(461,plain,
% 3.68/2.60 (((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | c0_1(a670) | (~ndr1_0) | (~c2_1(a670)) | c3_1(a670))) <=> ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp54 | hskp37 | c0_1(a670) | (~ndr1_0) | (~c2_1(a670)) | c3_1(a670))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(462,plain,
% 3.68/2.60 ((hskp54 | hskp37 | (~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670))) <=> (hskp54 | hskp37 | c0_1(a670) | (~ndr1_0) | (~c2_1(a670)) | c3_1(a670))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(463,plain,
% 3.68/2.60 (((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | (~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)))) <=> ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | c0_1(a670) | (~ndr1_0) | (~c2_1(a670)) | c3_1(a670)))),
% 3.68/2.60 inference(monotonicity,[status(thm)],[462])).
% 3.68/2.60 tff(464,plain,
% 3.68/2.60 (((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | (~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)))) <=> ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp54 | hskp37 | c0_1(a670) | (~ndr1_0) | (~c2_1(a670)) | c3_1(a670))),
% 3.68/2.60 inference(transitivity,[status(thm)],[463, 461])).
% 3.68/2.60 tff(465,plain,
% 3.68/2.60 ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | (~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)))),
% 3.68/2.60 inference(quant_inst,[status(thm)],[])).
% 3.68/2.60 tff(466,plain,
% 3.68/2.60 ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp54 | hskp37 | c0_1(a670) | (~ndr1_0) | (~c2_1(a670)) | c3_1(a670)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[465, 464])).
% 3.68/2.60 tff(467,plain,
% 3.68/2.60 (hskp54 | c3_1(a670)),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[466, 96, 460, 422, 388, 411])).
% 3.68/2.60 tff(468,plain,
% 3.68/2.60 (hskp54),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[467, 401])).
% 3.68/2.60 tff(469,plain,
% 3.68/2.60 (((~hskp54) | (~c0_1(a651))) <=> ((~hskp54) | (~c0_1(a651)))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(470,plain,
% 3.68/2.60 (((~c0_1(a651)) | (~hskp54)) <=> ((~hskp54) | (~c0_1(a651)))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(471,axiom,((~c0_1(a651)) | (~hskp54)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 3.68/2.60 tff(472,plain,
% 3.68/2.60 ((~hskp54) | (~c0_1(a651))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[471, 470])).
% 3.68/2.60 tff(473,plain,
% 3.68/2.60 ((~hskp54) | (~c0_1(a651))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[472, 469])).
% 3.68/2.60 tff(474,plain,
% 3.68/2.60 (~c0_1(a651)),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[473, 468])).
% 3.68/2.60 tff(475,plain,
% 3.68/2.60 (((~hskp54) | c2_1(a651)) <=> ((~hskp54) | c2_1(a651))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(476,axiom,((~hskp54) | c2_1(a651)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 3.68/2.60 tff(477,plain,
% 3.68/2.60 ((~hskp54) | c2_1(a651)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[476, 475])).
% 3.68/2.60 tff(478,plain,
% 3.68/2.60 ((~hskp54) | c2_1(a651)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[477, 475])).
% 3.68/2.60 tff(479,plain,
% 3.68/2.60 ((~hskp54) | c2_1(a651)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[478, 475])).
% 3.68/2.60 tff(480,plain,
% 3.68/2.60 ((~hskp54) | c2_1(a651)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[479, 475])).
% 3.68/2.60 tff(481,plain,
% 3.68/2.60 ((~hskp54) | c2_1(a651)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[480, 475])).
% 3.68/2.60 tff(482,plain,
% 3.68/2.60 ((~hskp54) | c2_1(a651)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[481, 475])).
% 3.68/2.60 tff(483,plain,
% 3.68/2.60 ((~hskp54) | c2_1(a651)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[482, 475])).
% 3.68/2.60 tff(484,plain,
% 3.68/2.60 ((~hskp54) | c2_1(a651)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[483, 475])).
% 3.68/2.60 tff(485,plain,
% 3.68/2.60 (c2_1(a651)),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[484, 468])).
% 3.68/2.60 tff(486,plain,
% 3.68/2.60 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a670) | c0_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c1_1(a651)) | (~c2_1(a670)) | c3_1(a670))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a670) | c0_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c1_1(a651)) | (~c2_1(a670)) | c3_1(a670))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(487,plain,
% 3.68/2.60 (((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a651) | (~c2_1(a651)) | (~c1_1(a651))) <=> (c0_1(a670) | c0_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c1_1(a651)) | (~c2_1(a670)) | c3_1(a670))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(488,plain,
% 3.68/2.60 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a651) | (~c2_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a670) | c0_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c1_1(a651)) | (~c2_1(a670)) | c3_1(a670)))),
% 3.68/2.60 inference(monotonicity,[status(thm)],[487])).
% 3.68/2.60 tff(489,plain,
% 3.68/2.60 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a651) | (~c2_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a670) | c0_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c1_1(a651)) | (~c2_1(a670)) | c3_1(a670))),
% 3.68/2.60 inference(transitivity,[status(thm)],[488, 486])).
% 3.68/2.60 tff(490,plain,
% 3.68/2.60 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a651) | (~c2_1(a651)) | (~c1_1(a651)))),
% 3.68/2.60 inference(quant_inst,[status(thm)],[])).
% 3.68/2.60 tff(491,plain,
% 3.68/2.60 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a670) | c0_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c1_1(a651)) | (~c2_1(a670)) | c3_1(a670)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[490, 489])).
% 3.68/2.60 tff(492,plain,
% 3.68/2.60 (~c1_1(a651)),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[491, 96, 422, 485, 388, 474, 23, 401])).
% 3.68/2.60 tff(493,plain,
% 3.68/2.60 (((~hskp54) | c3_1(a651)) <=> ((~hskp54) | c3_1(a651))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(494,axiom,((~hskp54) | c3_1(a651)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 3.68/2.60 tff(495,plain,
% 3.68/2.60 ((~hskp54) | c3_1(a651)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[494, 493])).
% 3.68/2.60 tff(496,plain,
% 3.68/2.60 ((~hskp54) | c3_1(a651)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[495, 493])).
% 3.68/2.60 tff(497,plain,
% 3.68/2.60 ((~hskp54) | c3_1(a651)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[496, 493])).
% 3.68/2.60 tff(498,plain,
% 3.68/2.60 ((~hskp54) | c3_1(a651)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[497, 493])).
% 3.68/2.60 tff(499,plain,
% 3.68/2.60 ((~hskp54) | c3_1(a651)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[498, 493])).
% 3.68/2.60 tff(500,plain,
% 3.68/2.60 ((~hskp54) | c3_1(a651)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[499, 493])).
% 3.68/2.60 tff(501,plain,
% 3.68/2.60 ((~hskp54) | c3_1(a651)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[500, 493])).
% 3.68/2.60 tff(502,plain,
% 3.68/2.60 ((~hskp54) | c3_1(a651)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[501, 493])).
% 3.68/2.60 tff(503,plain,
% 3.68/2.60 (c3_1(a651)),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[502, 468])).
% 3.68/2.60 tff(504,plain,
% 3.68/2.60 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c0_1(a651) | (~ndr1_0) | (~c3_1(a651)) | c1_1(a651))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c0_1(a651) | (~ndr1_0) | (~c3_1(a651)) | c1_1(a651))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(505,plain,
% 3.68/2.60 ((hskp53 | hskp17 | (~ndr1_0) | c1_1(a651) | c0_1(a651) | (~c3_1(a651))) <=> (hskp53 | hskp17 | c0_1(a651) | (~ndr1_0) | (~c3_1(a651)) | c1_1(a651))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(506,plain,
% 3.68/2.60 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a651) | c0_1(a651) | (~c3_1(a651)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c0_1(a651) | (~ndr1_0) | (~c3_1(a651)) | c1_1(a651)))),
% 3.68/2.60 inference(monotonicity,[status(thm)],[505])).
% 3.68/2.60 tff(507,plain,
% 3.68/2.60 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a651) | c0_1(a651) | (~c3_1(a651)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c0_1(a651) | (~ndr1_0) | (~c3_1(a651)) | c1_1(a651))),
% 3.68/2.60 inference(transitivity,[status(thm)],[506, 504])).
% 3.68/2.60 tff(508,plain,
% 3.68/2.60 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a651) | c0_1(a651) | (~c3_1(a651)))),
% 3.68/2.60 inference(quant_inst,[status(thm)],[])).
% 3.68/2.60 tff(509,plain,
% 3.68/2.60 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c0_1(a651) | (~ndr1_0) | (~c3_1(a651)) | c1_1(a651)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[508, 507])).
% 3.68/2.60 tff(510,plain,
% 3.68/2.60 ($false),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[509, 96, 35, 12, 503, 474, 34, 492])).
% 3.68/2.60 tff(511,plain,(hskp41 | hskp53 | hskp17 | hskp64), inference(lemma,lemma(discharge,[]))).
% 3.68/2.60 tff(512,plain,
% 3.68/2.60 (hskp41),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[511, 35, 12, 24])).
% 3.68/2.60 tff(513,plain,
% 3.68/2.60 (((~hskp41) | (~c1_1(a617))) <=> ((~hskp41) | (~c1_1(a617)))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(514,plain,
% 3.68/2.60 (((~c1_1(a617)) | (~hskp41)) <=> ((~hskp41) | (~c1_1(a617)))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(515,axiom,((~c1_1(a617)) | (~hskp41)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause203')).
% 3.68/2.60 tff(516,plain,
% 3.68/2.60 ((~hskp41) | (~c1_1(a617))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[515, 514])).
% 3.68/2.60 tff(517,plain,
% 3.68/2.60 ((~hskp41) | (~c1_1(a617))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[516, 513])).
% 3.68/2.60 tff(518,plain,
% 3.68/2.60 (~c1_1(a617)),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[517, 512])).
% 3.68/2.60 tff(519,plain,
% 3.68/2.60 (((~hskp41) | c3_1(a617)) <=> ((~hskp41) | c3_1(a617))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(520,axiom,((~hskp41) | c3_1(a617)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 3.68/2.60 tff(521,plain,
% 3.68/2.60 ((~hskp41) | c3_1(a617)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[520, 519])).
% 3.68/2.60 tff(522,plain,
% 3.68/2.60 ((~hskp41) | c3_1(a617)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[521, 519])).
% 3.68/2.60 tff(523,plain,
% 3.68/2.60 ((~hskp41) | c3_1(a617)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[522, 519])).
% 3.68/2.60 tff(524,plain,
% 3.68/2.60 ((~hskp41) | c3_1(a617)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[523, 519])).
% 3.68/2.60 tff(525,plain,
% 3.68/2.60 ((~hskp41) | c3_1(a617)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[524, 519])).
% 3.68/2.60 tff(526,plain,
% 3.68/2.60 ((~hskp41) | c3_1(a617)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[525, 519])).
% 3.68/2.60 tff(527,plain,
% 3.68/2.60 ((~hskp41) | c3_1(a617)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[526, 519])).
% 3.68/2.60 tff(528,plain,
% 3.68/2.60 ((~hskp41) | c3_1(a617)),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[527, 519])).
% 3.68/2.60 tff(529,plain,
% 3.68/2.60 (c3_1(a617)),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[528, 512])).
% 3.68/2.60 tff(530,plain,
% 3.68/2.60 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c3_1(a617)))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(531,plain,
% 3.68/2.60 ((hskp53 | hskp17 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c3_1(a617))) <=> (hskp53 | hskp17 | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c3_1(a617)))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(532,plain,
% 3.68/2.60 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c3_1(a617))))),
% 3.68/2.60 inference(monotonicity,[status(thm)],[531])).
% 3.68/2.60 tff(533,plain,
% 3.68/2.60 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c3_1(a617)))),
% 3.68/2.60 inference(transitivity,[status(thm)],[532, 530])).
% 3.68/2.60 tff(534,plain,
% 3.68/2.60 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))),
% 3.68/2.60 inference(quant_inst,[status(thm)],[])).
% 3.68/2.60 tff(535,plain,
% 3.68/2.60 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c3_1(a617))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[534, 533])).
% 3.68/2.60 tff(536,plain,
% 3.68/2.60 (c0_1(a617)),
% 3.68/2.60 inference(unit_resolution,[status(thm)],[535, 96, 35, 12, 529, 518, 34])).
% 3.68/2.60 tff(537,plain,
% 3.68/2.60 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 3.68/2.60 inference(bind,[status(th)],[])).
% 3.68/2.60 tff(538,plain,
% 3.68/2.60 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 3.68/2.60 inference(quant_intro,[status(thm)],[537])).
% 3.68/2.60 tff(539,plain,
% 3.68/2.60 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(540,plain,
% 3.68/2.60 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(U))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(U))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(U))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(U))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 3.68/2.60 inference(bind,[status(th)],[])).
% 3.68/2.60 tff(541,plain,
% 3.68/2.60 (![V: $i, U: $i] : (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(U))) | c1_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 3.68/2.60 inference(quant_intro,[status(thm)],[540])).
% 3.68/2.60 tff(542,axiom,(![V: $i, U: $i] : (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(U))) | c1_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause316')).
% 3.68/2.60 tff(543,plain,
% 3.68/2.60 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[542, 541])).
% 3.68/2.60 tff(544,plain,
% 3.68/2.60 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[543, 539])).
% 3.68/2.60 tff(545,plain,(
% 3.68/2.60 ![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 3.68/2.60 inference(skolemize,[status(sab)],[544])).
% 3.68/2.60 tff(546,plain,
% 3.68/2.60 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 3.68/2.60 inference(modus_ponens,[status(thm)],[545, 538])).
% 3.68/2.60 tff(547,plain,
% 3.68/2.60 (((~hskp41) | c2_1(a617)) <=> ((~hskp41) | c2_1(a617))),
% 3.68/2.60 inference(rewrite,[status(thm)],[])).
% 3.68/2.60 tff(548,axiom,((~hskp41) | c2_1(a617)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 3.68/2.60 tff(549,plain,
% 3.68/2.60 ((~hskp41) | c2_1(a617)),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[548, 547])).
% 3.68/2.61 tff(550,plain,
% 3.68/2.61 ((~hskp41) | c2_1(a617)),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[549, 547])).
% 3.68/2.61 tff(551,plain,
% 3.68/2.61 ((~hskp41) | c2_1(a617)),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[550, 547])).
% 3.68/2.61 tff(552,plain,
% 3.68/2.61 ((~hskp41) | c2_1(a617)),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[551, 547])).
% 3.68/2.61 tff(553,plain,
% 3.68/2.61 ((~hskp41) | c2_1(a617)),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[552, 547])).
% 3.68/2.61 tff(554,plain,
% 3.68/2.61 ((~hskp41) | c2_1(a617)),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[553, 547])).
% 3.68/2.61 tff(555,plain,
% 3.68/2.61 ((~hskp41) | c2_1(a617)),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[554, 547])).
% 3.68/2.61 tff(556,plain,
% 3.68/2.61 ((~hskp41) | c2_1(a617)),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[555, 547])).
% 3.68/2.61 tff(557,plain,
% 3.68/2.61 (c2_1(a617)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[556, 512])).
% 3.68/2.61 tff(558,plain,
% 3.68/2.61 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 3.68/2.61 inference(bind,[status(th)],[])).
% 3.68/2.61 tff(559,plain,
% 3.68/2.61 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 3.68/2.61 inference(quant_intro,[status(thm)],[558])).
% 3.68/2.61 tff(560,plain,
% 3.68/2.61 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(561,plain,
% 3.68/2.61 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c1_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c1_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c1_1(U)) | c2_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c1_1(U)) | c2_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 3.68/2.61 inference(bind,[status(th)],[])).
% 3.68/2.61 tff(562,plain,
% 3.68/2.61 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c1_1(U)) | c2_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 3.68/2.61 inference(quant_intro,[status(thm)],[561])).
% 3.68/2.61 tff(563,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c1_1(U)) | c2_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause312')).
% 3.68/2.61 tff(564,plain,
% 3.68/2.61 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[563, 562])).
% 3.68/2.61 tff(565,plain,
% 3.68/2.61 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[564, 560])).
% 3.68/2.61 tff(566,plain,(
% 3.68/2.61 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 3.68/2.61 inference(skolemize,[status(sab)],[565])).
% 3.68/2.61 tff(567,plain,
% 3.68/2.61 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[566, 559])).
% 3.68/2.61 tff(568,assumption,(hskp41), introduced(assumption)).
% 3.68/2.61 tff(569,plain,
% 3.68/2.61 (~c1_1(a617)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[517, 568])).
% 3.68/2.61 tff(570,plain,
% 3.68/2.61 (c3_1(a617)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[528, 568])).
% 3.68/2.61 tff(571,plain,
% 3.68/2.61 (c0_1(a617)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[535, 96, 35, 12, 570, 569, 34])).
% 3.68/2.61 tff(572,plain,
% 3.68/2.61 (^[U: $i] : refl((hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))),
% 3.68/2.61 inference(bind,[status(th)],[])).
% 3.68/2.61 tff(573,plain,
% 3.68/2.61 (![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 3.68/2.61 inference(quant_intro,[status(thm)],[572])).
% 3.68/2.61 tff(574,plain,
% 3.68/2.61 (![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(575,plain,
% 3.68/2.61 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp5))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) | hskp37) <=> ((hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp37))), rewrite(((hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp37) <=> (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) | hskp37) <=> (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))))),
% 3.68/2.61 inference(bind,[status(th)],[])).
% 3.68/2.61 tff(576,plain,
% 3.68/2.61 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) | hskp37) <=> ![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 3.68/2.61 inference(quant_intro,[status(thm)],[575])).
% 3.68/2.61 tff(577,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) | hskp37)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause298')).
% 3.68/2.61 tff(578,plain,
% 3.68/2.61 (![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[577, 576])).
% 3.68/2.61 tff(579,plain,
% 3.68/2.61 (![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[578, 574])).
% 3.68/2.61 tff(580,plain,(
% 3.68/2.61 ![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 3.68/2.61 inference(skolemize,[status(sab)],[579])).
% 3.68/2.61 tff(581,plain,
% 3.68/2.61 (![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[580, 573])).
% 3.68/2.61 tff(582,plain,
% 3.68/2.61 (c2_1(a617)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[556, 568])).
% 3.68/2.61 tff(583,assumption,(~hskp5), introduced(assumption)).
% 3.68/2.61 tff(584,plain,
% 3.68/2.61 (((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617)))) <=> ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp37 | hskp5 | (~ndr1_0) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(585,plain,
% 3.68/2.61 ((hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a617)) | (~c0_1(a617)) | (~c2_1(a617))) <=> (hskp37 | hskp5 | (~ndr1_0) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(586,plain,
% 3.68/2.61 (((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a617)) | (~c0_1(a617)) | (~c2_1(a617)))) <=> ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617))))),
% 3.68/2.61 inference(monotonicity,[status(thm)],[585])).
% 3.68/2.61 tff(587,plain,
% 3.68/2.61 (((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a617)) | (~c0_1(a617)) | (~c2_1(a617)))) <=> ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp37 | hskp5 | (~ndr1_0) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 3.68/2.61 inference(transitivity,[status(thm)],[586, 584])).
% 3.68/2.61 tff(588,plain,
% 3.68/2.61 ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a617)) | (~c0_1(a617)) | (~c2_1(a617)))),
% 3.68/2.61 inference(quant_inst,[status(thm)],[])).
% 3.68/2.61 tff(589,plain,
% 3.68/2.61 ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp37 | hskp5 | (~ndr1_0) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[588, 587])).
% 3.68/2.61 tff(590,plain,
% 3.68/2.61 (hskp37 | (~c0_1(a617))),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[589, 96, 583, 582, 570, 581])).
% 3.68/2.61 tff(591,plain,
% 3.68/2.61 (hskp37),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[590, 571])).
% 3.68/2.61 tff(592,plain,
% 3.68/2.61 (~c2_1(a607)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[428, 591])).
% 3.68/2.61 tff(593,plain,
% 3.68/2.61 (c0_1(a607)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[439, 591])).
% 3.68/2.61 tff(594,plain,
% 3.68/2.61 (c1_1(a607)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[450, 591])).
% 3.68/2.61 tff(595,assumption,(~c2_1(a607)), introduced(assumption)).
% 3.68/2.61 tff(596,assumption,(c0_1(a607)), introduced(assumption)).
% 3.68/2.61 tff(597,assumption,(c1_1(a607)), introduced(assumption)).
% 3.68/2.61 tff(598,plain,
% 3.68/2.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a607) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a607)) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a607) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(599,plain,
% 3.68/2.61 ((hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp5 | c2_1(a607) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(600,plain,
% 3.68/2.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a607) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a607)) | (~c1_1(a607))))),
% 3.68/2.61 inference(monotonicity,[status(thm)],[599])).
% 3.68/2.61 tff(601,plain,
% 3.68/2.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a607) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 3.68/2.61 inference(transitivity,[status(thm)],[600, 598])).
% 3.68/2.61 tff(602,plain,
% 3.68/2.61 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 3.68/2.61 inference(quant_inst,[status(thm)],[])).
% 3.68/2.61 tff(603,plain,
% 3.68/2.61 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a607) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a607)) | (~c1_1(a607))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[602, 601])).
% 3.68/2.61 tff(604,plain,
% 3.68/2.61 ($false),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[603, 96, 583, 597, 596, 218, 595, 231, 207, 567])).
% 3.68/2.61 tff(605,plain,((~hskp14) | hskp5 | (~c1_1(a607)) | (~c0_1(a607)) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.68/2.61 tff(606,plain,
% 3.68/2.61 (~hskp14),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[605, 594, 583, 593, 592])).
% 3.68/2.61 tff(607,plain,
% 3.68/2.61 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(608,plain,
% 3.68/2.61 ((hskp15 | hskp14 | (~ndr1_0) | c1_1(a617) | (~c0_1(a617)) | (~c2_1(a617))) <=> (hskp15 | hskp14 | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(609,plain,
% 3.68/2.61 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a617) | (~c0_1(a617)) | (~c2_1(a617)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617))))),
% 3.68/2.61 inference(monotonicity,[status(thm)],[608])).
% 3.68/2.61 tff(610,plain,
% 3.68/2.61 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a617) | (~c0_1(a617)) | (~c2_1(a617)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)))),
% 3.68/2.61 inference(transitivity,[status(thm)],[609, 607])).
% 3.68/2.61 tff(611,plain,
% 3.68/2.61 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a617) | (~c0_1(a617)) | (~c2_1(a617)))),
% 3.68/2.61 inference(quant_inst,[status(thm)],[])).
% 3.68/2.61 tff(612,plain,
% 3.68/2.61 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[611, 610])).
% 3.68/2.61 tff(613,plain,
% 3.68/2.61 (~c0_1(a617)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[612, 96, 281, 280, 582, 569, 250])).
% 3.68/2.61 tff(614,plain,
% 3.68/2.61 ($false),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[535, 96, 35, 12, 570, 569, 34, 613])).
% 3.68/2.61 tff(615,plain,((~hskp41) | hskp53 | hskp17 | hskp15 | hskp14), inference(lemma,lemma(discharge,[]))).
% 3.68/2.61 tff(616,plain,
% 3.68/2.61 (hskp15),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[615, 606, 12, 35, 568])).
% 3.68/2.61 tff(617,plain,
% 3.68/2.61 (~c1_1(a625)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[167, 616])).
% 3.68/2.61 tff(618,plain,
% 3.68/2.61 (~c2_1(a625)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[190, 616])).
% 3.68/2.61 tff(619,plain,
% 3.68/2.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a607) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a607)) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a607) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(620,plain,
% 3.68/2.61 ((hskp5 | (~ndr1_0) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp5 | c2_1(a607) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(621,plain,
% 3.68/2.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a607) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a607)) | (~c1_1(a607))))),
% 3.68/2.61 inference(monotonicity,[status(thm)],[620])).
% 3.68/2.61 tff(622,plain,
% 3.68/2.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a607) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 3.68/2.61 inference(transitivity,[status(thm)],[621, 619])).
% 3.68/2.61 tff(623,plain,
% 3.68/2.61 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 3.68/2.61 inference(quant_inst,[status(thm)],[])).
% 3.68/2.61 tff(624,plain,
% 3.68/2.61 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a607) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a607)) | (~c1_1(a607))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[623, 622])).
% 3.68/2.61 tff(625,plain,
% 3.68/2.61 (~c3_1(a625)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[624, 96, 583, 594, 593, 592, 618, 617, 567])).
% 3.68/2.61 tff(626,plain,
% 3.68/2.61 (~c0_1(a625)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[161, 616])).
% 3.68/2.61 tff(627,plain,
% 3.68/2.61 ($false),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[197, 96, 618, 617, 626, 185, 625])).
% 3.68/2.61 tff(628,plain,((~hskp41) | hskp5 | hskp17 | hskp53), inference(lemma,lemma(discharge,[]))).
% 3.68/2.61 tff(629,plain,
% 3.68/2.61 (hskp5),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[628, 512, 12, 35])).
% 3.68/2.61 tff(630,plain,
% 3.68/2.61 (((~hskp5) | (~c3_1(a606))) <=> ((~hskp5) | (~c3_1(a606)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(631,plain,
% 3.68/2.61 (((~c3_1(a606)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a606)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(632,axiom,((~c3_1(a606)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause266')).
% 3.68/2.61 tff(633,plain,
% 3.68/2.61 ((~hskp5) | (~c3_1(a606))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[632, 631])).
% 3.68/2.61 tff(634,plain,
% 3.68/2.61 ((~hskp5) | (~c3_1(a606))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[633, 630])).
% 3.68/2.61 tff(635,plain,
% 3.68/2.61 (~c3_1(a606)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[634, 629])).
% 3.68/2.61 tff(636,plain,
% 3.68/2.61 (((~hskp5) | (~c0_1(a606))) <=> ((~hskp5) | (~c0_1(a606)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(637,plain,
% 3.68/2.61 (((~c0_1(a606)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a606)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(638,axiom,((~c0_1(a606)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause265')).
% 3.68/2.61 tff(639,plain,
% 3.68/2.61 ((~hskp5) | (~c0_1(a606))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[638, 637])).
% 3.68/2.61 tff(640,plain,
% 3.68/2.61 ((~hskp5) | (~c0_1(a606))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[639, 636])).
% 3.68/2.61 tff(641,plain,
% 3.68/2.61 (~c0_1(a606)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[640, 629])).
% 3.68/2.61 tff(642,plain,
% 3.68/2.61 (((~hskp5) | c2_1(a606)) <=> ((~hskp5) | c2_1(a606))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(643,axiom,((~hskp5) | c2_1(a606)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 3.68/2.61 tff(644,plain,
% 3.68/2.61 ((~hskp5) | c2_1(a606)),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[643, 642])).
% 3.68/2.61 tff(645,plain,
% 3.68/2.61 ((~hskp5) | c2_1(a606)),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[644, 642])).
% 3.68/2.61 tff(646,plain,
% 3.68/2.61 ((~hskp5) | c2_1(a606)),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[645, 642])).
% 3.68/2.61 tff(647,plain,
% 3.68/2.61 ((~hskp5) | c2_1(a606)),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[646, 642])).
% 3.68/2.61 tff(648,plain,
% 3.68/2.61 ((~hskp5) | c2_1(a606)),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[647, 642])).
% 3.68/2.61 tff(649,plain,
% 3.68/2.61 ((~hskp5) | c2_1(a606)),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[648, 642])).
% 3.68/2.61 tff(650,plain,
% 3.68/2.61 ((~hskp5) | c2_1(a606)),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[649, 642])).
% 3.68/2.61 tff(651,plain,
% 3.68/2.61 ((~hskp5) | c2_1(a606)),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[650, 642])).
% 3.68/2.61 tff(652,plain,
% 3.68/2.61 (c2_1(a606)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[651, 629])).
% 3.68/2.61 tff(653,plain,
% 3.68/2.61 (^[V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))),
% 3.68/2.61 inference(bind,[status(th)],[])).
% 3.68/2.61 tff(654,plain,
% 3.68/2.61 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 3.68/2.61 inference(quant_intro,[status(thm)],[653])).
% 3.68/2.61 tff(655,plain,
% 3.68/2.61 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(656,plain,
% 3.68/2.61 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), (((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c1_1(V)))), ((((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))))),
% 3.68/2.61 inference(bind,[status(th)],[])).
% 3.68/2.61 tff(657,plain,
% 3.68/2.61 (![V: $i, U: $i] : (((((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(U)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 3.68/2.61 inference(quant_intro,[status(thm)],[656])).
% 3.68/2.61 tff(658,axiom,(![V: $i, U: $i] : (((((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(U)) | c3_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause299')).
% 3.68/2.61 tff(659,plain,
% 3.68/2.61 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[658, 657])).
% 3.68/2.61 tff(660,plain,
% 3.68/2.61 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[659, 655])).
% 3.68/2.61 tff(661,plain,(
% 3.68/2.61 ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 3.68/2.61 inference(skolemize,[status(sab)],[660])).
% 3.68/2.61 tff(662,plain,
% 3.68/2.61 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[661, 654])).
% 3.68/2.61 tff(663,assumption,(~c3_1(a606)), introduced(assumption)).
% 3.68/2.61 tff(664,assumption,(~c0_1(a606)), introduced(assumption)).
% 3.68/2.61 tff(665,assumption,(hskp20), introduced(assumption)).
% 3.68/2.61 tff(666,plain,
% 3.68/2.61 (((~hskp20) | (~c3_1(a635))) <=> ((~hskp20) | (~c3_1(a635)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(667,plain,
% 3.68/2.61 (((~c3_1(a635)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a635)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(668,axiom,((~c3_1(a635)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause237')).
% 3.68/2.61 tff(669,plain,
% 3.68/2.61 ((~hskp20) | (~c3_1(a635))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[668, 667])).
% 3.68/2.61 tff(670,plain,
% 3.68/2.61 ((~hskp20) | (~c3_1(a635))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[669, 666])).
% 3.68/2.61 tff(671,plain,
% 3.68/2.61 (~c3_1(a635)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[670, 665])).
% 3.68/2.61 tff(672,plain,
% 3.68/2.61 (((~hskp20) | (~c2_1(a635))) <=> ((~hskp20) | (~c2_1(a635)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(673,plain,
% 3.68/2.61 (((~c2_1(a635)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a635)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(674,axiom,((~c2_1(a635)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause236')).
% 3.68/2.61 tff(675,plain,
% 3.68/2.61 ((~hskp20) | (~c2_1(a635))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[674, 673])).
% 3.68/2.61 tff(676,plain,
% 3.68/2.61 ((~hskp20) | (~c2_1(a635))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[675, 672])).
% 3.68/2.61 tff(677,plain,
% 3.68/2.61 (~c2_1(a635)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[676, 665])).
% 3.68/2.61 tff(678,plain,
% 3.68/2.61 (((~hskp20) | (~c1_1(a635))) <=> ((~hskp20) | (~c1_1(a635)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(679,plain,
% 3.68/2.61 (((~c1_1(a635)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a635)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(680,axiom,((~c1_1(a635)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause235')).
% 3.68/2.61 tff(681,plain,
% 3.68/2.61 ((~hskp20) | (~c1_1(a635))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[680, 679])).
% 3.68/2.61 tff(682,plain,
% 3.68/2.61 ((~hskp20) | (~c1_1(a635))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[681, 678])).
% 3.68/2.61 tff(683,plain,
% 3.68/2.61 (~c1_1(a635)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[682, 665])).
% 3.68/2.61 tff(684,assumption,(c2_1(a606)), introduced(assumption)).
% 3.68/2.61 tff(685,plain,
% 3.68/2.61 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c1_1(a635) | c2_1(a635) | c3_1(a635) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c1_1(a635) | c2_1(a635) | c3_1(a635) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(686,plain,
% 3.68/2.61 (((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c1_1(a635) | c3_1(a635) | c2_1(a635)) <=> (c1_1(a635) | c2_1(a635) | c3_1(a635) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(687,plain,
% 3.68/2.61 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c1_1(a635) | c3_1(a635) | c2_1(a635))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c1_1(a635) | c2_1(a635) | c3_1(a635) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606))))),
% 3.68/2.61 inference(monotonicity,[status(thm)],[686])).
% 3.68/2.61 tff(688,plain,
% 3.68/2.61 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c1_1(a635) | c3_1(a635) | c2_1(a635))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c1_1(a635) | c2_1(a635) | c3_1(a635) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)))),
% 3.68/2.61 inference(transitivity,[status(thm)],[687, 685])).
% 3.68/2.61 tff(689,plain,
% 3.68/2.61 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c1_1(a635) | c3_1(a635) | c2_1(a635))),
% 3.68/2.61 inference(quant_inst,[status(thm)],[])).
% 3.68/2.61 tff(690,plain,
% 3.68/2.61 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c1_1(a635) | c2_1(a635) | c3_1(a635) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[689, 688])).
% 3.68/2.61 tff(691,plain,
% 3.68/2.61 ($false),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[690, 96, 684, 683, 677, 671, 664, 663, 662])).
% 3.68/2.61 tff(692,plain,((~hskp20) | (~c2_1(a606)) | c0_1(a606) | c3_1(a606)), inference(lemma,lemma(discharge,[]))).
% 3.68/2.61 tff(693,plain,
% 3.68/2.61 (~hskp20),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[692, 652, 641, 635])).
% 3.68/2.61 tff(694,plain,
% 3.68/2.61 (hskp14),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[615, 512, 12, 35, 200])).
% 3.68/2.61 tff(695,plain,
% 3.68/2.61 (~c2_1(a624)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[206, 694])).
% 3.68/2.61 tff(696,plain,
% 3.68/2.61 (~c1_1(a624)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[230, 694])).
% 3.68/2.61 tff(697,plain,
% 3.68/2.61 (c3_1(a624)),
% 3.68/2.61 inference(unit_resolution,[status(thm)],[217, 694])).
% 3.68/2.61 tff(698,assumption,(c0_1(a617)), introduced(assumption)).
% 3.68/2.61 tff(699,plain,
% 3.68/2.61 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))))),
% 3.68/2.61 inference(bind,[status(th)],[])).
% 3.68/2.61 tff(700,plain,
% 3.68/2.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 3.68/2.61 inference(quant_intro,[status(thm)],[699])).
% 3.68/2.61 tff(701,plain,
% 3.68/2.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(702,plain,
% 3.68/2.61 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c2_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))))), (((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))))),
% 3.68/2.61 inference(bind,[status(th)],[])).
% 3.68/2.61 tff(703,plain,
% 3.68/2.61 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 3.68/2.61 inference(quant_intro,[status(thm)],[702])).
% 3.68/2.61 tff(704,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause325')).
% 3.68/2.61 tff(705,plain,
% 3.68/2.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[704, 703])).
% 3.68/2.61 tff(706,plain,
% 3.68/2.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[705, 701])).
% 3.68/2.61 tff(707,plain,(
% 3.68/2.61 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 3.68/2.61 inference(skolemize,[status(sab)],[706])).
% 3.68/2.61 tff(708,plain,
% 3.68/2.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 3.68/2.61 inference(modus_ponens,[status(thm)],[707, 700])).
% 3.68/2.61 tff(709,assumption,(~hskp20), introduced(assumption)).
% 3.68/2.61 tff(710,assumption,(~c1_1(a617)), introduced(assumption)).
% 3.68/2.61 tff(711,assumption,(c3_1(a617)), introduced(assumption)).
% 3.68/2.61 tff(712,assumption,(c2_1(a617)), introduced(assumption)).
% 3.68/2.61 tff(713,assumption,(~c3_1(a607)), introduced(assumption)).
% 3.68/2.61 tff(714,plain,
% 3.68/2.61 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 3.68/2.61 inference(bind,[status(th)],[])).
% 3.68/2.61 tff(715,plain,
% 3.68/2.61 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 3.68/2.61 inference(quant_intro,[status(thm)],[714])).
% 3.68/2.61 tff(716,plain,
% 3.68/2.61 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 3.68/2.61 inference(rewrite,[status(thm)],[])).
% 3.68/2.61 tff(717,plain,
% 3.68/2.61 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(V)) | hskp20) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp20))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 3.68/2.62 inference(bind,[status(th)],[])).
% 3.68/2.62 tff(718,plain,
% 3.68/2.62 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 3.68/2.62 inference(quant_intro,[status(thm)],[717])).
% 3.68/2.62 tff(719,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(V)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause311')).
% 3.68/2.62 tff(720,plain,
% 3.68/2.62 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[719, 718])).
% 3.68/2.62 tff(721,plain,
% 3.68/2.62 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[720, 716])).
% 3.68/2.62 tff(722,plain,(
% 3.68/2.62 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 3.68/2.62 inference(skolemize,[status(sab)],[721])).
% 3.68/2.62 tff(723,plain,
% 3.68/2.62 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[722, 715])).
% 3.68/2.62 tff(724,plain,
% 3.68/2.62 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a617) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | c3_1(a607) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a617) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | c3_1(a607) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(725,plain,
% 3.68/2.62 ((hskp20 | (~ndr1_0) | c3_1(a607) | c2_1(a607) | (~c0_1(a607)) | c1_1(a617) | (~c2_1(a617)) | (~c3_1(a617))) <=> (hskp20 | c1_1(a617) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | c3_1(a607) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(726,plain,
% 3.68/2.62 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a607) | c2_1(a607) | (~c0_1(a607)) | c1_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a617) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | c3_1(a607) | (~c2_1(a617)) | (~c3_1(a617))))),
% 3.68/2.62 inference(monotonicity,[status(thm)],[725])).
% 3.68/2.62 tff(727,plain,
% 3.68/2.62 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a607) | c2_1(a607) | (~c0_1(a607)) | c1_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a617) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | c3_1(a607) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.62 inference(transitivity,[status(thm)],[726, 724])).
% 3.68/2.62 tff(728,plain,
% 3.68/2.62 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a607) | c2_1(a607) | (~c0_1(a607)) | c1_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.62 inference(quant_inst,[status(thm)],[])).
% 3.68/2.62 tff(729,plain,
% 3.68/2.62 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a617) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | c3_1(a607) | (~c2_1(a617)) | (~c3_1(a617))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[728, 727])).
% 3.68/2.62 tff(730,plain,
% 3.68/2.62 ($false),
% 3.68/2.62 inference(unit_resolution,[status(thm)],[729, 96, 709, 712, 711, 596, 710, 595, 723, 713])).
% 3.68/2.62 tff(731,plain,(c3_1(a607) | hskp20 | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a607)) | c1_1(a617) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.68/2.62 tff(732,plain,
% 3.68/2.62 (c3_1(a607)),
% 3.68/2.62 inference(unit_resolution,[status(thm)],[731, 429, 712, 711, 440, 710, 709])).
% 3.68/2.62 tff(733,plain,
% 3.68/2.62 (^[U: $i] : refl((hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 3.68/2.62 inference(bind,[status(th)],[])).
% 3.68/2.62 tff(734,plain,
% 3.68/2.62 (![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.68/2.62 inference(quant_intro,[status(thm)],[733])).
% 3.68/2.62 tff(735,plain,
% 3.68/2.62 (![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(736,plain,
% 3.68/2.62 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~c1_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | hskp6) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp6))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 3.68/2.62 inference(bind,[status(th)],[])).
% 3.68/2.62 tff(737,plain,
% 3.68/2.62 (![U: $i] : (((((~c0_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | hskp6) <=> ![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.68/2.62 inference(quant_intro,[status(thm)],[736])).
% 3.68/2.62 tff(738,axiom,(![U: $i] : (((((~c0_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause289')).
% 3.68/2.62 tff(739,plain,
% 3.68/2.62 (![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[738, 737])).
% 3.68/2.62 tff(740,plain,
% 3.68/2.62 (![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[739, 735])).
% 3.68/2.62 tff(741,plain,(
% 3.68/2.62 ![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.68/2.62 inference(skolemize,[status(sab)],[740])).
% 3.68/2.62 tff(742,plain,
% 3.68/2.62 (![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[741, 734])).
% 3.68/2.62 tff(743,plain,
% 3.68/2.62 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(744,plain,
% 3.68/2.62 ((hskp6 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp6 | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(745,plain,
% 3.68/2.62 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607))))),
% 3.68/2.62 inference(monotonicity,[status(thm)],[744])).
% 3.68/2.62 tff(746,plain,
% 3.68/2.62 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)))),
% 3.68/2.62 inference(transitivity,[status(thm)],[745, 743])).
% 3.68/2.62 tff(747,plain,
% 3.68/2.62 ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)))),
% 3.68/2.62 inference(quant_inst,[status(thm)],[])).
% 3.68/2.62 tff(748,plain,
% 3.68/2.62 ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[747, 746])).
% 3.68/2.62 tff(749,plain,
% 3.68/2.62 (hskp6),
% 3.68/2.62 inference(unit_resolution,[status(thm)],[748, 96, 451, 440, 742, 732])).
% 3.68/2.62 tff(750,plain,
% 3.68/2.62 (((~hskp6) | (~c0_1(a609))) <=> ((~hskp6) | (~c0_1(a609)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(751,plain,
% 3.68/2.62 (((~c0_1(a609)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a609)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(752,axiom,((~c0_1(a609)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause263')).
% 3.68/2.62 tff(753,plain,
% 3.68/2.62 ((~hskp6) | (~c0_1(a609))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[752, 751])).
% 3.68/2.62 tff(754,plain,
% 3.68/2.62 ((~hskp6) | (~c0_1(a609))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[753, 750])).
% 3.68/2.62 tff(755,plain,
% 3.68/2.62 (~c0_1(a609)),
% 3.68/2.62 inference(unit_resolution,[status(thm)],[754, 749])).
% 3.68/2.62 tff(756,assumption,(~c2_1(a624)), introduced(assumption)).
% 3.68/2.62 tff(757,assumption,(~c1_1(a624)), introduced(assumption)).
% 3.68/2.62 tff(758,plain,
% 3.68/2.62 (((~hskp6) | c2_1(a609)) <=> ((~hskp6) | c2_1(a609))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(759,axiom,((~hskp6) | c2_1(a609)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 3.68/2.62 tff(760,plain,
% 3.68/2.62 ((~hskp6) | c2_1(a609)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[759, 758])).
% 3.68/2.62 tff(761,plain,
% 3.68/2.62 ((~hskp6) | c2_1(a609)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[760, 758])).
% 3.68/2.62 tff(762,plain,
% 3.68/2.62 ((~hskp6) | c2_1(a609)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[761, 758])).
% 3.68/2.62 tff(763,plain,
% 3.68/2.62 ((~hskp6) | c2_1(a609)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[762, 758])).
% 3.68/2.62 tff(764,plain,
% 3.68/2.62 ((~hskp6) | c2_1(a609)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[763, 758])).
% 3.68/2.62 tff(765,plain,
% 3.68/2.62 ((~hskp6) | c2_1(a609)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[764, 758])).
% 3.68/2.62 tff(766,plain,
% 3.68/2.62 ((~hskp6) | c2_1(a609)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[765, 758])).
% 3.68/2.62 tff(767,plain,
% 3.68/2.62 ((~hskp6) | c2_1(a609)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[766, 758])).
% 3.68/2.62 tff(768,plain,
% 3.68/2.62 (c2_1(a609)),
% 3.68/2.62 inference(unit_resolution,[status(thm)],[767, 749])).
% 3.68/2.62 tff(769,assumption,(c3_1(a624)), introduced(assumption)).
% 3.68/2.62 tff(770,plain,
% 3.68/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a617) | c1_1(a624) | c2_1(a624) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a617) | c1_1(a624) | c2_1(a624) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(771,plain,
% 3.68/2.62 (((~ndr1_0) | c0_1(a609) | (~c3_1(a609)) | (~c2_1(a609)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624))) <=> (c1_1(a617) | c1_1(a624) | c2_1(a624) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(772,plain,
% 3.68/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a609) | (~c3_1(a609)) | (~c2_1(a609)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a617) | c1_1(a624) | c2_1(a624) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617))))),
% 3.68/2.62 inference(monotonicity,[status(thm)],[771])).
% 3.68/2.62 tff(773,plain,
% 3.68/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a609) | (~c3_1(a609)) | (~c2_1(a609)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a617) | c1_1(a624) | c2_1(a624) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)))),
% 3.68/2.62 inference(transitivity,[status(thm)],[772, 770])).
% 3.68/2.62 tff(774,plain,
% 3.68/2.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a609) | (~c3_1(a609)) | (~c2_1(a609)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624)))),
% 3.68/2.62 inference(quant_inst,[status(thm)],[])).
% 3.68/2.62 tff(775,plain,
% 3.68/2.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a617) | c1_1(a624) | c2_1(a624) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[774, 773])).
% 3.68/2.62 tff(776,plain,
% 3.68/2.62 (~c3_1(a609)),
% 3.68/2.62 inference(unit_resolution,[status(thm)],[775, 96, 712, 769, 768, 710, 757, 756, 755, 708, 698])).
% 3.68/2.62 tff(777,plain,
% 3.68/2.62 (^[V: $i, U: $i] : refl((hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 3.68/2.62 inference(bind,[status(th)],[])).
% 3.68/2.62 tff(778,plain,
% 3.68/2.62 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.68/2.62 inference(quant_intro,[status(thm)],[777])).
% 3.68/2.62 tff(779,plain,
% 3.68/2.62 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(780,plain,
% 3.68/2.62 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(V)) | hskp57) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp57))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp57) <=> (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(V)) | hskp57) <=> (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 3.68/2.62 inference(bind,[status(th)],[])).
% 3.68/2.62 tff(781,plain,
% 3.68/2.62 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(V)) | hskp57) <=> ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.68/2.62 inference(quant_intro,[status(thm)],[780])).
% 3.68/2.62 tff(782,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(V)) | hskp57)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause319')).
% 3.68/2.62 tff(783,plain,
% 3.68/2.62 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[782, 781])).
% 3.68/2.62 tff(784,plain,
% 3.68/2.62 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[783, 779])).
% 3.68/2.62 tff(785,plain,(
% 3.68/2.62 ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.68/2.62 inference(skolemize,[status(sab)],[784])).
% 3.68/2.62 tff(786,plain,
% 3.68/2.62 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[785, 778])).
% 3.68/2.62 tff(787,plain,
% 3.68/2.62 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a617) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c3_1(a617)) | (~c0_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a617) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(788,plain,
% 3.68/2.62 ((hskp57 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617))) <=> (hskp57 | c1_1(a617) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(789,plain,
% 3.68/2.62 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a617) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c3_1(a617)) | (~c0_1(a617))))),
% 3.68/2.62 inference(monotonicity,[status(thm)],[788])).
% 3.68/2.62 tff(790,plain,
% 3.68/2.62 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a617) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 3.68/2.62 inference(transitivity,[status(thm)],[789, 787])).
% 3.68/2.62 tff(791,plain,
% 3.68/2.62 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)))),
% 3.68/2.62 inference(quant_inst,[status(thm)],[])).
% 3.68/2.62 tff(792,plain,
% 3.68/2.62 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a617) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c3_1(a617)) | (~c0_1(a617))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[791, 790])).
% 3.68/2.62 tff(793,plain,
% 3.68/2.62 (hskp57),
% 3.68/2.62 inference(unit_resolution,[status(thm)],[792, 96, 711, 451, 440, 710, 786, 698, 732])).
% 3.68/2.62 tff(794,plain,
% 3.68/2.62 (((~hskp57) | (~c0_1(a662))) <=> ((~hskp57) | (~c0_1(a662)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(795,plain,
% 3.68/2.62 (((~c0_1(a662)) | (~hskp57)) <=> ((~hskp57) | (~c0_1(a662)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(796,axiom,((~c0_1(a662)) | (~hskp57)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 3.68/2.62 tff(797,plain,
% 3.68/2.62 ((~hskp57) | (~c0_1(a662))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[796, 795])).
% 3.68/2.62 tff(798,plain,
% 3.68/2.62 ((~hskp57) | (~c0_1(a662))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[797, 794])).
% 3.68/2.62 tff(799,plain,
% 3.68/2.62 (~c0_1(a662)),
% 3.68/2.62 inference(unit_resolution,[status(thm)],[798, 793])).
% 3.68/2.62 tff(800,plain,
% 3.68/2.62 (((~hskp57) | c2_1(a662)) <=> ((~hskp57) | c2_1(a662))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(801,axiom,((~hskp57) | c2_1(a662)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 3.68/2.62 tff(802,plain,
% 3.68/2.62 ((~hskp57) | c2_1(a662)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[801, 800])).
% 3.68/2.62 tff(803,plain,
% 3.68/2.62 ((~hskp57) | c2_1(a662)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[802, 800])).
% 3.68/2.62 tff(804,plain,
% 3.68/2.62 ((~hskp57) | c2_1(a662)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[803, 800])).
% 3.68/2.62 tff(805,plain,
% 3.68/2.62 ((~hskp57) | c2_1(a662)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[804, 800])).
% 3.68/2.62 tff(806,plain,
% 3.68/2.62 ((~hskp57) | c2_1(a662)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[805, 800])).
% 3.68/2.62 tff(807,plain,
% 3.68/2.62 ((~hskp57) | c2_1(a662)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[806, 800])).
% 3.68/2.62 tff(808,plain,
% 3.68/2.62 ((~hskp57) | c2_1(a662)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[807, 800])).
% 3.68/2.62 tff(809,plain,
% 3.68/2.62 ((~hskp57) | c2_1(a662)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[808, 800])).
% 3.68/2.62 tff(810,plain,
% 3.68/2.62 (c2_1(a662)),
% 3.68/2.62 inference(unit_resolution,[status(thm)],[809, 793])).
% 3.68/2.62 tff(811,plain,
% 3.68/2.62 (((~hskp57) | c1_1(a662)) <=> ((~hskp57) | c1_1(a662))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(812,axiom,((~hskp57) | c1_1(a662)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 3.68/2.62 tff(813,plain,
% 3.68/2.62 ((~hskp57) | c1_1(a662)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[812, 811])).
% 3.68/2.62 tff(814,plain,
% 3.68/2.62 ((~hskp57) | c1_1(a662)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[813, 811])).
% 3.68/2.62 tff(815,plain,
% 3.68/2.62 ((~hskp57) | c1_1(a662)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[814, 811])).
% 3.68/2.62 tff(816,plain,
% 3.68/2.62 ((~hskp57) | c1_1(a662)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[815, 811])).
% 3.68/2.62 tff(817,plain,
% 3.68/2.62 ((~hskp57) | c1_1(a662)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[816, 811])).
% 3.68/2.62 tff(818,plain,
% 3.68/2.62 ((~hskp57) | c1_1(a662)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[817, 811])).
% 3.68/2.62 tff(819,plain,
% 3.68/2.62 ((~hskp57) | c1_1(a662)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[818, 811])).
% 3.68/2.62 tff(820,plain,
% 3.68/2.62 ((~hskp57) | c1_1(a662)),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[819, 811])).
% 3.68/2.62 tff(821,plain,
% 3.68/2.62 (c1_1(a662)),
% 3.68/2.62 inference(unit_resolution,[status(thm)],[820, 793])).
% 3.68/2.62 tff(822,plain,
% 3.68/2.62 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a662) | c0_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c2_1(a662)) | (~c1_1(a662)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a662) | c0_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c2_1(a662)) | (~c1_1(a662)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(823,plain,
% 3.68/2.62 (((~ndr1_0) | c3_1(a609) | c0_1(a609) | (~c2_1(a609)) | c0_1(a662) | (~c2_1(a662)) | (~c1_1(a662))) <=> (c0_1(a662) | c0_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c2_1(a662)) | (~c1_1(a662)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(824,plain,
% 3.68/2.62 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a609) | c0_1(a609) | (~c2_1(a609)) | c0_1(a662) | (~c2_1(a662)) | (~c1_1(a662)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a662) | c0_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c2_1(a662)) | (~c1_1(a662))))),
% 3.68/2.62 inference(monotonicity,[status(thm)],[823])).
% 3.68/2.62 tff(825,plain,
% 3.68/2.62 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a609) | c0_1(a609) | (~c2_1(a609)) | c0_1(a662) | (~c2_1(a662)) | (~c1_1(a662)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a662) | c0_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c2_1(a662)) | (~c1_1(a662)))),
% 3.68/2.62 inference(transitivity,[status(thm)],[824, 822])).
% 3.68/2.62 tff(826,plain,
% 3.68/2.62 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a609) | c0_1(a609) | (~c2_1(a609)) | c0_1(a662) | (~c2_1(a662)) | (~c1_1(a662)))),
% 3.68/2.62 inference(quant_inst,[status(thm)],[])).
% 3.68/2.62 tff(827,plain,
% 3.68/2.62 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a662) | c0_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c2_1(a662)) | (~c1_1(a662))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[826, 825])).
% 3.68/2.62 tff(828,plain,
% 3.68/2.62 ($false),
% 3.68/2.62 inference(unit_resolution,[status(thm)],[827, 96, 821, 810, 768, 799, 755, 23, 776])).
% 3.68/2.62 tff(829,plain,((~hskp37) | (~c2_1(a617)) | (~c3_1(a624)) | c1_1(a617) | c1_1(a624) | c2_1(a624) | (~c0_1(a617)) | (~c3_1(a617)) | hskp20), inference(lemma,lemma(discharge,[]))).
% 3.68/2.62 tff(830,plain,
% 3.68/2.62 (~hskp37),
% 3.68/2.62 inference(unit_resolution,[status(thm)],[829, 557, 697, 518, 696, 695, 536, 529, 693])).
% 3.68/2.62 tff(831,plain,
% 3.68/2.62 (((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)))) <=> ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp54 | hskp37 | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(832,plain,
% 3.68/2.62 ((hskp54 | hskp37 | (~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606))) <=> (hskp54 | hskp37 | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(833,plain,
% 3.68/2.62 (((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | (~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)))) <=> ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606))))),
% 3.68/2.62 inference(monotonicity,[status(thm)],[832])).
% 3.68/2.62 tff(834,plain,
% 3.68/2.62 (((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | (~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)))) <=> ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp54 | hskp37 | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)))),
% 3.68/2.62 inference(transitivity,[status(thm)],[833, 831])).
% 3.68/2.62 tff(835,plain,
% 3.68/2.62 ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | (~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)))),
% 3.68/2.62 inference(quant_inst,[status(thm)],[])).
% 3.68/2.62 tff(836,plain,
% 3.68/2.62 ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp54 | hskp37 | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606))),
% 3.68/2.62 inference(modus_ponens,[status(thm)],[835, 834])).
% 3.68/2.62 tff(837,plain,
% 3.68/2.62 (hskp54 | hskp37),
% 3.68/2.62 inference(unit_resolution,[status(thm)],[836, 96, 652, 641, 635, 411])).
% 3.68/2.62 tff(838,plain,
% 3.68/2.62 (hskp54),
% 3.68/2.62 inference(unit_resolution,[status(thm)],[837, 830])).
% 3.68/2.62 tff(839,plain,
% 3.68/2.62 (c2_1(a651)),
% 3.68/2.62 inference(unit_resolution,[status(thm)],[484, 838])).
% 3.68/2.62 tff(840,plain,
% 3.68/2.62 (c3_1(a651)),
% 3.68/2.62 inference(unit_resolution,[status(thm)],[502, 838])).
% 3.68/2.62 tff(841,plain,
% 3.68/2.62 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c1_1(a651)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(842,plain,
% 3.68/2.62 (((~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651)) | (~c2_1(a651)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617))) <=> (c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c1_1(a651)))),
% 3.68/2.62 inference(rewrite,[status(thm)],[])).
% 3.68/2.62 tff(843,plain,
% 3.68/2.62 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651)) | (~c2_1(a651)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c1_1(a651))))),
% 3.68/2.62 inference(monotonicity,[status(thm)],[842])).
% 3.68/2.63 tff(844,plain,
% 3.68/2.63 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651)) | (~c2_1(a651)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c1_1(a651)))),
% 3.68/2.63 inference(transitivity,[status(thm)],[843, 841])).
% 3.68/2.63 tff(845,plain,
% 3.68/2.63 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651)) | (~c2_1(a651)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)))),
% 3.68/2.63 inference(quant_inst,[status(thm)],[])).
% 3.68/2.63 tff(846,plain,
% 3.68/2.63 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c1_1(a651))),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[845, 844])).
% 3.68/2.63 tff(847,plain,
% 3.68/2.63 (~c1_1(a651)),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[846, 96, 840, 839, 557, 518, 546, 536])).
% 3.68/2.63 tff(848,plain,
% 3.68/2.63 (~c0_1(a651)),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[473, 838])).
% 3.68/2.63 tff(849,plain,
% 3.68/2.63 ($false),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[509, 96, 35, 12, 840, 848, 34, 847])).
% 3.68/2.63 tff(850,plain,(hskp53 | hskp17 | hskp64), inference(lemma,lemma(discharge,[]))).
% 3.68/2.63 tff(851,plain,
% 3.68/2.63 (hskp53),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[850, 24, 12])).
% 3.68/2.63 tff(852,plain,
% 3.68/2.63 (((~hskp53) | (~c2_1(a648))) <=> ((~hskp53) | (~c2_1(a648)))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(853,plain,
% 3.68/2.63 (((~c2_1(a648)) | (~hskp53)) <=> ((~hskp53) | (~c2_1(a648)))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(854,axiom,((~c2_1(a648)) | (~hskp53)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 3.68/2.63 tff(855,plain,
% 3.68/2.63 ((~hskp53) | (~c2_1(a648))),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[854, 853])).
% 3.68/2.63 tff(856,plain,
% 3.68/2.63 ((~hskp53) | (~c2_1(a648))),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[855, 852])).
% 3.68/2.63 tff(857,plain,
% 3.68/2.63 (~c2_1(a648)),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[856, 851])).
% 3.68/2.63 tff(858,plain,
% 3.68/2.63 (((~hskp53) | c0_1(a648)) <=> ((~hskp53) | c0_1(a648))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(859,axiom,((~hskp53) | c0_1(a648)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 3.68/2.63 tff(860,plain,
% 3.68/2.63 ((~hskp53) | c0_1(a648)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[859, 858])).
% 3.68/2.63 tff(861,plain,
% 3.68/2.63 ((~hskp53) | c0_1(a648)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[860, 858])).
% 3.68/2.63 tff(862,plain,
% 3.68/2.63 ((~hskp53) | c0_1(a648)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[861, 858])).
% 3.68/2.63 tff(863,plain,
% 3.68/2.63 ((~hskp53) | c0_1(a648)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[862, 858])).
% 3.68/2.63 tff(864,plain,
% 3.68/2.63 ((~hskp53) | c0_1(a648)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[863, 858])).
% 3.68/2.63 tff(865,plain,
% 3.68/2.63 ((~hskp53) | c0_1(a648)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[864, 858])).
% 3.68/2.63 tff(866,plain,
% 3.68/2.63 ((~hskp53) | c0_1(a648)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[865, 858])).
% 3.68/2.63 tff(867,plain,
% 3.68/2.63 ((~hskp53) | c0_1(a648)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[866, 858])).
% 3.68/2.63 tff(868,plain,
% 3.68/2.63 (c0_1(a648)),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[867, 851])).
% 3.68/2.63 tff(869,plain,
% 3.68/2.63 (((~hskp53) | c3_1(a648)) <=> ((~hskp53) | c3_1(a648))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(870,axiom,((~hskp53) | c3_1(a648)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 3.68/2.63 tff(871,plain,
% 3.68/2.63 ((~hskp53) | c3_1(a648)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[870, 869])).
% 3.68/2.63 tff(872,plain,
% 3.68/2.63 ((~hskp53) | c3_1(a648)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[871, 869])).
% 3.68/2.63 tff(873,plain,
% 3.68/2.63 ((~hskp53) | c3_1(a648)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[872, 869])).
% 3.68/2.63 tff(874,plain,
% 3.68/2.63 ((~hskp53) | c3_1(a648)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[873, 869])).
% 3.68/2.63 tff(875,plain,
% 3.68/2.63 ((~hskp53) | c3_1(a648)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[874, 869])).
% 3.68/2.63 tff(876,plain,
% 3.68/2.63 ((~hskp53) | c3_1(a648)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[875, 869])).
% 3.68/2.63 tff(877,plain,
% 3.68/2.63 ((~hskp53) | c3_1(a648)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[876, 869])).
% 3.68/2.63 tff(878,plain,
% 3.68/2.63 ((~hskp53) | c3_1(a648)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[877, 869])).
% 3.68/2.63 tff(879,plain,
% 3.68/2.63 (c3_1(a648)),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[878, 851])).
% 3.68/2.63 tff(880,assumption,(~c2_1(a648)), introduced(assumption)).
% 3.68/2.63 tff(881,assumption,(c0_1(a648)), introduced(assumption)).
% 3.68/2.63 tff(882,assumption,(c3_1(a648)), introduced(assumption)).
% 3.68/2.63 tff(883,plain,
% 3.68/2.63 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648)))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(884,plain,
% 3.68/2.63 ((hskp41 | (~ndr1_0) | c2_1(a648) | (~c3_1(a648)) | (~c1_1(a648)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648))) <=> (hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648)))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(885,plain,
% 3.68/2.63 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a648) | (~c3_1(a648)) | (~c1_1(a648)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648))))),
% 3.68/2.63 inference(monotonicity,[status(thm)],[884])).
% 3.68/2.63 tff(886,plain,
% 3.68/2.63 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a648) | (~c3_1(a648)) | (~c1_1(a648)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648)))),
% 3.68/2.63 inference(transitivity,[status(thm)],[885, 883])).
% 3.68/2.63 tff(887,plain,
% 3.68/2.63 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a648) | (~c3_1(a648)) | (~c1_1(a648)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)))),
% 3.68/2.63 inference(quant_inst,[status(thm)],[])).
% 3.68/2.63 tff(888,plain,
% 3.68/2.63 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648))),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[887, 886])).
% 3.68/2.63 tff(889,plain,
% 3.68/2.63 (hskp41 | (~c1_1(a648))),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[888, 96, 882, 881, 880, 329])).
% 3.68/2.63 tff(890,plain,
% 3.68/2.63 (~c1_1(a648)),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[889, 106])).
% 3.68/2.63 tff(891,plain,
% 3.68/2.63 (^[V: $i, U: $i] : refl((hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 3.68/2.63 inference(bind,[status(th)],[])).
% 3.68/2.63 tff(892,plain,
% 3.68/2.63 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.68/2.63 inference(quant_intro,[status(thm)],[891])).
% 3.68/2.63 tff(893,plain,
% 3.68/2.63 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(894,plain,
% 3.68/2.63 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp42) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp42))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp42) <=> (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp42) <=> (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 3.68/2.63 inference(bind,[status(th)],[])).
% 3.68/2.63 tff(895,plain,
% 3.68/2.63 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp42) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.68/2.63 inference(quant_intro,[status(thm)],[894])).
% 3.68/2.63 tff(896,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause303')).
% 3.68/2.63 tff(897,plain,
% 3.68/2.63 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[896, 895])).
% 3.68/2.63 tff(898,plain,
% 3.68/2.63 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[897, 893])).
% 3.68/2.63 tff(899,plain,(
% 3.68/2.63 ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.68/2.63 inference(skolemize,[status(sab)],[898])).
% 3.68/2.63 tff(900,plain,
% 3.68/2.63 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[899, 892])).
% 3.68/2.63 tff(901,plain,
% 3.68/2.63 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(902,plain,
% 3.68/2.63 ((hskp58 | hskp41 | (~ndr1_0) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648))) <=> (hskp58 | hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(903,plain,
% 3.68/2.63 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648))))),
% 3.68/2.63 inference(monotonicity,[status(thm)],[902])).
% 3.68/2.63 tff(904,plain,
% 3.68/2.63 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.63 inference(transitivity,[status(thm)],[903, 901])).
% 3.68/2.63 tff(905,plain,
% 3.68/2.63 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)))),
% 3.68/2.63 inference(quant_inst,[status(thm)],[])).
% 3.68/2.63 tff(906,plain,
% 3.68/2.63 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648))),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[905, 904])).
% 3.68/2.63 tff(907,plain,
% 3.68/2.63 (hskp58 | hskp41),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[906, 96, 882, 881, 880, 116])).
% 3.68/2.63 tff(908,plain,
% 3.68/2.63 (hskp58),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[907, 106])).
% 3.68/2.63 tff(909,plain,
% 3.68/2.63 (~c1_1(a663)),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[41, 908])).
% 3.68/2.63 tff(910,plain,
% 3.68/2.63 (~c0_1(a663)),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[47, 908])).
% 3.68/2.63 tff(911,plain,
% 3.68/2.63 (c3_1(a663)),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[58, 908])).
% 3.68/2.63 tff(912,plain,
% 3.68/2.63 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | c1_1(a648) | (~c3_1(a663)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | c1_1(a648) | (~c3_1(a663)))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(913,plain,
% 3.68/2.63 ((hskp42 | (~ndr1_0) | c1_1(a648) | c2_1(a648) | (~c0_1(a648)) | c1_1(a663) | c0_1(a663) | (~c3_1(a663))) <=> (hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | c1_1(a648) | (~c3_1(a663)))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(914,plain,
% 3.68/2.63 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a648) | c2_1(a648) | (~c0_1(a648)) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | c1_1(a648) | (~c3_1(a663))))),
% 3.68/2.63 inference(monotonicity,[status(thm)],[913])).
% 3.68/2.63 tff(915,plain,
% 3.68/2.63 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a648) | c2_1(a648) | (~c0_1(a648)) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | c1_1(a648) | (~c3_1(a663)))),
% 3.68/2.63 inference(transitivity,[status(thm)],[914, 912])).
% 3.68/2.63 tff(916,plain,
% 3.68/2.63 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a648) | c2_1(a648) | (~c0_1(a648)) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)))),
% 3.68/2.63 inference(quant_inst,[status(thm)],[])).
% 3.68/2.63 tff(917,plain,
% 3.68/2.63 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | c1_1(a648) | (~c3_1(a663))),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[916, 915])).
% 3.68/2.63 tff(918,plain,
% 3.68/2.63 (hskp42),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[917, 96, 911, 881, 910, 909, 880, 900, 890])).
% 3.68/2.63 tff(919,plain,
% 3.68/2.63 (((~hskp42) | (~c2_1(a618))) <=> ((~hskp42) | (~c2_1(a618)))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(920,plain,
% 3.68/2.63 (((~c2_1(a618)) | (~hskp42)) <=> ((~hskp42) | (~c2_1(a618)))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(921,axiom,((~c2_1(a618)) | (~hskp42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause201')).
% 3.68/2.63 tff(922,plain,
% 3.68/2.63 ((~hskp42) | (~c2_1(a618))),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[921, 920])).
% 3.68/2.63 tff(923,plain,
% 3.68/2.63 ((~hskp42) | (~c2_1(a618))),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[922, 919])).
% 3.68/2.63 tff(924,plain,
% 3.68/2.63 (~c2_1(a618)),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[923, 918])).
% 3.68/2.63 tff(925,plain,
% 3.68/2.63 (^[V: $i, U: $i] : refl((hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 3.68/2.63 inference(bind,[status(th)],[])).
% 3.68/2.63 tff(926,plain,
% 3.68/2.63 (![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.68/2.63 inference(quant_intro,[status(thm)],[925])).
% 3.68/2.63 tff(927,plain,
% 3.68/2.63 (![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(928,plain,
% 3.68/2.63 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c0_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c0_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c0_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c0_1(U)) | c1_1(V)) | hskp55) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp55))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp55) <=> (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c0_1(U)) | c1_1(V)) | hskp55) <=> (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 3.68/2.63 inference(bind,[status(th)],[])).
% 3.68/2.63 tff(929,plain,
% 3.68/2.63 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c0_1(U)) | c1_1(V)) | hskp55) <=> ![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.68/2.63 inference(quant_intro,[status(thm)],[928])).
% 3.68/2.63 tff(930,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c0_1(U)) | c1_1(V)) | hskp55)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause313')).
% 3.68/2.63 tff(931,plain,
% 3.68/2.63 (![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[930, 929])).
% 3.68/2.63 tff(932,plain,
% 3.68/2.63 (![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[931, 927])).
% 3.68/2.63 tff(933,plain,(
% 3.68/2.63 ![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.68/2.63 inference(skolemize,[status(sab)],[932])).
% 3.68/2.63 tff(934,plain,
% 3.68/2.63 (![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[933, 926])).
% 3.68/2.63 tff(935,plain,
% 3.68/2.63 (((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c3_1(a663)))) <=> ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp55 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c3_1(a663)))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(936,plain,
% 3.68/2.63 ((hskp55 | (~ndr1_0) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648))) <=> (hskp55 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c3_1(a663)))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(937,plain,
% 3.68/2.63 (((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | (~ndr1_0) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c3_1(a663))))),
% 3.68/2.63 inference(monotonicity,[status(thm)],[936])).
% 3.68/2.63 tff(938,plain,
% 3.68/2.63 (((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | (~ndr1_0) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp55 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c3_1(a663)))),
% 3.68/2.63 inference(transitivity,[status(thm)],[937, 935])).
% 3.68/2.63 tff(939,plain,
% 3.68/2.63 ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | (~ndr1_0) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)))),
% 3.68/2.63 inference(quant_inst,[status(thm)],[])).
% 3.68/2.63 tff(940,plain,
% 3.68/2.63 ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp55 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c3_1(a663))),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[939, 938])).
% 3.68/2.63 tff(941,plain,
% 3.68/2.63 (hskp55),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[940, 96, 911, 882, 881, 910, 909, 934, 890])).
% 3.68/2.63 tff(942,plain,
% 3.68/2.63 (((~hskp55) | (~c2_1(a653))) <=> ((~hskp55) | (~c2_1(a653)))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(943,plain,
% 3.68/2.63 (((~c2_1(a653)) | (~hskp55)) <=> ((~hskp55) | (~c2_1(a653)))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(944,axiom,((~c2_1(a653)) | (~hskp55)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 3.68/2.63 tff(945,plain,
% 3.68/2.63 ((~hskp55) | (~c2_1(a653))),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[944, 943])).
% 3.68/2.63 tff(946,plain,
% 3.68/2.63 ((~hskp55) | (~c2_1(a653))),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[945, 942])).
% 3.68/2.63 tff(947,plain,
% 3.68/2.63 (~c2_1(a653)),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[946, 941])).
% 3.68/2.63 tff(948,plain,
% 3.68/2.63 (((~hskp42) | c1_1(a618)) <=> ((~hskp42) | c1_1(a618))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(949,axiom,((~hskp42) | c1_1(a618)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 3.68/2.63 tff(950,plain,
% 3.68/2.63 ((~hskp42) | c1_1(a618)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[949, 948])).
% 3.68/2.63 tff(951,plain,
% 3.68/2.63 ((~hskp42) | c1_1(a618)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[950, 948])).
% 3.68/2.63 tff(952,plain,
% 3.68/2.63 ((~hskp42) | c1_1(a618)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[951, 948])).
% 3.68/2.63 tff(953,plain,
% 3.68/2.63 ((~hskp42) | c1_1(a618)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[952, 948])).
% 3.68/2.63 tff(954,plain,
% 3.68/2.63 ((~hskp42) | c1_1(a618)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[953, 948])).
% 3.68/2.63 tff(955,plain,
% 3.68/2.63 ((~hskp42) | c1_1(a618)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[954, 948])).
% 3.68/2.63 tff(956,plain,
% 3.68/2.63 ((~hskp42) | c1_1(a618)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[955, 948])).
% 3.68/2.63 tff(957,plain,
% 3.68/2.63 ((~hskp42) | c1_1(a618)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[956, 948])).
% 3.68/2.63 tff(958,plain,
% 3.68/2.63 (c1_1(a618)),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[957, 918])).
% 3.68/2.63 tff(959,plain,
% 3.68/2.63 (((~hskp55) | c1_1(a653)) <=> ((~hskp55) | c1_1(a653))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(960,axiom,((~hskp55) | c1_1(a653)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 3.68/2.63 tff(961,plain,
% 3.68/2.63 ((~hskp55) | c1_1(a653)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[960, 959])).
% 3.68/2.63 tff(962,plain,
% 3.68/2.63 ((~hskp55) | c1_1(a653)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[961, 959])).
% 3.68/2.63 tff(963,plain,
% 3.68/2.63 ((~hskp55) | c1_1(a653)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[962, 959])).
% 3.68/2.63 tff(964,plain,
% 3.68/2.63 ((~hskp55) | c1_1(a653)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[963, 959])).
% 3.68/2.63 tff(965,plain,
% 3.68/2.63 ((~hskp55) | c1_1(a653)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[964, 959])).
% 3.68/2.63 tff(966,plain,
% 3.68/2.63 ((~hskp55) | c1_1(a653)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[965, 959])).
% 3.68/2.63 tff(967,plain,
% 3.68/2.63 ((~hskp55) | c1_1(a653)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[966, 959])).
% 3.68/2.63 tff(968,plain,
% 3.68/2.63 ((~hskp55) | c1_1(a653)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[967, 959])).
% 3.68/2.63 tff(969,plain,
% 3.68/2.63 (c1_1(a653)),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[968, 941])).
% 3.68/2.63 tff(970,plain,
% 3.68/2.63 (((~hskp55) | c3_1(a653)) <=> ((~hskp55) | c3_1(a653))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(971,axiom,((~hskp55) | c3_1(a653)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 3.68/2.63 tff(972,plain,
% 3.68/2.63 ((~hskp55) | c3_1(a653)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[971, 970])).
% 3.68/2.63 tff(973,plain,
% 3.68/2.63 ((~hskp55) | c3_1(a653)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[972, 970])).
% 3.68/2.63 tff(974,plain,
% 3.68/2.63 ((~hskp55) | c3_1(a653)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[973, 970])).
% 3.68/2.63 tff(975,plain,
% 3.68/2.63 ((~hskp55) | c3_1(a653)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[974, 970])).
% 3.68/2.63 tff(976,plain,
% 3.68/2.63 ((~hskp55) | c3_1(a653)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[975, 970])).
% 3.68/2.63 tff(977,plain,
% 3.68/2.63 ((~hskp55) | c3_1(a653)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[976, 970])).
% 3.68/2.63 tff(978,plain,
% 3.68/2.63 ((~hskp55) | c3_1(a653)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[977, 970])).
% 3.68/2.63 tff(979,plain,
% 3.68/2.63 ((~hskp55) | c3_1(a653)),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[978, 970])).
% 3.68/2.63 tff(980,plain,
% 3.68/2.63 (c3_1(a653)),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[979, 941])).
% 3.68/2.63 tff(981,plain,
% 3.68/2.63 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a653) | c2_1(a618) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a653)) | (~c1_1(a653)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a653) | c2_1(a618) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a653)) | (~c1_1(a653)))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(982,plain,
% 3.68/2.63 ((hskp41 | (~ndr1_0) | c2_1(a653) | (~c3_1(a653)) | (~c1_1(a653)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618))) <=> (hskp41 | c2_1(a653) | c2_1(a618) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a653)) | (~c1_1(a653)))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(983,plain,
% 3.68/2.63 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a653) | (~c3_1(a653)) | (~c1_1(a653)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a653) | c2_1(a618) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a653)) | (~c1_1(a653))))),
% 3.68/2.63 inference(monotonicity,[status(thm)],[982])).
% 3.68/2.63 tff(984,plain,
% 3.68/2.63 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a653) | (~c3_1(a653)) | (~c1_1(a653)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a653) | c2_1(a618) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a653)) | (~c1_1(a653)))),
% 3.68/2.63 inference(transitivity,[status(thm)],[983, 981])).
% 3.68/2.63 tff(985,plain,
% 3.68/2.63 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a653) | (~c3_1(a653)) | (~c1_1(a653)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618)))),
% 3.68/2.63 inference(quant_inst,[status(thm)],[])).
% 3.68/2.63 tff(986,plain,
% 3.68/2.63 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a653) | c2_1(a618) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a653)) | (~c1_1(a653))),
% 3.68/2.63 inference(modus_ponens,[status(thm)],[985, 984])).
% 3.68/2.63 tff(987,plain,
% 3.68/2.63 (~c0_1(a618)),
% 3.68/2.63 inference(unit_resolution,[status(thm)],[986, 96, 106, 980, 969, 958, 947, 924, 329])).
% 3.68/2.63 tff(988,plain,
% 3.68/2.63 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 3.68/2.63 inference(bind,[status(th)],[])).
% 3.68/2.63 tff(989,plain,
% 3.68/2.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 3.68/2.63 inference(quant_intro,[status(thm)],[988])).
% 3.68/2.63 tff(990,plain,
% 3.68/2.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 3.68/2.63 inference(rewrite,[status(thm)],[])).
% 3.68/2.63 tff(991,plain,
% 3.68/2.63 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W))), (((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W)))), ((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W)) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W))), ((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W)))), (((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))), ((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) | c2_1(W)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), ((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) | c2_1(W)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))), (((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) | c2_1(W)) | c1_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) | c2_1(W)) | c1_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 3.68/2.64 inference(bind,[status(th)],[])).
% 3.68/2.64 tff(992,plain,
% 3.68/2.64 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) | c2_1(W)) | c1_1(U)) | c2_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 3.68/2.64 inference(quant_intro,[status(thm)],[991])).
% 3.68/2.64 tff(993,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) | c2_1(W)) | c1_1(U)) | c2_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause322')).
% 3.68/2.64 tff(994,plain,
% 3.68/2.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[993, 992])).
% 3.68/2.64 tff(995,plain,
% 3.68/2.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[994, 990])).
% 3.68/2.64 tff(996,plain,(
% 3.68/2.64 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 3.68/2.64 inference(skolemize,[status(sab)],[995])).
% 3.68/2.64 tff(997,plain,
% 3.68/2.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[996, 989])).
% 3.68/2.64 tff(998,plain,
% 3.68/2.64 (((~hskp42) | (~c3_1(a618))) <=> ((~hskp42) | (~c3_1(a618)))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(999,plain,
% 3.68/2.64 (((~c3_1(a618)) | (~hskp42)) <=> ((~hskp42) | (~c3_1(a618)))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1000,axiom,((~c3_1(a618)) | (~hskp42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause202')).
% 3.68/2.64 tff(1001,plain,
% 3.68/2.64 ((~hskp42) | (~c3_1(a618))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1000, 999])).
% 3.68/2.64 tff(1002,plain,
% 3.68/2.64 ((~hskp42) | (~c3_1(a618))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1001, 998])).
% 3.68/2.64 tff(1003,plain,
% 3.68/2.64 (~c3_1(a618)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1002, 918])).
% 3.68/2.64 tff(1004,plain,
% 3.68/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a648) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | c0_1(a618) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a648) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | c0_1(a618) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1005,plain,
% 3.68/2.64 (((~ndr1_0) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a618) | c0_1(a618) | c3_1(a618)) <=> (c2_1(a648) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | c0_1(a618) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1006,plain,
% 3.68/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a618) | c0_1(a618) | c3_1(a618))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a648) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | c0_1(a618) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648)))),
% 3.68/2.64 inference(monotonicity,[status(thm)],[1005])).
% 3.68/2.64 tff(1007,plain,
% 3.68/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a618) | c0_1(a618) | c3_1(a618))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a648) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | c0_1(a618) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648))),
% 3.68/2.64 inference(transitivity,[status(thm)],[1006, 1004])).
% 3.68/2.64 tff(1008,plain,
% 3.68/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a618) | c0_1(a618) | c3_1(a618))),
% 3.68/2.64 inference(quant_inst,[status(thm)],[])).
% 3.68/2.64 tff(1009,plain,
% 3.68/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a648) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | c0_1(a618) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1008, 1007])).
% 3.68/2.64 tff(1010,plain,
% 3.68/2.64 ($false),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1009, 96, 882, 881, 880, 924, 1003, 997, 987, 890])).
% 3.68/2.64 tff(1011,plain,(hskp41 | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648)), inference(lemma,lemma(discharge,[]))).
% 3.68/2.64 tff(1012,plain,
% 3.68/2.64 (hskp41),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1011, 868, 879, 857])).
% 3.68/2.64 tff(1013,plain,
% 3.68/2.64 (c2_1(a617)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[556, 1012])).
% 3.68/2.64 tff(1014,plain,
% 3.68/2.64 (c3_1(a617)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[528, 1012])).
% 3.68/2.64 tff(1015,plain,
% 3.68/2.64 (^[U: $i] : refl((hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 3.68/2.64 inference(bind,[status(th)],[])).
% 3.68/2.64 tff(1016,plain,
% 3.68/2.64 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.68/2.64 inference(quant_intro,[status(thm)],[1015])).
% 3.68/2.64 tff(1017,plain,
% 3.68/2.64 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1018,plain,
% 3.68/2.64 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp3) | hskp29) <=> ((hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp29))), rewrite(((hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp29) <=> (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp3) | hskp29) <=> (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 3.68/2.64 inference(bind,[status(th)],[])).
% 3.68/2.64 tff(1019,plain,
% 3.68/2.64 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp3) | hskp29) <=> ![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.68/2.64 inference(quant_intro,[status(thm)],[1018])).
% 3.68/2.64 tff(1020,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp3) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause288')).
% 3.68/2.64 tff(1021,plain,
% 3.68/2.64 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1020, 1019])).
% 3.68/2.64 tff(1022,plain,
% 3.68/2.64 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1021, 1017])).
% 3.68/2.64 tff(1023,plain,(
% 3.68/2.64 ![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.68/2.64 inference(skolemize,[status(sab)],[1022])).
% 3.68/2.64 tff(1024,plain,
% 3.68/2.64 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1023, 1016])).
% 3.68/2.64 tff(1025,assumption,(~c0_1(a617)), introduced(assumption)).
% 3.68/2.64 tff(1026,plain,
% 3.68/2.64 (~hskp65),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[289, 280, 281])).
% 3.68/2.64 tff(1027,plain,
% 3.68/2.64 (hskp66),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[94, 1026, 24])).
% 3.68/2.64 tff(1028,plain,
% 3.68/2.64 (~c2_1(a675)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[296, 1027])).
% 3.68/2.64 tff(1029,plain,
% 3.68/2.64 (c3_1(a675)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[307, 1027])).
% 3.68/2.64 tff(1030,assumption,(~c3_1(a603)), introduced(assumption)).
% 3.68/2.64 tff(1031,plain,
% 3.68/2.64 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W))))),
% 3.68/2.64 inference(bind,[status(th)],[])).
% 3.68/2.64 tff(1032,plain,
% 3.68/2.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 3.68/2.64 inference(quant_intro,[status(thm)],[1031])).
% 3.68/2.64 tff(1033,plain,
% 3.68/2.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1034,plain,
% 3.68/2.64 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))))),
% 3.68/2.64 inference(bind,[status(th)],[])).
% 3.68/2.64 tff(1035,plain,
% 3.68/2.64 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 3.68/2.64 inference(quant_intro,[status(thm)],[1034])).
% 3.68/2.64 tff(1036,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause327')).
% 3.68/2.64 tff(1037,plain,
% 3.68/2.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 3.68/2.64 tff(1038,plain,
% 3.68/2.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1037, 1033])).
% 3.68/2.64 tff(1039,plain,(
% 3.68/2.64 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 3.68/2.64 inference(skolemize,[status(sab)],[1038])).
% 3.68/2.64 tff(1040,plain,
% 3.68/2.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1039, 1032])).
% 3.68/2.64 tff(1041,plain,
% 3.68/2.64 (hskp41),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1011, 881, 882, 880])).
% 3.68/2.64 tff(1042,plain,
% 3.68/2.64 (~c1_1(a617)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[517, 1041])).
% 3.68/2.64 tff(1043,plain,
% 3.68/2.64 (c3_1(a617)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[528, 1041])).
% 3.68/2.64 tff(1044,plain,
% 3.68/2.64 (c2_1(a617)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[556, 1041])).
% 3.68/2.64 tff(1045,assumption,(c0_1(a635)), introduced(assumption)).
% 3.68/2.64 tff(1046,assumption,(~c1_1(a635)), introduced(assumption)).
% 3.68/2.64 tff(1047,plain,
% 3.68/2.64 (hskp41),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1011, 882, 881, 880])).
% 3.68/2.64 tff(1048,plain,
% 3.68/2.64 (~c1_1(a617)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[517, 1047])).
% 3.68/2.64 tff(1049,assumption,(~c2_1(a635)), introduced(assumption)).
% 3.68/2.64 tff(1050,plain,
% 3.68/2.64 (c3_1(a617)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[528, 1047])).
% 3.68/2.64 tff(1051,plain,
% 3.68/2.64 (c2_1(a617)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[556, 1047])).
% 3.68/2.64 tff(1052,plain,
% 3.68/2.64 (hskp15 | hskp14 | (~c0_1(a617))),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[612, 96, 1051, 1048, 250])).
% 3.68/2.64 tff(1053,plain,
% 3.68/2.64 (~c0_1(a617)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1052, 281, 280])).
% 3.68/2.64 tff(1054,plain,
% 3.68/2.64 (^[V: $i, U: $i] : refl((hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 3.68/2.64 inference(bind,[status(th)],[])).
% 3.68/2.64 tff(1055,plain,
% 3.68/2.64 (![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 3.68/2.64 inference(quant_intro,[status(thm)],[1054])).
% 3.68/2.64 tff(1056,plain,
% 3.68/2.64 (![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1057,plain,
% 3.68/2.64 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp45) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp45))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp45) <=> (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp45) <=> (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 3.68/2.64 inference(bind,[status(th)],[])).
% 3.68/2.64 tff(1058,plain,
% 3.68/2.64 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp45) <=> ![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 3.68/2.64 inference(quant_intro,[status(thm)],[1057])).
% 3.68/2.64 tff(1059,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp45)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause308')).
% 3.68/2.64 tff(1060,plain,
% 3.68/2.64 (![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 3.68/2.64 tff(1061,plain,
% 3.68/2.64 (![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1060, 1056])).
% 3.68/2.64 tff(1062,plain,(
% 3.68/2.64 ![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 3.68/2.64 inference(skolemize,[status(sab)],[1061])).
% 3.68/2.64 tff(1063,plain,
% 3.68/2.64 (![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1062, 1055])).
% 3.68/2.64 tff(1064,plain,
% 3.68/2.64 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a617) | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c0_1(a635)) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a617) | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c0_1(a635)) | c0_1(a617) | (~c3_1(a617)))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1065,plain,
% 3.68/2.64 ((hskp42 | (~ndr1_0) | c1_1(a635) | c2_1(a635) | (~c0_1(a635)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617))) <=> (hskp42 | c1_1(a617) | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c0_1(a635)) | c0_1(a617) | (~c3_1(a617)))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1066,plain,
% 3.68/2.64 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a635) | c2_1(a635) | (~c0_1(a635)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a617) | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c0_1(a635)) | c0_1(a617) | (~c3_1(a617))))),
% 3.68/2.64 inference(monotonicity,[status(thm)],[1065])).
% 3.68/2.64 tff(1067,plain,
% 3.68/2.64 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a635) | c2_1(a635) | (~c0_1(a635)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a617) | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c0_1(a635)) | c0_1(a617) | (~c3_1(a617)))),
% 3.68/2.64 inference(transitivity,[status(thm)],[1066, 1064])).
% 3.68/2.64 tff(1068,plain,
% 3.68/2.64 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a635) | c2_1(a635) | (~c0_1(a635)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))),
% 3.68/2.64 inference(quant_inst,[status(thm)],[])).
% 3.68/2.64 tff(1069,plain,
% 3.68/2.64 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a617) | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c0_1(a635)) | c0_1(a617) | (~c3_1(a617))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 3.68/2.64 tff(1070,plain,
% 3.68/2.64 (hskp42 | (~c0_1(a635)) | c0_1(a617)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1069, 96, 711, 710, 1046, 1049, 900])).
% 3.68/2.64 tff(1071,plain,
% 3.68/2.64 (hskp42),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1070, 1025, 1045])).
% 3.68/2.64 tff(1072,plain,
% 3.68/2.64 (~c3_1(a618)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1002, 1071])).
% 3.68/2.64 tff(1073,plain,
% 3.68/2.64 (~c2_1(a618)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[923, 1071])).
% 3.68/2.64 tff(1074,plain,
% 3.68/2.64 (c1_1(a618)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[957, 1071])).
% 3.68/2.64 tff(1075,assumption,(~hskp45), introduced(assumption)).
% 3.68/2.64 tff(1076,plain,
% 3.68/2.64 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp45 | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1077,plain,
% 3.68/2.64 ((hskp45 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))) <=> (hskp45 | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1078,plain,
% 3.68/2.64 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))))),
% 3.68/2.64 inference(monotonicity,[status(thm)],[1077])).
% 3.68/2.64 tff(1079,plain,
% 3.68/2.64 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp45 | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.64 inference(transitivity,[status(thm)],[1078, 1076])).
% 3.68/2.64 tff(1080,plain,
% 3.68/2.64 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.64 inference(quant_inst,[status(thm)],[])).
% 3.68/2.64 tff(1081,plain,
% 3.68/2.64 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp45 | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 3.68/2.64 tff(1082,plain,
% 3.68/2.64 ($false),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1081, 96, 1075, 1074, 712, 711, 1073, 1072, 1063, 1025])).
% 3.68/2.64 tff(1083,plain,(c0_1(a617) | hskp45 | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a635)) | c1_1(a617) | c1_1(a635) | c2_1(a635)), inference(lemma,lemma(discharge,[]))).
% 3.68/2.64 tff(1084,plain,
% 3.68/2.64 (hskp45),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1083, 1053, 1051, 1050, 1049, 1048, 1046, 1045])).
% 3.68/2.64 tff(1085,plain,
% 3.68/2.64 (((~hskp45) | (~c0_1(a623))) <=> ((~hskp45) | (~c0_1(a623)))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1086,plain,
% 3.68/2.64 (((~c0_1(a623)) | (~hskp45)) <=> ((~hskp45) | (~c0_1(a623)))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1087,axiom,((~c0_1(a623)) | (~hskp45)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 3.68/2.64 tff(1088,plain,
% 3.68/2.64 ((~hskp45) | (~c0_1(a623))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 3.68/2.64 tff(1089,plain,
% 3.68/2.64 ((~hskp45) | (~c0_1(a623))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1088, 1085])).
% 3.68/2.64 tff(1090,plain,
% 3.68/2.64 (~c0_1(a623)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1089, 1084])).
% 3.68/2.64 tff(1091,plain,
% 3.68/2.64 (((~hskp45) | c3_1(a623)) <=> ((~hskp45) | c3_1(a623))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1092,axiom,((~hskp45) | c3_1(a623)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 3.68/2.64 tff(1093,plain,
% 3.68/2.64 ((~hskp45) | c3_1(a623)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 3.68/2.64 tff(1094,plain,
% 3.68/2.64 ((~hskp45) | c3_1(a623)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1093, 1091])).
% 3.68/2.64 tff(1095,plain,
% 3.68/2.64 ((~hskp45) | c3_1(a623)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1094, 1091])).
% 3.68/2.64 tff(1096,plain,
% 3.68/2.64 ((~hskp45) | c3_1(a623)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1095, 1091])).
% 3.68/2.64 tff(1097,plain,
% 3.68/2.64 ((~hskp45) | c3_1(a623)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1096, 1091])).
% 3.68/2.64 tff(1098,plain,
% 3.68/2.64 ((~hskp45) | c3_1(a623)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1097, 1091])).
% 3.68/2.64 tff(1099,plain,
% 3.68/2.64 ((~hskp45) | c3_1(a623)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1098, 1091])).
% 3.68/2.64 tff(1100,plain,
% 3.68/2.64 ((~hskp45) | c3_1(a623)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1099, 1091])).
% 3.68/2.64 tff(1101,plain,
% 3.68/2.64 (c3_1(a623)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1100, 1084])).
% 3.68/2.64 tff(1102,plain,
% 3.68/2.64 (((~hskp45) | c2_1(a623)) <=> ((~hskp45) | c2_1(a623))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1103,axiom,((~hskp45) | c2_1(a623)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 3.68/2.64 tff(1104,plain,
% 3.68/2.64 ((~hskp45) | c2_1(a623)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 3.68/2.64 tff(1105,plain,
% 3.68/2.64 ((~hskp45) | c2_1(a623)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1104, 1102])).
% 3.68/2.64 tff(1106,plain,
% 3.68/2.64 ((~hskp45) | c2_1(a623)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1105, 1102])).
% 3.68/2.64 tff(1107,plain,
% 3.68/2.64 ((~hskp45) | c2_1(a623)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1106, 1102])).
% 3.68/2.64 tff(1108,plain,
% 3.68/2.64 ((~hskp45) | c2_1(a623)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1107, 1102])).
% 3.68/2.64 tff(1109,plain,
% 3.68/2.64 ((~hskp45) | c2_1(a623)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1108, 1102])).
% 3.68/2.64 tff(1110,plain,
% 3.68/2.64 ((~hskp45) | c2_1(a623)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1109, 1102])).
% 3.68/2.64 tff(1111,plain,
% 3.68/2.64 ((~hskp45) | c2_1(a623)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1110, 1102])).
% 3.68/2.64 tff(1112,plain,
% 3.68/2.64 (c2_1(a623)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1111, 1084])).
% 3.68/2.64 tff(1113,assumption,(hskp9), introduced(assumption)).
% 3.68/2.64 tff(1114,plain,
% 3.68/2.64 (((~hskp9) | (~c3_1(a613))) <=> ((~hskp9) | (~c3_1(a613)))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1115,plain,
% 3.68/2.64 (((~c3_1(a613)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a613)))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1116,axiom,((~c3_1(a613)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause258')).
% 3.68/2.64 tff(1117,plain,
% 3.68/2.64 ((~hskp9) | (~c3_1(a613))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1116, 1115])).
% 3.68/2.64 tff(1118,plain,
% 3.68/2.64 ((~hskp9) | (~c3_1(a613))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1117, 1114])).
% 3.68/2.64 tff(1119,plain,
% 3.68/2.64 (~c3_1(a613)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1118, 1113])).
% 3.68/2.64 tff(1120,assumption,(~c0_1(a623)), introduced(assumption)).
% 3.68/2.64 tff(1121,plain,
% 3.68/2.64 (((~hskp9) | c2_1(a613)) <=> ((~hskp9) | c2_1(a613))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1122,axiom,((~hskp9) | c2_1(a613)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 3.68/2.64 tff(1123,plain,
% 3.68/2.64 ((~hskp9) | c2_1(a613)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 3.68/2.64 tff(1124,plain,
% 3.68/2.64 ((~hskp9) | c2_1(a613)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1123, 1121])).
% 3.68/2.64 tff(1125,plain,
% 3.68/2.64 ((~hskp9) | c2_1(a613)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1124, 1121])).
% 3.68/2.64 tff(1126,plain,
% 3.68/2.64 ((~hskp9) | c2_1(a613)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1125, 1121])).
% 3.68/2.64 tff(1127,plain,
% 3.68/2.64 ((~hskp9) | c2_1(a613)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1126, 1121])).
% 3.68/2.64 tff(1128,plain,
% 3.68/2.64 ((~hskp9) | c2_1(a613)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1127, 1121])).
% 3.68/2.64 tff(1129,plain,
% 3.68/2.64 ((~hskp9) | c2_1(a613)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1128, 1121])).
% 3.68/2.64 tff(1130,plain,
% 3.68/2.64 ((~hskp9) | c2_1(a613)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1129, 1121])).
% 3.68/2.64 tff(1131,plain,
% 3.68/2.64 (c2_1(a613)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1130, 1113])).
% 3.68/2.64 tff(1132,plain,
% 3.68/2.64 (((~hskp9) | c1_1(a613)) <=> ((~hskp9) | c1_1(a613))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1133,axiom,((~hskp9) | c1_1(a613)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 3.68/2.64 tff(1134,plain,
% 3.68/2.64 ((~hskp9) | c1_1(a613)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 3.68/2.64 tff(1135,plain,
% 3.68/2.64 ((~hskp9) | c1_1(a613)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1134, 1132])).
% 3.68/2.64 tff(1136,plain,
% 3.68/2.64 ((~hskp9) | c1_1(a613)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1135, 1132])).
% 3.68/2.64 tff(1137,plain,
% 3.68/2.64 ((~hskp9) | c1_1(a613)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1136, 1132])).
% 3.68/2.64 tff(1138,plain,
% 3.68/2.64 ((~hskp9) | c1_1(a613)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1137, 1132])).
% 3.68/2.64 tff(1139,plain,
% 3.68/2.64 ((~hskp9) | c1_1(a613)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1138, 1132])).
% 3.68/2.64 tff(1140,plain,
% 3.68/2.64 ((~hskp9) | c1_1(a613)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1139, 1132])).
% 3.68/2.64 tff(1141,plain,
% 3.68/2.64 ((~hskp9) | c1_1(a613)),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1140, 1132])).
% 3.68/2.64 tff(1142,plain,
% 3.68/2.64 (c1_1(a613)),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1141, 1113])).
% 3.68/2.64 tff(1143,assumption,(c2_1(a623)), introduced(assumption)).
% 3.68/2.64 tff(1144,assumption,(c3_1(a623)), introduced(assumption)).
% 3.68/2.64 tff(1145,plain,
% 3.68/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a648) | c0_1(a623) | c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c2_1(a623)) | (~c3_1(a623)) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | c0_1(a623) | c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c2_1(a623)) | (~c3_1(a623)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1146,plain,
% 3.68/2.64 (((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648))) <=> (c2_1(a648) | c0_1(a623) | c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c2_1(a623)) | (~c3_1(a623)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.64 inference(rewrite,[status(thm)],[])).
% 3.68/2.64 tff(1147,plain,
% 3.68/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a648) | c0_1(a623) | c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c2_1(a623)) | (~c3_1(a623)) | (~c0_1(a648)) | (~c3_1(a648))))),
% 3.68/2.64 inference(monotonicity,[status(thm)],[1146])).
% 3.68/2.64 tff(1148,plain,
% 3.68/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | c0_1(a623) | c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c2_1(a623)) | (~c3_1(a623)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.64 inference(transitivity,[status(thm)],[1147, 1145])).
% 3.68/2.64 tff(1149,plain,
% 3.68/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.64 inference(quant_inst,[status(thm)],[])).
% 3.68/2.64 tff(1150,plain,
% 3.68/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | c0_1(a623) | c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c2_1(a623)) | (~c3_1(a623)) | (~c0_1(a648)) | (~c3_1(a648))),
% 3.68/2.64 inference(modus_ponens,[status(thm)],[1149, 1148])).
% 3.68/2.64 tff(1151,plain,
% 3.68/2.64 ($false),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1150, 96, 882, 881, 1144, 1143, 1142, 1131, 880, 1120, 1119, 1040])).
% 3.68/2.64 tff(1152,plain,((~hskp9) | (~c3_1(a648)) | (~c0_1(a648)) | (~c3_1(a623)) | (~c2_1(a623)) | c2_1(a648) | c0_1(a623)), inference(lemma,lemma(discharge,[]))).
% 3.68/2.64 tff(1153,plain,
% 3.68/2.64 (~hskp9),
% 3.68/2.64 inference(unit_resolution,[status(thm)],[1152, 1112, 882, 881, 1101, 880, 1090])).
% 3.68/2.64 tff(1154,plain,
% 3.68/2.65 ((hskp17 | hskp16 | hskp9) <=> (hskp17 | hskp16 | hskp9)),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1155,plain,
% 3.68/2.65 (((hskp16 | hskp17) | hskp9) <=> (hskp17 | hskp16 | hskp9)),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1156,axiom,((hskp16 | hskp17) | hskp9), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 3.68/2.65 tff(1157,plain,
% 3.68/2.65 (hskp17 | hskp16 | hskp9),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 3.68/2.65 tff(1158,plain,
% 3.68/2.65 (hskp17 | hskp16 | hskp9),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1157, 1154])).
% 3.68/2.65 tff(1159,plain,
% 3.68/2.65 (hskp17 | hskp16 | hskp9),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1158, 1154])).
% 3.68/2.65 tff(1160,plain,
% 3.68/2.65 (hskp17 | hskp16 | hskp9),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1159, 1154])).
% 3.68/2.65 tff(1161,plain,
% 3.68/2.65 (hskp17 | hskp16 | hskp9),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1160, 1154])).
% 3.68/2.65 tff(1162,plain,
% 3.68/2.65 (hskp17 | hskp16 | hskp9),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1161, 1154])).
% 3.68/2.65 tff(1163,plain,
% 3.68/2.65 (hskp17 | hskp16 | hskp9),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1162, 1154])).
% 3.68/2.65 tff(1164,plain,
% 3.68/2.65 (hskp17 | hskp16 | hskp9),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1163, 1154])).
% 3.68/2.65 tff(1165,plain,
% 3.68/2.65 (hskp16),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[1164, 1153, 12])).
% 3.68/2.65 tff(1166,plain,
% 3.68/2.65 (((~hskp16) | (~c3_1(a627))) <=> ((~hskp16) | (~c3_1(a627)))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1167,plain,
% 3.68/2.65 (((~c3_1(a627)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a627)))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1168,axiom,((~c3_1(a627)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause244')).
% 3.68/2.65 tff(1169,plain,
% 3.68/2.65 ((~hskp16) | (~c3_1(a627))),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1168, 1167])).
% 3.68/2.65 tff(1170,plain,
% 3.68/2.65 ((~hskp16) | (~c3_1(a627))),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1169, 1166])).
% 3.68/2.65 tff(1171,plain,
% 3.68/2.65 (~c3_1(a627)),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[1170, 1165])).
% 3.68/2.65 tff(1172,plain,
% 3.68/2.65 (((~hskp16) | c2_1(a627)) <=> ((~hskp16) | c2_1(a627))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1173,axiom,((~hskp16) | c2_1(a627)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 3.68/2.65 tff(1174,plain,
% 3.68/2.65 ((~hskp16) | c2_1(a627)),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 3.68/2.65 tff(1175,plain,
% 3.68/2.65 ((~hskp16) | c2_1(a627)),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1174, 1172])).
% 3.68/2.65 tff(1176,plain,
% 3.68/2.65 ((~hskp16) | c2_1(a627)),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1175, 1172])).
% 3.68/2.65 tff(1177,plain,
% 3.68/2.65 ((~hskp16) | c2_1(a627)),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1176, 1172])).
% 3.68/2.65 tff(1178,plain,
% 3.68/2.65 ((~hskp16) | c2_1(a627)),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1177, 1172])).
% 3.68/2.65 tff(1179,plain,
% 3.68/2.65 ((~hskp16) | c2_1(a627)),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1178, 1172])).
% 3.68/2.65 tff(1180,plain,
% 3.68/2.65 ((~hskp16) | c2_1(a627)),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1179, 1172])).
% 3.68/2.65 tff(1181,plain,
% 3.68/2.65 ((~hskp16) | c2_1(a627)),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1180, 1172])).
% 3.68/2.65 tff(1182,plain,
% 3.68/2.65 (c2_1(a627)),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[1181, 1165])).
% 3.68/2.65 tff(1183,plain,
% 3.68/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a648) | c0_1(a623) | c3_1(a627) | (~ndr1_0) | (~c2_1(a623)) | (~c3_1(a623)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | c0_1(a623) | c3_1(a627) | (~ndr1_0) | (~c2_1(a623)) | (~c3_1(a623)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1184,plain,
% 3.68/2.65 (((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648))) <=> (c2_1(a648) | c0_1(a623) | c3_1(a627) | (~ndr1_0) | (~c2_1(a623)) | (~c3_1(a623)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1185,plain,
% 3.68/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a648) | c0_1(a623) | c3_1(a627) | (~ndr1_0) | (~c2_1(a623)) | (~c3_1(a623)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648))))),
% 3.68/2.65 inference(monotonicity,[status(thm)],[1184])).
% 3.68/2.65 tff(1186,plain,
% 3.68/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | c0_1(a623) | c3_1(a627) | (~ndr1_0) | (~c2_1(a623)) | (~c3_1(a623)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.65 inference(transitivity,[status(thm)],[1185, 1183])).
% 3.68/2.65 tff(1187,plain,
% 3.68/2.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.65 inference(quant_inst,[status(thm)],[])).
% 3.68/2.65 tff(1188,plain,
% 3.68/2.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | c0_1(a623) | c3_1(a627) | (~ndr1_0) | (~c2_1(a623)) | (~c3_1(a623)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648))),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 3.68/2.65 tff(1189,plain,
% 3.68/2.65 (~c1_1(a627)),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[1188, 96, 882, 881, 1101, 1112, 1182, 880, 1090, 1171, 1040])).
% 3.68/2.65 tff(1190,plain,
% 3.68/2.65 (((~hskp16) | c0_1(a627)) <=> ((~hskp16) | c0_1(a627))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1191,axiom,((~hskp16) | c0_1(a627)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 3.68/2.65 tff(1192,plain,
% 3.68/2.65 ((~hskp16) | c0_1(a627)),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1191, 1190])).
% 3.68/2.65 tff(1193,plain,
% 3.68/2.65 ((~hskp16) | c0_1(a627)),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1192, 1190])).
% 3.68/2.65 tff(1194,plain,
% 3.68/2.65 ((~hskp16) | c0_1(a627)),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1193, 1190])).
% 3.68/2.65 tff(1195,plain,
% 3.68/2.65 ((~hskp16) | c0_1(a627)),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1194, 1190])).
% 3.68/2.65 tff(1196,plain,
% 3.68/2.65 ((~hskp16) | c0_1(a627)),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1195, 1190])).
% 3.68/2.65 tff(1197,plain,
% 3.68/2.65 ((~hskp16) | c0_1(a627)),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1196, 1190])).
% 3.68/2.65 tff(1198,plain,
% 3.68/2.65 ((~hskp16) | c0_1(a627)),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1197, 1190])).
% 3.68/2.65 tff(1199,plain,
% 3.68/2.65 ((~hskp16) | c0_1(a627)),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1198, 1190])).
% 3.68/2.65 tff(1200,plain,
% 3.68/2.65 (c0_1(a627)),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[1199, 1165])).
% 3.68/2.65 tff(1201,plain,
% 3.68/2.65 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | c1_1(a627))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | c1_1(a627))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1202,plain,
% 3.68/2.65 ((hskp15 | hskp14 | (~ndr1_0) | c1_1(a627) | (~c0_1(a627)) | (~c2_1(a627))) <=> (hskp15 | hskp14 | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | c1_1(a627))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1203,plain,
% 3.68/2.65 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a627) | (~c0_1(a627)) | (~c2_1(a627)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | c1_1(a627)))),
% 3.68/2.65 inference(monotonicity,[status(thm)],[1202])).
% 3.68/2.65 tff(1204,plain,
% 3.68/2.65 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a627) | (~c0_1(a627)) | (~c2_1(a627)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | c1_1(a627))),
% 3.68/2.65 inference(transitivity,[status(thm)],[1203, 1201])).
% 3.68/2.65 tff(1205,plain,
% 3.68/2.65 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a627) | (~c0_1(a627)) | (~c2_1(a627)))),
% 3.68/2.65 inference(quant_inst,[status(thm)],[])).
% 3.68/2.65 tff(1206,plain,
% 3.68/2.65 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | c1_1(a627)),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1205, 1204])).
% 3.68/2.65 tff(1207,plain,
% 3.68/2.65 ($false),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[1206, 96, 281, 280, 1182, 1200, 250, 1189])).
% 3.68/2.65 tff(1208,plain,(hskp15 | hskp14 | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | hskp17 | c2_1(a635) | c1_1(a635) | (~c0_1(a635))), inference(lemma,lemma(discharge,[]))).
% 3.68/2.65 tff(1209,plain,
% 3.68/2.65 (~c0_1(a635)),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[1208, 677, 882, 881, 880, 12, 281, 683, 280])).
% 3.68/2.65 tff(1210,plain,
% 3.68/2.65 (hskp15 | hskp14 | (~c0_1(a617))),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[612, 96, 1044, 1042, 250])).
% 3.68/2.65 tff(1211,plain,
% 3.68/2.65 (~c0_1(a617)),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[1210, 280, 281])).
% 3.68/2.65 tff(1212,plain,
% 3.68/2.65 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 3.68/2.65 inference(bind,[status(th)],[])).
% 3.68/2.65 tff(1213,plain,
% 3.68/2.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 3.68/2.65 inference(quant_intro,[status(thm)],[1212])).
% 3.68/2.65 tff(1214,plain,
% 3.68/2.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1215,plain,
% 3.68/2.65 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c2_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))))), (((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W))), (((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W)))), ((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c3_1(W))), ((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c3_1(W)))), (((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c1_1(W)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c3_1(W)) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c3_1(W)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c1_1(W)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 3.68/2.65 inference(bind,[status(th)],[])).
% 3.68/2.65 tff(1216,plain,
% 3.68/2.65 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c1_1(W)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 3.68/2.65 inference(quant_intro,[status(thm)],[1215])).
% 3.68/2.65 tff(1217,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c1_1(W)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause321')).
% 3.68/2.65 tff(1218,plain,
% 3.68/2.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1217, 1216])).
% 3.68/2.65 tff(1219,plain,
% 3.68/2.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1218, 1214])).
% 3.68/2.65 tff(1220,plain,(
% 3.68/2.65 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 3.68/2.65 inference(skolemize,[status(sab)],[1219])).
% 3.68/2.65 tff(1221,plain,
% 3.68/2.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1220, 1213])).
% 3.68/2.65 tff(1222,plain,
% 3.68/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c1_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1223,plain,
% 3.68/2.65 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a635) | c0_1(a635) | c3_1(a635)) <=> (c1_1(a617) | c1_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1224,plain,
% 3.68/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a635) | c0_1(a635) | c3_1(a635))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c1_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))))),
% 3.68/2.65 inference(monotonicity,[status(thm)],[1223])).
% 3.68/2.65 tff(1225,plain,
% 3.68/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a635) | c0_1(a635) | c3_1(a635))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.65 inference(transitivity,[status(thm)],[1224, 1222])).
% 3.68/2.65 tff(1226,plain,
% 3.68/2.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a635) | c0_1(a635) | c3_1(a635))),
% 3.68/2.65 inference(quant_inst,[status(thm)],[])).
% 3.68/2.65 tff(1227,plain,
% 3.68/2.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1226, 1225])).
% 3.68/2.65 tff(1228,plain,
% 3.68/2.65 ($false),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[1227, 96, 1044, 1043, 1042, 683, 671, 1221, 1211, 1209])).
% 3.68/2.65 tff(1229,plain,((~hskp20) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | hskp17 | hskp15 | hskp14), inference(lemma,lemma(discharge,[]))).
% 3.68/2.65 tff(1230,plain,
% 3.68/2.65 (~hskp20),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[1229, 280, 881, 880, 12, 281, 882])).
% 3.68/2.65 tff(1231,plain,
% 3.68/2.65 (hskp15 | hskp14 | (~c0_1(a617))),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[612, 96, 712, 710, 250])).
% 3.68/2.65 tff(1232,plain,
% 3.68/2.65 (~c0_1(a617)),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[1231, 280, 281])).
% 3.68/2.65 tff(1233,assumption,(~c1_1(a603)), introduced(assumption)).
% 3.68/2.65 tff(1234,plain,
% 3.68/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a603) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1235,plain,
% 3.68/2.65 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a603) | c0_1(a603) | c3_1(a603)) <=> (c0_1(a603) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1236,plain,
% 3.68/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a603) | c0_1(a603) | c3_1(a603))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a603) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))))),
% 3.68/2.65 inference(monotonicity,[status(thm)],[1235])).
% 3.68/2.65 tff(1237,plain,
% 3.68/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a603) | c0_1(a603) | c3_1(a603))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.65 inference(transitivity,[status(thm)],[1236, 1234])).
% 3.68/2.65 tff(1238,plain,
% 3.68/2.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a603) | c0_1(a603) | c3_1(a603))),
% 3.68/2.65 inference(quant_inst,[status(thm)],[])).
% 3.68/2.65 tff(1239,plain,
% 3.68/2.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 3.68/2.65 tff(1240,plain,
% 3.68/2.65 (c0_1(a603)),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[1239, 96, 712, 711, 710, 1233, 1030, 1221, 1232])).
% 3.68/2.65 tff(1241,plain,
% 3.68/2.65 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1242,plain,
% 3.68/2.65 ((hskp15 | hskp14 | (~ndr1_0) | c1_1(a603) | (~c0_1(a603)) | (~c2_1(a603))) <=> (hskp15 | hskp14 | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1243,plain,
% 3.68/2.65 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a603) | (~c0_1(a603)) | (~c2_1(a603)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603))))),
% 3.68/2.65 inference(monotonicity,[status(thm)],[1242])).
% 3.68/2.65 tff(1244,plain,
% 3.68/2.65 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a603) | (~c0_1(a603)) | (~c2_1(a603)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.68/2.65 inference(transitivity,[status(thm)],[1243, 1241])).
% 3.68/2.65 tff(1245,plain,
% 3.68/2.65 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a603) | (~c0_1(a603)) | (~c2_1(a603)))),
% 3.68/2.65 inference(quant_inst,[status(thm)],[])).
% 3.68/2.65 tff(1246,plain,
% 3.68/2.65 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603))),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 3.68/2.65 tff(1247,plain,
% 3.68/2.65 (~c2_1(a603)),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[1246, 96, 281, 280, 1240, 1233, 250])).
% 3.68/2.65 tff(1248,plain,
% 3.68/2.65 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a617) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a617) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1249,plain,
% 3.68/2.65 ((hskp20 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a617) | (~c2_1(a617)) | (~c3_1(a617))) <=> (hskp20 | c1_1(a617) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1250,plain,
% 3.68/2.65 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a617) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a617)) | (~c3_1(a617))))),
% 3.68/2.65 inference(monotonicity,[status(thm)],[1249])).
% 3.68/2.65 tff(1251,plain,
% 3.68/2.65 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a617) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.65 inference(transitivity,[status(thm)],[1250, 1248])).
% 3.68/2.65 tff(1252,plain,
% 3.68/2.65 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.65 inference(quant_inst,[status(thm)],[])).
% 3.68/2.65 tff(1253,plain,
% 3.68/2.65 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a617) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a617)) | (~c3_1(a617))),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 3.68/2.65 tff(1254,plain,
% 3.68/2.65 (hskp20 | c2_1(a603) | (~c0_1(a603))),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[1253, 96, 712, 711, 710, 1030, 723])).
% 3.68/2.65 tff(1255,plain,
% 3.68/2.65 ($false),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[1254, 1247, 1240, 709])).
% 3.68/2.65 tff(1256,plain,(c1_1(a603) | hskp20 | (~c2_1(a617)) | (~c3_1(a617)) | c1_1(a617) | c3_1(a603) | hskp15 | hskp14), inference(lemma,lemma(discharge,[]))).
% 3.68/2.65 tff(1257,plain,
% 3.68/2.65 (c1_1(a603)),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[1256, 1230, 1044, 1043, 1042, 1030, 281, 280])).
% 3.68/2.65 tff(1258,plain,
% 3.68/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a648) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1259,plain,
% 3.68/2.65 (((~ndr1_0) | c3_1(a603) | (~c1_1(a603)) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648))) <=> (c2_1(a648) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.65 inference(rewrite,[status(thm)],[])).
% 3.68/2.65 tff(1260,plain,
% 3.68/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c1_1(a603)) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a648) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a648)) | (~c3_1(a648))))),
% 3.68/2.65 inference(monotonicity,[status(thm)],[1259])).
% 3.68/2.65 tff(1261,plain,
% 3.68/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c1_1(a603)) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.65 inference(transitivity,[status(thm)],[1260, 1258])).
% 3.68/2.65 tff(1262,plain,
% 3.68/2.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c1_1(a603)) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.65 inference(quant_inst,[status(thm)],[])).
% 3.68/2.65 tff(1263,plain,
% 3.68/2.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a648)) | (~c3_1(a648))),
% 3.68/2.65 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 3.68/2.65 tff(1264,plain,
% 3.68/2.65 ((~c1_1(a603)) | (~c2_1(a603))),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[1263, 96, 882, 881, 1044, 1043, 880, 1030, 1040, 1211])).
% 3.68/2.65 tff(1265,plain,
% 3.68/2.65 (~c2_1(a603)),
% 3.68/2.65 inference(unit_resolution,[status(thm)],[1264, 1257])).
% 3.68/2.65 tff(1266,plain,
% 3.68/2.65 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp45 | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.66 inference(rewrite,[status(thm)],[])).
% 3.68/2.66 tff(1267,plain,
% 3.68/2.66 ((hskp45 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))) <=> (hskp45 | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.66 inference(rewrite,[status(thm)],[])).
% 3.68/2.66 tff(1268,plain,
% 3.68/2.66 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))))),
% 3.68/2.66 inference(monotonicity,[status(thm)],[1267])).
% 3.68/2.66 tff(1269,plain,
% 3.68/2.66 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp45 | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.66 inference(transitivity,[status(thm)],[1268, 1266])).
% 3.68/2.66 tff(1270,plain,
% 3.68/2.66 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.66 inference(quant_inst,[status(thm)],[])).
% 3.68/2.66 tff(1271,plain,
% 3.68/2.66 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp45 | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1270, 1269])).
% 3.68/2.66 tff(1272,plain,
% 3.68/2.66 (hskp45 | (~c1_1(a603)) | c2_1(a603)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1271, 96, 1044, 1043, 1030, 1063, 1211])).
% 3.68/2.66 tff(1273,plain,
% 3.68/2.66 (hskp45),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1272, 1257, 1265])).
% 3.68/2.66 tff(1274,plain,
% 3.68/2.66 (~c0_1(a623)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1089, 1273])).
% 3.68/2.66 tff(1275,plain,
% 3.68/2.66 (c3_1(a623)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1100, 1273])).
% 3.68/2.66 tff(1276,plain,
% 3.68/2.66 (c2_1(a623)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1111, 1273])).
% 3.68/2.66 tff(1277,plain,
% 3.68/2.66 (~hskp9),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1152, 1276, 882, 881, 1275, 880, 1274])).
% 3.68/2.66 tff(1278,plain,
% 3.68/2.66 (hskp16),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1164, 1277, 12])).
% 3.68/2.66 tff(1279,plain,
% 3.68/2.66 (~c3_1(a627)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1170, 1278])).
% 3.68/2.66 tff(1280,plain,
% 3.68/2.66 (c2_1(a627)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1181, 1278])).
% 3.68/2.66 tff(1281,plain,
% 3.68/2.66 (~c1_1(a627)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1188, 96, 882, 881, 1275, 1276, 1280, 880, 1274, 1279, 1040])).
% 3.68/2.66 tff(1282,plain,
% 3.68/2.66 (c0_1(a627)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1199, 1278])).
% 3.68/2.66 tff(1283,plain,
% 3.68/2.66 ($false),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1206, 96, 281, 280, 1280, 1282, 250, 1281])).
% 3.68/2.66 tff(1284,plain,(hskp14 | hskp15 | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | hskp17 | c3_1(a603)), inference(lemma,lemma(discharge,[]))).
% 3.68/2.66 tff(1285,plain,
% 3.68/2.66 (hskp14),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1284, 1030, 882, 881, 880, 12, 281])).
% 3.68/2.66 tff(1286,plain,
% 3.68/2.66 (c3_1(a624)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[217, 1285])).
% 3.68/2.66 tff(1287,plain,
% 3.68/2.66 (~c2_1(a624)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[206, 1285])).
% 3.68/2.66 tff(1288,plain,
% 3.68/2.66 (~c1_1(a624)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[230, 1285])).
% 3.68/2.66 tff(1289,plain,
% 3.68/2.66 (~hskp37),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[829, 698, 712, 710, 757, 756, 769, 711, 709])).
% 3.68/2.66 tff(1290,plain,
% 3.68/2.66 (hskp37 | hskp5 | (~c0_1(a617))),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[589, 96, 712, 711, 581])).
% 3.68/2.66 tff(1291,plain,
% 3.68/2.66 (hskp5),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1290, 1289, 698])).
% 3.68/2.66 tff(1292,plain,
% 3.68/2.66 (~c3_1(a606)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[634, 1291])).
% 3.68/2.66 tff(1293,plain,
% 3.68/2.66 (~c0_1(a606)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[640, 1291])).
% 3.68/2.66 tff(1294,plain,
% 3.68/2.66 (c2_1(a606)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[651, 1291])).
% 3.68/2.66 tff(1295,plain,
% 3.68/2.66 (hskp54),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[836, 96, 1289, 1294, 1293, 1292, 411])).
% 3.68/2.66 tff(1296,plain,
% 3.68/2.66 (~c0_1(a651)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[473, 1295])).
% 3.68/2.66 tff(1297,plain,
% 3.68/2.66 (c2_1(a651)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[484, 1295])).
% 3.68/2.66 tff(1298,plain,
% 3.68/2.66 (c3_1(a651)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[502, 1295])).
% 3.68/2.66 tff(1299,plain,
% 3.68/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a651) | c1_1(a617) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a651) | c1_1(a617) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)))),
% 3.68/2.66 inference(rewrite,[status(thm)],[])).
% 3.68/2.66 tff(1300,plain,
% 3.68/2.66 (((~ndr1_0) | c0_1(a651) | (~c3_1(a651)) | (~c2_1(a651)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624))) <=> (c0_1(a651) | c1_1(a617) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)))),
% 3.68/2.66 inference(rewrite,[status(thm)],[])).
% 3.68/2.66 tff(1301,plain,
% 3.68/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a651) | (~c3_1(a651)) | (~c2_1(a651)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a651) | c1_1(a617) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651))))),
% 3.68/2.66 inference(monotonicity,[status(thm)],[1300])).
% 3.68/2.66 tff(1302,plain,
% 3.68/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a651) | (~c3_1(a651)) | (~c2_1(a651)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a651) | c1_1(a617) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)))),
% 3.68/2.66 inference(transitivity,[status(thm)],[1301, 1299])).
% 3.68/2.66 tff(1303,plain,
% 3.68/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a651) | (~c3_1(a651)) | (~c2_1(a651)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624)))),
% 3.68/2.66 inference(quant_inst,[status(thm)],[])).
% 3.68/2.66 tff(1304,plain,
% 3.68/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a651) | c1_1(a617) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651))),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1303, 1302])).
% 3.68/2.66 tff(1305,plain,
% 3.68/2.66 ($false),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1304, 96, 1298, 1297, 712, 769, 1296, 710, 757, 756, 708, 698])).
% 3.68/2.66 tff(1306,plain,((~c0_1(a617)) | (~c2_1(a617)) | (~c3_1(a624)) | c1_1(a617) | c1_1(a624) | c2_1(a624) | (~c3_1(a617)) | hskp20), inference(lemma,lemma(discharge,[]))).
% 3.68/2.66 tff(1307,plain,
% 3.68/2.66 (~c0_1(a617)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1306, 709, 769, 1042, 757, 756, 1043, 1044])).
% 3.68/2.66 tff(1308,plain,
% 3.68/2.66 (c0_1(a603) | c0_1(a617)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1239, 96, 712, 711, 710, 1233, 1030, 1221])).
% 3.68/2.66 tff(1309,plain,
% 3.68/2.66 (c0_1(a603)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1308, 1025])).
% 3.68/2.66 tff(1310,plain,
% 3.68/2.66 (c2_1(a603)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1254, 1309, 709])).
% 3.68/2.66 tff(1311,plain,
% 3.68/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a624) | c2_1(a624) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a624)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a624) | c2_1(a624) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a624)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.66 inference(rewrite,[status(thm)],[])).
% 3.68/2.66 tff(1312,plain,
% 3.68/2.66 (((~ndr1_0) | c0_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624))) <=> (c1_1(a624) | c2_1(a624) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a624)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.66 inference(rewrite,[status(thm)],[])).
% 3.68/2.66 tff(1313,plain,
% 3.68/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a624) | c2_1(a624) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a624)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))))),
% 3.68/2.66 inference(monotonicity,[status(thm)],[1312])).
% 3.68/2.66 tff(1314,plain,
% 3.68/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a624) | c2_1(a624) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a624)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.66 inference(transitivity,[status(thm)],[1313, 1311])).
% 3.68/2.66 tff(1315,plain,
% 3.68/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624)))),
% 3.68/2.66 inference(quant_inst,[status(thm)],[])).
% 3.68/2.66 tff(1316,plain,
% 3.68/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a624) | c2_1(a624) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a624)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 3.68/2.66 tff(1317,plain,
% 3.68/2.66 ($false),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1316, 96, 712, 711, 769, 1309, 757, 756, 1233, 708, 1310, 1025])).
% 3.68/2.66 tff(1318,plain,(c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c3_1(a624)) | c1_1(a624) | c2_1(a624) | c1_1(a603) | hskp20 | c1_1(a617) | c3_1(a603)), inference(lemma,lemma(discharge,[]))).
% 3.68/2.66 tff(1319,plain,
% 3.68/2.66 (c1_1(a603)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1318, 1307, 1043, 769, 757, 756, 1044, 709, 1042, 1030])).
% 3.68/2.66 tff(1320,plain,
% 3.68/2.66 (~c2_1(a603)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1263, 96, 882, 881, 1044, 1043, 880, 1319, 1030, 1040, 1307])).
% 3.68/2.66 tff(1321,plain,
% 3.68/2.66 (hskp45),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1271, 96, 1044, 1043, 1319, 1030, 1063, 1320, 1307])).
% 3.68/2.66 tff(1322,plain,
% 3.68/2.66 (~c0_1(a623)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1089, 1321])).
% 3.68/2.66 tff(1323,plain,
% 3.68/2.66 (c3_1(a623)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1100, 1321])).
% 3.68/2.66 tff(1324,plain,
% 3.68/2.66 (c2_1(a623)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1111, 1321])).
% 3.68/2.66 tff(1325,plain,
% 3.68/2.66 (~hskp9),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1152, 1324, 882, 881, 1323, 880, 1322])).
% 3.68/2.66 tff(1326,plain,
% 3.68/2.66 (hskp16),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1164, 1325, 12])).
% 3.68/2.66 tff(1327,plain,
% 3.68/2.66 (~c3_1(a627)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1170, 1326])).
% 3.68/2.66 tff(1328,plain,
% 3.68/2.66 (c2_1(a627)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1181, 1326])).
% 3.68/2.66 tff(1329,plain,
% 3.68/2.66 (~c1_1(a627)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1188, 96, 882, 881, 1323, 1324, 1328, 880, 1322, 1327, 1040])).
% 3.68/2.66 tff(1330,plain,
% 3.68/2.66 (hskp20 | c2_1(a603) | (~c0_1(a603))),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1253, 96, 1044, 1043, 1042, 1030, 723])).
% 3.68/2.66 tff(1331,plain,
% 3.68/2.66 (~c0_1(a603)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1330, 1320, 709])).
% 3.68/2.66 tff(1332,plain,
% 3.68/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a603) | c2_1(a648) | c1_1(a624) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c2_1(a648) | c1_1(a624) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.66 inference(rewrite,[status(thm)],[])).
% 3.68/2.66 tff(1333,plain,
% 3.68/2.66 (((~ndr1_0) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a603) | c0_1(a603) | c3_1(a603)) <=> (c0_1(a603) | c2_1(a648) | c1_1(a624) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.66 inference(rewrite,[status(thm)],[])).
% 3.68/2.66 tff(1334,plain,
% 3.68/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a603) | c0_1(a603) | c3_1(a603))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a603) | c2_1(a648) | c1_1(a624) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648))))),
% 3.68/2.66 inference(monotonicity,[status(thm)],[1333])).
% 3.68/2.66 tff(1335,plain,
% 3.68/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a603) | c0_1(a603) | c3_1(a603))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c2_1(a648) | c1_1(a624) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.66 inference(transitivity,[status(thm)],[1334, 1332])).
% 3.68/2.66 tff(1336,plain,
% 3.68/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a603) | c0_1(a603) | c3_1(a603))),
% 3.68/2.66 inference(quant_inst,[status(thm)],[])).
% 3.68/2.66 tff(1337,plain,
% 3.68/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c2_1(a648) | c1_1(a624) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648))),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 3.68/2.66 tff(1338,plain,
% 3.68/2.66 (~c0_1(a624)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1337, 96, 882, 881, 769, 1331, 880, 757, 1030, 997, 1320])).
% 3.68/2.66 tff(1339,plain,
% 3.68/2.66 (^[V: $i, U: $i] : refl((hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 3.68/2.66 inference(bind,[status(th)],[])).
% 3.68/2.66 tff(1340,plain,
% 3.68/2.66 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.68/2.66 inference(quant_intro,[status(thm)],[1339])).
% 3.68/2.66 tff(1341,plain,
% 3.68/2.66 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.68/2.66 inference(rewrite,[status(thm)],[])).
% 3.68/2.66 tff(1342,plain,
% 3.68/2.66 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c1_1(V)) | hskp56) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp56))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp56) <=> (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c1_1(V)) | hskp56) <=> (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 3.68/2.66 inference(bind,[status(th)],[])).
% 3.68/2.66 tff(1343,plain,
% 3.68/2.66 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c1_1(V)) | hskp56) <=> ![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.68/2.66 inference(quant_intro,[status(thm)],[1342])).
% 3.68/2.66 tff(1344,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c1_1(V)) | hskp56)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause306')).
% 3.68/2.66 tff(1345,plain,
% 3.68/2.66 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1344, 1343])).
% 3.68/2.66 tff(1346,plain,
% 3.68/2.66 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1345, 1341])).
% 3.68/2.66 tff(1347,plain,(
% 3.68/2.66 ![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.68/2.66 inference(skolemize,[status(sab)],[1346])).
% 3.68/2.66 tff(1348,plain,
% 3.68/2.66 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1347, 1340])).
% 3.68/2.66 tff(1349,plain,
% 3.68/2.66 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | c1_1(a624) | c2_1(a624) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a624)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c1_1(a624) | c2_1(a624) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a624)))),
% 3.68/2.66 inference(rewrite,[status(thm)],[])).
% 3.68/2.66 tff(1350,plain,
% 3.68/2.66 ((hskp56 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c1_1(a624) | c2_1(a624) | (~c3_1(a624))) <=> (hskp56 | c1_1(a624) | c2_1(a624) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a624)))),
% 3.68/2.66 inference(rewrite,[status(thm)],[])).
% 3.68/2.66 tff(1351,plain,
% 3.68/2.66 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | c1_1(a624) | c2_1(a624) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a624))))),
% 3.68/2.66 inference(monotonicity,[status(thm)],[1350])).
% 3.68/2.66 tff(1352,plain,
% 3.68/2.66 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c1_1(a624) | c2_1(a624) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a624)))),
% 3.68/2.66 inference(transitivity,[status(thm)],[1351, 1349])).
% 3.68/2.66 tff(1353,plain,
% 3.68/2.66 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)))),
% 3.68/2.66 inference(quant_inst,[status(thm)],[])).
% 3.68/2.66 tff(1354,plain,
% 3.68/2.66 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c1_1(a624) | c2_1(a624) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a624))),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1353, 1352])).
% 3.68/2.66 tff(1355,plain,
% 3.68/2.66 (hskp56 | (~c1_1(a603)) | c2_1(a603)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1354, 96, 769, 757, 756, 1030, 1348])).
% 3.68/2.66 tff(1356,plain,
% 3.68/2.66 (hskp56),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1355, 1320, 1319])).
% 3.68/2.66 tff(1357,plain,
% 3.68/2.66 (((~hskp56) | (~c1_1(a658))) <=> ((~hskp56) | (~c1_1(a658)))),
% 3.68/2.66 inference(rewrite,[status(thm)],[])).
% 3.68/2.66 tff(1358,plain,
% 3.68/2.66 (((~c1_1(a658)) | (~hskp56)) <=> ((~hskp56) | (~c1_1(a658)))),
% 3.68/2.66 inference(rewrite,[status(thm)],[])).
% 3.68/2.66 tff(1359,axiom,((~c1_1(a658)) | (~hskp56)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 3.68/2.66 tff(1360,plain,
% 3.68/2.66 ((~hskp56) | (~c1_1(a658))),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 3.68/2.66 tff(1361,plain,
% 3.68/2.66 ((~hskp56) | (~c1_1(a658))),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1360, 1357])).
% 3.68/2.66 tff(1362,plain,
% 3.68/2.66 (~c1_1(a658)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1361, 1356])).
% 3.68/2.66 tff(1363,plain,
% 3.68/2.66 (((~hskp56) | c3_1(a658)) <=> ((~hskp56) | c3_1(a658))),
% 3.68/2.66 inference(rewrite,[status(thm)],[])).
% 3.68/2.66 tff(1364,axiom,((~hskp56) | c3_1(a658)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 3.68/2.66 tff(1365,plain,
% 3.68/2.66 ((~hskp56) | c3_1(a658)),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1364, 1363])).
% 3.68/2.66 tff(1366,plain,
% 3.68/2.66 ((~hskp56) | c3_1(a658)),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1365, 1363])).
% 3.68/2.66 tff(1367,plain,
% 3.68/2.66 ((~hskp56) | c3_1(a658)),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1366, 1363])).
% 3.68/2.66 tff(1368,plain,
% 3.68/2.66 ((~hskp56) | c3_1(a658)),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1367, 1363])).
% 3.68/2.66 tff(1369,plain,
% 3.68/2.66 ((~hskp56) | c3_1(a658)),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1368, 1363])).
% 3.68/2.66 tff(1370,plain,
% 3.68/2.66 ((~hskp56) | c3_1(a658)),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1369, 1363])).
% 3.68/2.66 tff(1371,plain,
% 3.68/2.66 ((~hskp56) | c3_1(a658)),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1370, 1363])).
% 3.68/2.66 tff(1372,plain,
% 3.68/2.66 ((~hskp56) | c3_1(a658)),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1371, 1363])).
% 3.68/2.66 tff(1373,plain,
% 3.68/2.66 (c3_1(a658)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1372, 1356])).
% 3.68/2.66 tff(1374,plain,
% 3.68/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a603) | c1_1(a658) | c2_1(a648) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c1_1(a658) | c2_1(a648) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.66 inference(rewrite,[status(thm)],[])).
% 3.68/2.66 tff(1375,plain,
% 3.68/2.66 (((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c0_1(a658)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a603) | c0_1(a603) | c3_1(a603)) <=> (c0_1(a603) | c1_1(a658) | c2_1(a648) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.66 inference(rewrite,[status(thm)],[])).
% 3.68/2.66 tff(1376,plain,
% 3.68/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c0_1(a658)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a603) | c0_1(a603) | c3_1(a603))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a603) | c1_1(a658) | c2_1(a648) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a648)) | (~c3_1(a648))))),
% 3.68/2.66 inference(monotonicity,[status(thm)],[1375])).
% 3.68/2.66 tff(1377,plain,
% 3.68/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c0_1(a658)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a603) | c0_1(a603) | c3_1(a603))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c1_1(a658) | c2_1(a648) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.68/2.66 inference(transitivity,[status(thm)],[1376, 1374])).
% 3.68/2.66 tff(1378,plain,
% 3.68/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c0_1(a658)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a603) | c0_1(a603) | c3_1(a603))),
% 3.68/2.66 inference(quant_inst,[status(thm)],[])).
% 3.68/2.66 tff(1379,plain,
% 3.68/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c1_1(a658) | c2_1(a648) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a648)) | (~c3_1(a648))),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1378, 1377])).
% 3.68/2.66 tff(1380,plain,
% 3.68/2.66 (~c0_1(a658)),
% 3.68/2.66 inference(unit_resolution,[status(thm)],[1379, 96, 1373, 882, 881, 1331, 1362, 880, 1030, 997, 1320])).
% 3.68/2.66 tff(1381,plain,
% 3.68/2.66 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 3.68/2.66 inference(bind,[status(th)],[])).
% 3.68/2.66 tff(1382,plain,
% 3.68/2.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 3.68/2.66 inference(quant_intro,[status(thm)],[1381])).
% 3.68/2.66 tff(1383,plain,
% 3.68/2.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 3.68/2.66 inference(rewrite,[status(thm)],[])).
% 3.68/2.66 tff(1384,plain,
% 3.68/2.66 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), (((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c0_1(W))), (((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c0_1(W)))), ((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))), ((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), ((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))), (((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 3.68/2.66 inference(bind,[status(th)],[])).
% 3.68/2.66 tff(1385,plain,
% 3.68/2.66 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 3.68/2.66 inference(quant_intro,[status(thm)],[1384])).
% 3.68/2.66 tff(1386,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause320')).
% 3.68/2.66 tff(1387,plain,
% 3.68/2.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 3.68/2.66 tff(1388,plain,
% 3.68/2.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1387, 1383])).
% 3.68/2.66 tff(1389,plain,(
% 3.68/2.66 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 3.68/2.66 inference(skolemize,[status(sab)],[1388])).
% 3.68/2.66 tff(1390,plain,
% 3.68/2.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1389, 1382])).
% 3.68/2.66 tff(1391,plain,
% 3.68/2.66 (((~hskp56) | c2_1(a658)) <=> ((~hskp56) | c2_1(a658))),
% 3.68/2.66 inference(rewrite,[status(thm)],[])).
% 3.68/2.66 tff(1392,axiom,((~hskp56) | c2_1(a658)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 3.68/2.66 tff(1393,plain,
% 3.68/2.66 ((~hskp56) | c2_1(a658)),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 3.68/2.66 tff(1394,plain,
% 3.68/2.66 ((~hskp56) | c2_1(a658)),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1393, 1391])).
% 3.68/2.66 tff(1395,plain,
% 3.68/2.66 ((~hskp56) | c2_1(a658)),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1394, 1391])).
% 3.68/2.66 tff(1396,plain,
% 3.68/2.66 ((~hskp56) | c2_1(a658)),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1395, 1391])).
% 3.68/2.66 tff(1397,plain,
% 3.68/2.66 ((~hskp56) | c2_1(a658)),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1396, 1391])).
% 3.68/2.66 tff(1398,plain,
% 3.68/2.66 ((~hskp56) | c2_1(a658)),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1397, 1391])).
% 3.68/2.66 tff(1399,plain,
% 3.68/2.66 ((~hskp56) | c2_1(a658)),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1398, 1391])).
% 3.68/2.66 tff(1400,plain,
% 3.68/2.66 ((~hskp56) | c2_1(a658)),
% 3.68/2.66 inference(modus_ponens,[status(thm)],[1399, 1391])).
% 3.68/2.67 tff(1401,plain,
% 3.68/2.67 (c2_1(a658)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1400, 1356])).
% 3.68/2.67 tff(1402,plain,
% 3.68/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a658) | c3_1(a627) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | c0_1(a624) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a658) | c3_1(a627) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | c0_1(a624) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1403,plain,
% 3.68/2.67 (((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a624) | c1_1(a624) | c0_1(a624)) <=> (c1_1(a658) | c3_1(a627) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | c0_1(a624) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1404,plain,
% 3.68/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a624) | c1_1(a624) | c0_1(a624))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a658) | c3_1(a627) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | c0_1(a624) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627)))),
% 3.68/2.67 inference(monotonicity,[status(thm)],[1403])).
% 3.68/2.67 tff(1405,plain,
% 3.68/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a624) | c1_1(a624) | c0_1(a624))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a658) | c3_1(a627) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | c0_1(a624) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627))),
% 3.68/2.67 inference(transitivity,[status(thm)],[1404, 1402])).
% 3.68/2.67 tff(1406,plain,
% 3.68/2.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a624) | c1_1(a624) | c0_1(a624))),
% 3.68/2.67 inference(quant_inst,[status(thm)],[])).
% 3.68/2.67 tff(1407,plain,
% 3.68/2.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a658) | c3_1(a627) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | c0_1(a624) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627)),
% 3.68/2.67 inference(modus_ponens,[status(thm)],[1406, 1405])).
% 3.68/2.67 tff(1408,plain,
% 3.68/2.67 ($false),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1407, 96, 1401, 1328, 1362, 1327, 757, 756, 1390, 1380, 1338, 1329])).
% 3.68/2.67 tff(1409,plain,(hskp20 | c1_1(a624) | c2_1(a624) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | (~c3_1(a624)) | c3_1(a603) | hskp17), inference(lemma,lemma(discharge,[]))).
% 3.68/2.67 tff(1410,plain,
% 3.68/2.67 (hskp20),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1409, 1288, 1287, 882, 881, 880, 1286, 1030, 12])).
% 3.68/2.67 tff(1411,plain,
% 3.68/2.67 (~c2_1(a635)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[676, 1410])).
% 3.68/2.67 tff(1412,plain,
% 3.68/2.67 (~c1_1(a635)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[682, 1410])).
% 3.68/2.67 tff(1413,plain,
% 3.68/2.67 (~c3_1(a635)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[670, 1410])).
% 3.68/2.67 tff(1414,plain,
% 3.68/2.67 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1415,plain,
% 3.68/2.67 (((~ndr1_0) | c3_1(a635) | c2_1(a635) | c0_1(a635) | c1_1(a635) | c3_1(a635) | c0_1(a635)) <=> (c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1416,plain,
% 3.68/2.67 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a635) | c2_1(a635) | c0_1(a635) | c1_1(a635) | c3_1(a635) | c0_1(a635))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635)))),
% 3.68/2.67 inference(monotonicity,[status(thm)],[1415])).
% 3.68/2.67 tff(1417,plain,
% 3.68/2.67 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a635) | c2_1(a635) | c0_1(a635) | c1_1(a635) | c3_1(a635) | c0_1(a635))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635))),
% 3.68/2.67 inference(transitivity,[status(thm)],[1416, 1414])).
% 3.68/2.67 tff(1418,plain,
% 3.68/2.67 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a635) | c2_1(a635) | c0_1(a635) | c1_1(a635) | c3_1(a635) | c0_1(a635))),
% 3.68/2.67 inference(quant_inst,[status(thm)],[])).
% 3.68/2.67 tff(1419,plain,
% 3.68/2.67 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635)),
% 3.68/2.67 inference(modus_ponens,[status(thm)],[1418, 1417])).
% 3.68/2.67 tff(1420,plain,
% 3.68/2.67 (c0_1(a635)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1419, 96, 1412, 1411, 1413, 185])).
% 3.68/2.67 tff(1421,plain,
% 3.68/2.67 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a648) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a648)) | (~c1_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a648) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a648)) | (~c1_1(a648)))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1422,plain,
% 3.68/2.67 ((hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648))) <=> (hskp5 | c2_1(a648) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a648)) | (~c1_1(a648)))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1423,plain,
% 3.68/2.67 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a648) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a648)) | (~c1_1(a648))))),
% 3.68/2.67 inference(monotonicity,[status(thm)],[1422])).
% 3.68/2.67 tff(1424,plain,
% 3.68/2.67 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a648) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a648)) | (~c1_1(a648)))),
% 3.68/2.67 inference(transitivity,[status(thm)],[1423, 1421])).
% 3.68/2.67 tff(1425,plain,
% 3.68/2.67 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)))),
% 3.68/2.67 inference(quant_inst,[status(thm)],[])).
% 3.68/2.67 tff(1426,plain,
% 3.68/2.67 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a648) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a648)) | (~c1_1(a648))),
% 3.68/2.67 inference(modus_ponens,[status(thm)],[1425, 1424])).
% 3.68/2.67 tff(1427,plain,
% 3.68/2.67 (~c1_1(a648)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1426, 96, 583, 881, 218, 880, 231, 207, 567])).
% 3.68/2.67 tff(1428,plain,
% 3.68/2.67 ($false),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[605, 440, 451, 583, 201, 429])).
% 3.68/2.67 tff(1429,plain,((~hskp37) | hskp5 | (~hskp14)), inference(lemma,lemma(discharge,[]))).
% 3.68/2.67 tff(1430,plain,
% 3.68/2.67 (~hskp37),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1429, 201, 583])).
% 3.68/2.67 tff(1431,plain,
% 3.68/2.67 (hskp37 | (~c0_1(a617))),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[589, 96, 583, 1051, 1050, 581])).
% 3.68/2.67 tff(1432,plain,
% 3.68/2.67 (~c0_1(a617)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1431, 1430])).
% 3.68/2.67 tff(1433,plain,
% 3.68/2.67 (hskp42 | (~c0_1(a635)) | c0_1(a617)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1069, 96, 1050, 1048, 1046, 1049, 900])).
% 3.68/2.67 tff(1434,plain,
% 3.68/2.67 (hskp42),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1433, 1432, 1045])).
% 3.68/2.67 tff(1435,plain,
% 3.68/2.67 (~c3_1(a618)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1002, 1434])).
% 3.68/2.67 tff(1436,plain,
% 3.68/2.67 (~c2_1(a618)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[923, 1434])).
% 3.68/2.67 tff(1437,plain,
% 3.68/2.67 (c0_1(a618)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1009, 96, 882, 881, 880, 1436, 1435, 997, 1427])).
% 3.68/2.67 tff(1438,plain,
% 3.68/2.67 (c1_1(a618)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[957, 1434])).
% 3.68/2.67 tff(1439,plain,
% 3.68/2.67 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a618) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c1_1(a618)) | (~c0_1(a618)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a618) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c1_1(a618)) | (~c0_1(a618)))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1440,plain,
% 3.68/2.67 ((hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618))) <=> (hskp5 | c2_1(a618) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c1_1(a618)) | (~c0_1(a618)))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1441,plain,
% 3.68/2.67 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a618) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c1_1(a618)) | (~c0_1(a618))))),
% 3.68/2.67 inference(monotonicity,[status(thm)],[1440])).
% 3.68/2.67 tff(1442,plain,
% 3.68/2.67 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a618) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c1_1(a618)) | (~c0_1(a618)))),
% 3.68/2.67 inference(transitivity,[status(thm)],[1441, 1439])).
% 3.68/2.67 tff(1443,plain,
% 3.68/2.67 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618)))),
% 3.68/2.67 inference(quant_inst,[status(thm)],[])).
% 3.68/2.67 tff(1444,plain,
% 3.68/2.67 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a618) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c1_1(a618)) | (~c0_1(a618))),
% 3.68/2.67 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 3.68/2.67 tff(1445,plain,
% 3.68/2.67 ($false),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1444, 96, 583, 1438, 218, 1436, 231, 207, 567, 1437])).
% 3.68/2.67 tff(1446,plain,((~hskp14) | hskp5 | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | (~c0_1(a635)) | c1_1(a635) | c2_1(a635)), inference(lemma,lemma(discharge,[]))).
% 3.68/2.67 tff(1447,plain,
% 3.68/2.67 (hskp5),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1446, 1420, 882, 881, 880, 1285, 1412, 1411])).
% 3.68/2.67 tff(1448,plain,
% 3.68/2.67 (~c3_1(a606)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[634, 1447])).
% 3.68/2.67 tff(1449,plain,
% 3.68/2.67 (c2_1(a606)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[651, 1447])).
% 3.68/2.67 tff(1450,plain,
% 3.68/2.67 (~c0_1(a606)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[640, 1447])).
% 3.68/2.67 tff(1451,plain,
% 3.68/2.67 ($false),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[692, 1450, 1449, 1410, 1448])).
% 3.68/2.67 tff(1452,plain,(c3_1(a603) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | hskp17 | hskp15), inference(lemma,lemma(discharge,[]))).
% 3.68/2.67 tff(1453,plain,
% 3.68/2.67 (c3_1(a603)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1452, 281, 868, 857, 12, 879])).
% 3.68/2.67 tff(1454,plain,
% 3.68/2.67 (((~hskp3) | (~c3_1(a603))) <=> ((~hskp3) | (~c3_1(a603)))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1455,plain,
% 3.68/2.67 (((~c3_1(a603)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a603)))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1456,axiom,((~c3_1(a603)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause271')).
% 3.68/2.67 tff(1457,plain,
% 3.68/2.67 ((~hskp3) | (~c3_1(a603))),
% 3.68/2.67 inference(modus_ponens,[status(thm)],[1456, 1455])).
% 3.68/2.67 tff(1458,plain,
% 3.68/2.67 ((~hskp3) | (~c3_1(a603))),
% 3.68/2.67 inference(modus_ponens,[status(thm)],[1457, 1454])).
% 3.68/2.67 tff(1459,plain,
% 3.68/2.67 (~hskp3),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1458, 1453])).
% 3.68/2.67 tff(1460,plain,
% 3.68/2.67 (~c1_1(a617)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[517, 1012])).
% 3.68/2.67 tff(1461,assumption,(hskp29), introduced(assumption)).
% 3.68/2.67 tff(1462,plain,
% 3.68/2.67 (((~hskp29) | (~c0_1(a660))) <=> ((~hskp29) | (~c0_1(a660)))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1463,plain,
% 3.68/2.67 (((~c0_1(a660)) | (~hskp29)) <=> ((~hskp29) | (~c0_1(a660)))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1464,axiom,((~c0_1(a660)) | (~hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause219')).
% 3.68/2.67 tff(1465,plain,
% 3.68/2.67 ((~hskp29) | (~c0_1(a660))),
% 3.68/2.67 inference(modus_ponens,[status(thm)],[1464, 1463])).
% 3.68/2.67 tff(1466,plain,
% 3.68/2.67 ((~hskp29) | (~c0_1(a660))),
% 3.68/2.67 inference(modus_ponens,[status(thm)],[1465, 1462])).
% 3.68/2.67 tff(1467,plain,
% 3.68/2.67 (~c0_1(a660)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1466, 1461])).
% 3.68/2.67 tff(1468,plain,
% 3.68/2.67 (((~hskp29) | (~c3_1(a660))) <=> ((~hskp29) | (~c3_1(a660)))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1469,plain,
% 3.68/2.67 (((~c3_1(a660)) | (~hskp29)) <=> ((~hskp29) | (~c3_1(a660)))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1470,axiom,((~c3_1(a660)) | (~hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause218')).
% 3.68/2.67 tff(1471,plain,
% 3.68/2.67 ((~hskp29) | (~c3_1(a660))),
% 3.68/2.67 inference(modus_ponens,[status(thm)],[1470, 1469])).
% 3.68/2.67 tff(1472,plain,
% 3.68/2.67 ((~hskp29) | (~c3_1(a660))),
% 3.68/2.67 inference(modus_ponens,[status(thm)],[1471, 1468])).
% 3.68/2.67 tff(1473,plain,
% 3.68/2.67 (~c3_1(a660)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1472, 1461])).
% 3.68/2.67 tff(1474,plain,
% 3.68/2.67 (((~hskp29) | (~c1_1(a660))) <=> ((~hskp29) | (~c1_1(a660)))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1475,plain,
% 3.68/2.67 (((~c1_1(a660)) | (~hskp29)) <=> ((~hskp29) | (~c1_1(a660)))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1476,axiom,((~c1_1(a660)) | (~hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause217')).
% 3.68/2.67 tff(1477,plain,
% 3.68/2.67 ((~hskp29) | (~c1_1(a660))),
% 3.68/2.67 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 3.68/2.67 tff(1478,plain,
% 3.68/2.67 ((~hskp29) | (~c1_1(a660))),
% 3.68/2.67 inference(modus_ponens,[status(thm)],[1477, 1474])).
% 3.68/2.67 tff(1479,plain,
% 3.68/2.67 (~c1_1(a660)),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1478, 1461])).
% 3.68/2.67 tff(1480,plain,
% 3.68/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1481,plain,
% 3.68/2.67 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a660) | c0_1(a660) | c3_1(a660)) <=> (c1_1(a617) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1482,plain,
% 3.68/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a660) | c0_1(a660) | c3_1(a660))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))))),
% 3.68/2.67 inference(monotonicity,[status(thm)],[1481])).
% 3.68/2.67 tff(1483,plain,
% 3.68/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a660) | c0_1(a660) | c3_1(a660))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.68/2.67 inference(transitivity,[status(thm)],[1482, 1480])).
% 3.68/2.67 tff(1484,plain,
% 3.68/2.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a660) | c0_1(a660) | c3_1(a660))),
% 3.68/2.67 inference(quant_inst,[status(thm)],[])).
% 3.68/2.67 tff(1485,plain,
% 3.68/2.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))),
% 3.68/2.67 inference(modus_ponens,[status(thm)],[1484, 1483])).
% 3.68/2.67 tff(1486,plain,
% 3.68/2.67 ($false),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1485, 96, 712, 711, 710, 1479, 1473, 1467, 1221, 1025])).
% 3.68/2.67 tff(1487,plain,((~hskp29) | (~c2_1(a617)) | (~c3_1(a617)) | c1_1(a617) | c0_1(a617)), inference(lemma,lemma(discharge,[]))).
% 3.68/2.67 tff(1488,plain,
% 3.68/2.67 (~hskp29),
% 3.68/2.67 inference(unit_resolution,[status(thm)],[1487, 1025, 1014, 1460, 1013])).
% 3.68/2.67 tff(1489,plain,
% 3.68/2.67 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a675) | (~ndr1_0) | c0_1(a675) | (~c3_1(a675)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a675) | (~ndr1_0) | c0_1(a675) | (~c3_1(a675)))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1490,plain,
% 3.68/2.67 ((hskp29 | hskp3 | (~ndr1_0) | c2_1(a675) | c0_1(a675) | (~c3_1(a675))) <=> (hskp29 | hskp3 | c2_1(a675) | (~ndr1_0) | c0_1(a675) | (~c3_1(a675)))),
% 3.68/2.67 inference(rewrite,[status(thm)],[])).
% 3.68/2.67 tff(1491,plain,
% 3.68/2.67 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a675) | c0_1(a675) | (~c3_1(a675)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a675) | (~ndr1_0) | c0_1(a675) | (~c3_1(a675))))),
% 3.68/2.67 inference(monotonicity,[status(thm)],[1490])).
% 3.68/2.67 tff(1492,plain,
% 3.68/2.67 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a675) | c0_1(a675) | (~c3_1(a675)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a675) | (~ndr1_0) | c0_1(a675) | (~c3_1(a675)))),
% 3.68/2.67 inference(transitivity,[status(thm)],[1491, 1489])).
% 3.68/2.67 tff(1493,plain,
% 3.68/2.67 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a675) | c0_1(a675) | (~c3_1(a675)))),
% 3.76/2.67 inference(quant_inst,[status(thm)],[])).
% 3.76/2.67 tff(1494,plain,
% 3.76/2.67 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a675) | (~ndr1_0) | c0_1(a675) | (~c3_1(a675))),
% 3.76/2.67 inference(modus_ponens,[status(thm)],[1493, 1492])).
% 3.76/2.67 tff(1495,plain,
% 3.76/2.67 (c0_1(a675)),
% 3.76/2.67 inference(unit_resolution,[status(thm)],[1494, 96, 1488, 1459, 1029, 1028, 1024])).
% 3.76/2.67 tff(1496,plain,
% 3.76/2.67 (c1_1(a675)),
% 3.76/2.67 inference(unit_resolution,[status(thm)],[318, 1027])).
% 3.76/2.67 tff(1497,plain,
% 3.76/2.67 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a675)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a675)))),
% 3.76/2.67 inference(rewrite,[status(thm)],[])).
% 3.76/2.67 tff(1498,plain,
% 3.76/2.67 ((hskp6 | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | (~c0_1(a675))) <=> (hskp6 | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a675)))),
% 3.76/2.67 inference(rewrite,[status(thm)],[])).
% 3.76/2.67 tff(1499,plain,
% 3.76/2.67 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | (~c0_1(a675)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a675))))),
% 3.76/2.67 inference(monotonicity,[status(thm)],[1498])).
% 3.76/2.67 tff(1500,plain,
% 3.76/2.67 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | (~c0_1(a675)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a675)))),
% 3.76/2.67 inference(transitivity,[status(thm)],[1499, 1497])).
% 3.76/2.67 tff(1501,plain,
% 3.76/2.67 ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | (~c0_1(a675)))),
% 3.76/2.67 inference(quant_inst,[status(thm)],[])).
% 3.76/2.67 tff(1502,plain,
% 3.76/2.67 ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a675))),
% 3.76/2.67 inference(modus_ponens,[status(thm)],[1501, 1500])).
% 3.76/2.67 tff(1503,plain,
% 3.76/2.67 (hskp6 | (~c0_1(a675))),
% 3.76/2.67 inference(unit_resolution,[status(thm)],[1502, 96, 1496, 1029, 742])).
% 3.76/2.67 tff(1504,plain,
% 3.76/2.67 (hskp6),
% 3.76/2.67 inference(unit_resolution,[status(thm)],[1503, 1495])).
% 3.76/2.67 tff(1505,plain,
% 3.76/2.67 (((~hskp6) | (~c1_1(a609))) <=> ((~hskp6) | (~c1_1(a609)))),
% 3.76/2.67 inference(rewrite,[status(thm)],[])).
% 3.76/2.67 tff(1506,plain,
% 3.76/2.67 (((~c1_1(a609)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a609)))),
% 3.76/2.67 inference(rewrite,[status(thm)],[])).
% 3.76/2.67 tff(1507,axiom,((~c1_1(a609)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause264')).
% 3.76/2.67 tff(1508,plain,
% 3.76/2.67 ((~hskp6) | (~c1_1(a609))),
% 3.76/2.67 inference(modus_ponens,[status(thm)],[1507, 1506])).
% 3.76/2.67 tff(1509,plain,
% 3.76/2.67 ((~hskp6) | (~c1_1(a609))),
% 3.76/2.67 inference(modus_ponens,[status(thm)],[1508, 1505])).
% 3.76/2.67 tff(1510,plain,
% 3.76/2.67 (~c1_1(a609)),
% 3.76/2.67 inference(unit_resolution,[status(thm)],[1509, 1504])).
% 3.76/2.67 tff(1511,plain,
% 3.76/2.67 (~c0_1(a609)),
% 3.76/2.67 inference(unit_resolution,[status(thm)],[754, 1504])).
% 3.76/2.67 tff(1512,plain,
% 3.76/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.76/2.67 inference(rewrite,[status(thm)],[])).
% 3.76/2.67 tff(1513,plain,
% 3.76/2.67 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a609) | c0_1(a609) | c3_1(a609)) <=> (c1_1(a617) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.76/2.67 inference(rewrite,[status(thm)],[])).
% 3.76/2.67 tff(1514,plain,
% 3.76/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a609) | c0_1(a609) | c3_1(a609))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))))),
% 3.76/2.67 inference(monotonicity,[status(thm)],[1513])).
% 3.76/2.67 tff(1515,plain,
% 3.76/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a609) | c0_1(a609) | c3_1(a609))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.76/2.67 inference(transitivity,[status(thm)],[1514, 1512])).
% 3.76/2.67 tff(1516,plain,
% 3.76/2.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a609) | c0_1(a609) | c3_1(a609))),
% 3.76/2.67 inference(quant_inst,[status(thm)],[])).
% 3.76/2.67 tff(1517,plain,
% 3.76/2.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))),
% 3.76/2.67 inference(modus_ponens,[status(thm)],[1516, 1515])).
% 3.76/2.67 tff(1518,plain,
% 3.76/2.67 (c3_1(a609)),
% 3.76/2.67 inference(unit_resolution,[status(thm)],[1517, 96, 1013, 1014, 1460, 1511, 1510, 1221, 1025])).
% 3.76/2.67 tff(1519,plain,
% 3.76/2.67 (c2_1(a609)),
% 3.76/2.67 inference(unit_resolution,[status(thm)],[767, 1504])).
% 3.76/2.67 tff(1520,assumption,(c0_1(a675)), introduced(assumption)).
% 3.76/2.67 tff(1521,assumption,(c3_1(a609)), introduced(assumption)).
% 3.76/2.67 tff(1522,assumption,(~c0_1(a609)), introduced(assumption)).
% 3.76/2.67 tff(1523,assumption,(c2_1(a609)), introduced(assumption)).
% 3.76/2.67 tff(1524,plain,
% 3.76/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a675) | c3_1(a613) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a613)) | (~c2_1(a613)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a675) | c3_1(a613) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a613)) | (~c2_1(a613)))),
% 3.76/2.67 inference(rewrite,[status(thm)],[])).
% 3.76/2.67 tff(1525,plain,
% 3.76/2.67 (((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a675) | (~c0_1(a675)) | (~c3_1(a675))) <=> (c2_1(a675) | c3_1(a613) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a613)) | (~c2_1(a613)))),
% 3.76/2.67 inference(rewrite,[status(thm)],[])).
% 3.76/2.67 tff(1526,plain,
% 3.76/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a675) | (~c0_1(a675)) | (~c3_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a675) | c3_1(a613) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a613)) | (~c2_1(a613))))),
% 3.76/2.67 inference(monotonicity,[status(thm)],[1525])).
% 3.76/2.67 tff(1527,plain,
% 3.76/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a675) | (~c0_1(a675)) | (~c3_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a675) | c3_1(a613) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a613)) | (~c2_1(a613)))),
% 3.76/2.68 inference(transitivity,[status(thm)],[1526, 1524])).
% 3.76/2.68 tff(1528,plain,
% 3.76/2.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a675) | (~c0_1(a675)) | (~c3_1(a675)))),
% 3.76/2.68 inference(quant_inst,[status(thm)],[])).
% 3.76/2.68 tff(1529,plain,
% 3.76/2.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a675) | c3_1(a613) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a613)) | (~c2_1(a613))),
% 3.76/2.68 inference(modus_ponens,[status(thm)],[1528, 1527])).
% 3.76/2.68 tff(1530,plain,
% 3.76/2.68 ($false),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[1529, 96, 360, 1142, 1131, 1523, 337, 1119, 1522, 1040, 1521, 1520])).
% 3.76/2.68 tff(1531,plain,((~hskp9) | (~c3_1(a675)) | (~c2_1(a609)) | c2_1(a675) | c0_1(a609) | (~c3_1(a609)) | (~c0_1(a675))), inference(lemma,lemma(discharge,[]))).
% 3.76/2.68 tff(1532,plain,
% 3.76/2.68 (~hskp9),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[1531, 1029, 1519, 1028, 1511, 1518, 1495])).
% 3.76/2.68 tff(1533,plain,
% 3.76/2.68 (hskp16),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[1164, 1532, 12])).
% 3.76/2.68 tff(1534,plain,
% 3.76/2.68 (c0_1(a627)),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[1199, 1533])).
% 3.76/2.68 tff(1535,plain,
% 3.76/2.68 (c2_1(a627)),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[1181, 1533])).
% 3.76/2.68 tff(1536,plain,
% 3.76/2.68 (c1_1(a627)),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[1206, 96, 281, 280, 1535, 1534, 250])).
% 3.76/2.68 tff(1537,plain,
% 3.76/2.68 (~c3_1(a627)),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[1170, 1533])).
% 3.76/2.68 tff(1538,plain,
% 3.76/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a675) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a675) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)))),
% 3.76/2.68 inference(rewrite,[status(thm)],[])).
% 3.76/2.68 tff(1539,plain,
% 3.76/2.68 (((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a675) | (~c0_1(a675)) | (~c3_1(a675))) <=> (c2_1(a675) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)))),
% 3.76/2.68 inference(rewrite,[status(thm)],[])).
% 3.76/2.68 tff(1540,plain,
% 3.76/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a675) | (~c0_1(a675)) | (~c3_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a675) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627))))),
% 3.76/2.68 inference(monotonicity,[status(thm)],[1539])).
% 3.76/2.68 tff(1541,plain,
% 3.76/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a675) | (~c0_1(a675)) | (~c3_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a675) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)))),
% 3.76/2.68 inference(transitivity,[status(thm)],[1540, 1538])).
% 3.76/2.68 tff(1542,plain,
% 3.76/2.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a675) | (~c0_1(a675)) | (~c3_1(a675)))),
% 3.76/2.68 inference(quant_inst,[status(thm)],[])).
% 3.76/2.68 tff(1543,plain,
% 3.76/2.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a675) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627))),
% 3.76/2.68 inference(modus_ponens,[status(thm)],[1542, 1541])).
% 3.76/2.68 tff(1544,plain,
% 3.76/2.68 ($false),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[1543, 96, 1029, 1535, 1519, 1028, 1537, 1511, 1040, 1518, 1495, 1536])).
% 3.76/2.68 tff(1545,plain,(hskp14 | hskp15 | hskp17 | c0_1(a617) | hskp64), inference(lemma,lemma(discharge,[]))).
% 3.76/2.68 tff(1546,plain,
% 3.76/2.68 (hskp14),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[1545, 1025, 12, 281, 24])).
% 3.76/2.68 tff(1547,plain,
% 3.76/2.68 (~c2_1(a624)),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[206, 1546])).
% 3.76/2.68 tff(1548,plain,
% 3.76/2.68 (c3_1(a624)),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[217, 1546])).
% 3.76/2.68 tff(1549,plain,
% 3.76/2.68 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624)))),
% 3.76/2.68 inference(rewrite,[status(thm)],[])).
% 3.76/2.68 tff(1550,plain,
% 3.76/2.68 ((hskp29 | hskp3 | (~ndr1_0) | c2_1(a624) | c0_1(a624) | (~c3_1(a624))) <=> (hskp29 | hskp3 | c2_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624)))),
% 3.76/2.68 inference(rewrite,[status(thm)],[])).
% 3.76/2.68 tff(1551,plain,
% 3.76/2.68 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a624) | c0_1(a624) | (~c3_1(a624)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624))))),
% 3.76/2.68 inference(monotonicity,[status(thm)],[1550])).
% 3.76/2.68 tff(1552,plain,
% 3.76/2.68 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a624) | c0_1(a624) | (~c3_1(a624)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624)))),
% 3.76/2.68 inference(transitivity,[status(thm)],[1551, 1549])).
% 3.76/2.68 tff(1553,plain,
% 3.76/2.68 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a624) | c0_1(a624) | (~c3_1(a624)))),
% 3.76/2.68 inference(quant_inst,[status(thm)],[])).
% 3.76/2.68 tff(1554,plain,
% 3.76/2.68 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624))),
% 3.76/2.68 inference(modus_ponens,[status(thm)],[1553, 1552])).
% 3.76/2.68 tff(1555,plain,
% 3.76/2.68 (c0_1(a624)),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[1554, 96, 1488, 1459, 1548, 1547, 1024])).
% 3.76/2.68 tff(1556,plain,
% 3.76/2.68 (~c1_1(a624)),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[230, 1546])).
% 3.76/2.68 tff(1557,plain,
% 3.76/2.68 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))))),
% 3.76/2.68 inference(bind,[status(th)],[])).
% 3.76/2.68 tff(1558,plain,
% 3.76/2.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 3.76/2.68 inference(quant_intro,[status(thm)],[1557])).
% 3.76/2.68 tff(1559,plain,
% 3.76/2.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 3.76/2.68 inference(rewrite,[status(thm)],[])).
% 3.76/2.68 tff(1560,plain,
% 3.76/2.68 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))))),
% 3.76/2.68 inference(bind,[status(th)],[])).
% 3.76/2.68 tff(1561,plain,
% 3.76/2.68 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 3.76/2.68 inference(quant_intro,[status(thm)],[1560])).
% 3.76/2.68 tff(1562,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause326')).
% 3.76/2.68 tff(1563,plain,
% 3.76/2.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 3.76/2.68 inference(modus_ponens,[status(thm)],[1562, 1561])).
% 3.76/2.68 tff(1564,plain,
% 3.76/2.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 3.76/2.68 inference(modus_ponens,[status(thm)],[1563, 1559])).
% 3.76/2.68 tff(1565,plain,(
% 3.76/2.68 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 3.76/2.68 inference(skolemize,[status(sab)],[1564])).
% 3.76/2.68 tff(1566,plain,
% 3.76/2.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 3.76/2.68 inference(modus_ponens,[status(thm)],[1565, 1558])).
% 3.76/2.68 tff(1567,assumption,(hskp57), introduced(assumption)).
% 3.76/2.68 tff(1568,plain,
% 3.76/2.68 (~c0_1(a662)),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[798, 1567])).
% 3.76/2.68 tff(1569,plain,
% 3.76/2.68 (c2_1(a662)),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[809, 1567])).
% 3.76/2.68 tff(1570,plain,
% 3.76/2.68 (c1_1(a662)),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[820, 1567])).
% 3.76/2.68 tff(1571,plain,
% 3.76/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a662) | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c2_1(a662)) | (~c1_1(a662)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a662) | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c2_1(a662)) | (~c1_1(a662)))),
% 3.76/2.68 inference(rewrite,[status(thm)],[])).
% 3.76/2.68 tff(1572,plain,
% 3.76/2.68 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c0_1(a662) | (~c1_1(a662)) | (~c2_1(a662))) <=> (c0_1(a662) | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c2_1(a662)) | (~c1_1(a662)))),
% 3.76/2.68 inference(rewrite,[status(thm)],[])).
% 3.76/2.68 tff(1573,plain,
% 3.76/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c0_1(a662) | (~c1_1(a662)) | (~c2_1(a662)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a662) | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c2_1(a662)) | (~c1_1(a662))))),
% 3.76/2.68 inference(monotonicity,[status(thm)],[1572])).
% 3.76/2.68 tff(1574,plain,
% 3.76/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c0_1(a662) | (~c1_1(a662)) | (~c2_1(a662)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a662) | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c2_1(a662)) | (~c1_1(a662)))),
% 3.76/2.68 inference(transitivity,[status(thm)],[1573, 1571])).
% 3.76/2.68 tff(1575,plain,
% 3.76/2.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c0_1(a662) | (~c1_1(a662)) | (~c2_1(a662)))),
% 3.76/2.68 inference(quant_inst,[status(thm)],[])).
% 3.76/2.68 tff(1576,plain,
% 3.76/2.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a662) | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c2_1(a662)) | (~c1_1(a662))),
% 3.76/2.68 inference(modus_ponens,[status(thm)],[1575, 1574])).
% 3.76/2.68 tff(1577,plain,
% 3.76/2.68 ($false),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[1576, 96, 1570, 1569, 712, 711, 1568, 710, 1566, 1025])).
% 3.76/2.68 tff(1578,plain,((~hskp57) | (~c2_1(a617)) | (~c3_1(a617)) | c1_1(a617) | c0_1(a617)), inference(lemma,lemma(discharge,[]))).
% 3.76/2.68 tff(1579,plain,
% 3.76/2.68 (~hskp57),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[1578, 1025, 1014, 1460, 1013])).
% 3.76/2.68 tff(1580,plain,
% 3.76/2.68 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648)))),
% 3.76/2.68 inference(rewrite,[status(thm)],[])).
% 3.76/2.68 tff(1581,plain,
% 3.76/2.68 ((hskp57 | (~ndr1_0) | (~c3_1(a648)) | (~c1_1(a648)) | (~c0_1(a648)) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624))) <=> (hskp57 | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648)))),
% 3.76/2.68 inference(rewrite,[status(thm)],[])).
% 3.76/2.68 tff(1582,plain,
% 3.76/2.68 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c3_1(a648)) | (~c1_1(a648)) | (~c0_1(a648)) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648))))),
% 3.76/2.68 inference(monotonicity,[status(thm)],[1581])).
% 3.76/2.68 tff(1583,plain,
% 3.76/2.68 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c3_1(a648)) | (~c1_1(a648)) | (~c0_1(a648)) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648)))),
% 3.76/2.68 inference(transitivity,[status(thm)],[1582, 1580])).
% 3.76/2.68 tff(1584,plain,
% 3.76/2.68 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c3_1(a648)) | (~c1_1(a648)) | (~c0_1(a648)) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)))),
% 3.76/2.68 inference(quant_inst,[status(thm)],[])).
% 3.76/2.68 tff(1585,plain,
% 3.76/2.68 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648))),
% 3.76/2.68 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 3.76/2.68 tff(1586,plain,
% 3.76/2.68 (~c1_1(a648)),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[1585, 96, 1579, 879, 868, 1548, 1556, 786, 1555])).
% 3.76/2.68 tff(1587,plain,
% 3.76/2.68 (((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | c1_1(a617) | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp55 | c1_1(a617) | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | c0_1(a617) | (~c3_1(a617)))),
% 3.76/2.68 inference(rewrite,[status(thm)],[])).
% 3.76/2.68 tff(1588,plain,
% 3.76/2.68 ((hskp55 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624))) <=> (hskp55 | c1_1(a617) | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | c0_1(a617) | (~c3_1(a617)))),
% 3.76/2.68 inference(rewrite,[status(thm)],[])).
% 3.76/2.68 tff(1589,plain,
% 3.76/2.68 (((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)))) <=> ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | c1_1(a617) | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | c0_1(a617) | (~c3_1(a617))))),
% 3.76/2.68 inference(monotonicity,[status(thm)],[1588])).
% 3.76/2.68 tff(1590,plain,
% 3.76/2.68 (((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)))) <=> ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp55 | c1_1(a617) | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | c0_1(a617) | (~c3_1(a617)))),
% 3.76/2.68 inference(transitivity,[status(thm)],[1589, 1587])).
% 3.76/2.68 tff(1591,plain,
% 3.76/2.68 ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)))),
% 3.76/2.68 inference(quant_inst,[status(thm)],[])).
% 3.76/2.68 tff(1592,plain,
% 3.76/2.68 ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp55 | c1_1(a617) | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | c0_1(a617) | (~c3_1(a617))),
% 3.76/2.68 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 3.76/2.68 tff(1593,plain,
% 3.76/2.68 (hskp55),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[1592, 96, 1014, 1548, 1460, 1556, 934, 1025, 1555])).
% 3.76/2.68 tff(1594,plain,
% 3.76/2.68 (c1_1(a653)),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[968, 1593])).
% 3.76/2.68 tff(1595,plain,
% 3.76/2.68 (c3_1(a653)),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[979, 1593])).
% 3.76/2.68 tff(1596,plain,
% 3.76/2.68 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c0_1(a653)) | (~c3_1(a653)) | (~c1_1(a653)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c0_1(a653)) | (~c3_1(a653)) | (~c1_1(a653)))),
% 3.76/2.68 inference(rewrite,[status(thm)],[])).
% 3.76/2.68 tff(1597,plain,
% 3.76/2.68 ((hskp57 | (~ndr1_0) | (~c3_1(a653)) | (~c1_1(a653)) | (~c0_1(a653)) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648))) <=> (hskp57 | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c0_1(a653)) | (~c3_1(a653)) | (~c1_1(a653)))),
% 3.76/2.68 inference(rewrite,[status(thm)],[])).
% 3.76/2.68 tff(1598,plain,
% 3.76/2.68 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c3_1(a653)) | (~c1_1(a653)) | (~c0_1(a653)) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c0_1(a653)) | (~c3_1(a653)) | (~c1_1(a653))))),
% 3.76/2.68 inference(monotonicity,[status(thm)],[1597])).
% 3.76/2.68 tff(1599,plain,
% 3.76/2.68 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c3_1(a653)) | (~c1_1(a653)) | (~c0_1(a653)) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c0_1(a653)) | (~c3_1(a653)) | (~c1_1(a653)))),
% 3.76/2.68 inference(transitivity,[status(thm)],[1598, 1596])).
% 3.76/2.68 tff(1600,plain,
% 3.76/2.68 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c3_1(a653)) | (~c1_1(a653)) | (~c0_1(a653)) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)))),
% 3.76/2.68 inference(quant_inst,[status(thm)],[])).
% 3.76/2.68 tff(1601,plain,
% 3.76/2.68 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c0_1(a653)) | (~c3_1(a653)) | (~c1_1(a653))),
% 3.76/2.68 inference(modus_ponens,[status(thm)],[1600, 1599])).
% 3.76/2.68 tff(1602,plain,
% 3.76/2.68 (~c0_1(a653)),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[1601, 96, 1579, 1595, 1594, 879, 868, 786, 1586])).
% 3.76/2.68 tff(1603,plain,
% 3.76/2.68 (~c2_1(a653)),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[946, 1593])).
% 3.76/2.68 tff(1604,plain,
% 3.76/2.68 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a653) | (~ndr1_0) | c0_1(a653) | (~c3_1(a653)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a653) | (~ndr1_0) | c0_1(a653) | (~c3_1(a653)))),
% 3.76/2.68 inference(rewrite,[status(thm)],[])).
% 3.76/2.68 tff(1605,plain,
% 3.76/2.68 ((hskp29 | hskp3 | (~ndr1_0) | c2_1(a653) | c0_1(a653) | (~c3_1(a653))) <=> (hskp29 | hskp3 | c2_1(a653) | (~ndr1_0) | c0_1(a653) | (~c3_1(a653)))),
% 3.76/2.68 inference(rewrite,[status(thm)],[])).
% 3.76/2.68 tff(1606,plain,
% 3.76/2.68 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a653) | c0_1(a653) | (~c3_1(a653)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a653) | (~ndr1_0) | c0_1(a653) | (~c3_1(a653))))),
% 3.76/2.68 inference(monotonicity,[status(thm)],[1605])).
% 3.76/2.68 tff(1607,plain,
% 3.76/2.68 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a653) | c0_1(a653) | (~c3_1(a653)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a653) | (~ndr1_0) | c0_1(a653) | (~c3_1(a653)))),
% 3.76/2.68 inference(transitivity,[status(thm)],[1606, 1604])).
% 3.76/2.68 tff(1608,plain,
% 3.76/2.68 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a653) | c0_1(a653) | (~c3_1(a653)))),
% 3.76/2.68 inference(quant_inst,[status(thm)],[])).
% 3.76/2.68 tff(1609,plain,
% 3.76/2.68 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a653) | (~ndr1_0) | c0_1(a653) | (~c3_1(a653))),
% 3.76/2.68 inference(modus_ponens,[status(thm)],[1608, 1607])).
% 3.76/2.68 tff(1610,plain,
% 3.76/2.68 ($false),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[1609, 96, 1488, 1459, 1595, 1603, 1024, 1602])).
% 3.76/2.68 tff(1611,plain,(c0_1(a617) | hskp17 | hskp15 | hskp64), inference(lemma,lemma(discharge,[]))).
% 3.76/2.68 tff(1612,plain,
% 3.76/2.68 (c0_1(a617)),
% 3.76/2.68 inference(unit_resolution,[status(thm)],[1611, 281, 12, 24])).
% 3.76/2.69 tff(1613,plain,
% 3.76/2.69 (hskp15 | hskp14 | (~c0_1(a617))),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[612, 96, 1013, 1460, 250])).
% 3.76/2.69 tff(1614,plain,
% 3.76/2.69 (hskp14),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1613, 1612, 281])).
% 3.76/2.69 tff(1615,plain,
% 3.76/2.69 (~c2_1(a624)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[206, 1614])).
% 3.76/2.69 tff(1616,plain,
% 3.76/2.69 (~c1_1(a624)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[230, 1614])).
% 3.76/2.69 tff(1617,plain,
% 3.76/2.69 (c3_1(a624)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[217, 1614])).
% 3.76/2.69 tff(1618,plain,
% 3.76/2.69 (hskp20),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1306, 1617, 1612, 1460, 1616, 1615, 1014, 1013])).
% 3.76/2.69 tff(1619,plain,
% 3.76/2.69 (~c2_1(a635)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[676, 1618])).
% 3.76/2.69 tff(1620,plain,
% 3.76/2.69 (~c1_1(a635)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[682, 1618])).
% 3.76/2.69 tff(1621,plain,
% 3.76/2.69 (~c3_1(a635)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[670, 1618])).
% 3.76/2.69 tff(1622,plain,
% 3.76/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a648) | c1_1(a617) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a648) | c1_1(a617) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1623,plain,
% 3.76/2.69 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a635) | c0_1(a635) | c3_1(a635)) <=> (c2_1(a648) | c1_1(a617) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1624,plain,
% 3.76/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a635) | c0_1(a635) | c3_1(a635))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a648) | c1_1(a617) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648))))),
% 3.76/2.69 inference(monotonicity,[status(thm)],[1623])).
% 3.76/2.69 tff(1625,plain,
% 3.76/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a635) | c0_1(a635) | c3_1(a635))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a648) | c1_1(a617) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.76/2.69 inference(transitivity,[status(thm)],[1624, 1622])).
% 3.76/2.69 tff(1626,plain,
% 3.76/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a635) | c0_1(a635) | c3_1(a635))),
% 3.76/2.69 inference(quant_inst,[status(thm)],[])).
% 3.76/2.69 tff(1627,plain,
% 3.76/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a648) | c1_1(a617) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648))),
% 3.76/2.69 inference(modus_ponens,[status(thm)],[1626, 1625])).
% 3.76/2.69 tff(1628,plain,
% 3.76/2.69 (c0_1(a635)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1627, 96, 879, 868, 1014, 857, 1460, 1619, 1621, 997, 1612])).
% 3.76/2.69 tff(1629,plain,
% 3.76/2.69 (hskp5),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1446, 1628, 879, 868, 857, 1614, 1620, 1619])).
% 3.76/2.69 tff(1630,plain,
% 3.76/2.69 (~c3_1(a606)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[634, 1629])).
% 3.76/2.69 tff(1631,plain,
% 3.76/2.69 (c2_1(a606)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[651, 1629])).
% 3.76/2.69 tff(1632,plain,
% 3.76/2.69 (~c0_1(a606)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[640, 1629])).
% 3.76/2.69 tff(1633,plain,
% 3.76/2.69 ($false),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[692, 1632, 1631, 1618, 1630])).
% 3.76/2.69 tff(1634,plain,(hskp15 | hskp17 | hskp64), inference(lemma,lemma(discharge,[]))).
% 3.76/2.69 tff(1635,plain,
% 3.76/2.69 (hskp15),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1634, 24, 12])).
% 3.76/2.69 tff(1636,plain,
% 3.76/2.69 (~c0_1(a625)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[161, 1635])).
% 3.76/2.69 tff(1637,plain,
% 3.76/2.69 (~c1_1(a625)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[167, 1635])).
% 3.76/2.69 tff(1638,plain,
% 3.76/2.69 (~c2_1(a625)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[190, 1635])).
% 3.76/2.69 tff(1639,assumption,(~c0_1(a625)), introduced(assumption)).
% 3.76/2.69 tff(1640,assumption,(~c1_1(a625)), introduced(assumption)).
% 3.76/2.69 tff(1641,plain,
% 3.76/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1642,plain,
% 3.76/2.69 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a625) | c0_1(a625) | c3_1(a625)) <=> (c1_1(a617) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1643,plain,
% 3.76/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a625) | c0_1(a625) | c3_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))))),
% 3.76/2.69 inference(monotonicity,[status(thm)],[1642])).
% 3.76/2.69 tff(1644,plain,
% 3.76/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a625) | c0_1(a625) | c3_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.76/2.69 inference(transitivity,[status(thm)],[1643, 1641])).
% 3.76/2.69 tff(1645,plain,
% 3.76/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a625) | c0_1(a625) | c3_1(a625))),
% 3.76/2.69 inference(quant_inst,[status(thm)],[])).
% 3.76/2.69 tff(1646,plain,
% 3.76/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))),
% 3.76/2.69 inference(modus_ponens,[status(thm)],[1645, 1644])).
% 3.76/2.69 tff(1647,plain,
% 3.76/2.69 (c3_1(a625) | c0_1(a617)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1646, 96, 1044, 1043, 1042, 1640, 1639, 1221])).
% 3.76/2.69 tff(1648,plain,
% 3.76/2.69 (c3_1(a625)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1647, 1025])).
% 3.76/2.69 tff(1649,plain,
% 3.76/2.69 (~hskp29),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1487, 1025, 1043, 1042, 1044])).
% 3.76/2.69 tff(1650,assumption,(~c2_1(a625)), introduced(assumption)).
% 3.76/2.69 tff(1651,plain,
% 3.76/2.69 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1652,plain,
% 3.76/2.69 ((hskp29 | hskp3 | (~ndr1_0) | c2_1(a625) | c0_1(a625) | (~c3_1(a625))) <=> (hskp29 | hskp3 | c2_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1653,plain,
% 3.76/2.69 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625))))),
% 3.76/2.69 inference(monotonicity,[status(thm)],[1652])).
% 3.76/2.69 tff(1654,plain,
% 3.76/2.69 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)))),
% 3.76/2.69 inference(transitivity,[status(thm)],[1653, 1651])).
% 3.76/2.69 tff(1655,plain,
% 3.76/2.69 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a625) | c0_1(a625) | (~c3_1(a625)))),
% 3.76/2.69 inference(quant_inst,[status(thm)],[])).
% 3.76/2.69 tff(1656,plain,
% 3.76/2.69 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625))),
% 3.76/2.69 inference(modus_ponens,[status(thm)],[1655, 1654])).
% 3.76/2.69 tff(1657,plain,
% 3.76/2.69 (hskp29 | hskp3 | (~c3_1(a625))),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1656, 96, 1650, 1639, 1024])).
% 3.76/2.69 tff(1658,plain,
% 3.76/2.69 (hskp3),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1657, 1649, 1648])).
% 3.76/2.69 tff(1659,plain,
% 3.76/2.69 (~c3_1(a603)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1458, 1658])).
% 3.76/2.69 tff(1660,plain,
% 3.76/2.69 (((~hskp3) | (~c1_1(a603))) <=> ((~hskp3) | (~c1_1(a603)))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1661,plain,
% 3.76/2.69 (((~c1_1(a603)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a603)))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1662,axiom,((~c1_1(a603)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause270')).
% 3.76/2.69 tff(1663,plain,
% 3.76/2.69 ((~hskp3) | (~c1_1(a603))),
% 3.76/2.69 inference(modus_ponens,[status(thm)],[1662, 1661])).
% 3.76/2.69 tff(1664,plain,
% 3.76/2.69 ((~hskp3) | (~c1_1(a603))),
% 3.76/2.69 inference(modus_ponens,[status(thm)],[1663, 1660])).
% 3.76/2.69 tff(1665,plain,
% 3.76/2.69 (~c1_1(a603)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1664, 1658])).
% 3.76/2.69 tff(1666,plain,
% 3.76/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a617) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a617) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1667,plain,
% 3.76/2.69 (((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c2_1(a625) | c1_1(a625) | c0_1(a625)) <=> (c1_1(a617) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1668,plain,
% 3.76/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c2_1(a625) | c1_1(a625) | c0_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a617) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617))))),
% 3.76/2.69 inference(monotonicity,[status(thm)],[1667])).
% 3.76/2.69 tff(1669,plain,
% 3.76/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c2_1(a625) | c1_1(a625) | c0_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a617) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)))),
% 3.76/2.69 inference(transitivity,[status(thm)],[1668, 1666])).
% 3.76/2.69 tff(1670,plain,
% 3.76/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c2_1(a625) | c1_1(a625) | c0_1(a625))),
% 3.76/2.69 inference(quant_inst,[status(thm)],[])).
% 3.76/2.69 tff(1671,plain,
% 3.76/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a617) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617))),
% 3.76/2.69 inference(modus_ponens,[status(thm)],[1670, 1669])).
% 3.76/2.69 tff(1672,plain,
% 3.76/2.69 (~c2_1(a603)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1671, 96, 1044, 1042, 1650, 1640, 1639, 1665, 1659, 1390, 1025])).
% 3.76/2.69 tff(1673,plain,
% 3.76/2.69 (((~hskp3) | c0_1(a603)) <=> ((~hskp3) | c0_1(a603))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1674,axiom,((~hskp3) | c0_1(a603)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 3.76/2.69 tff(1675,plain,
% 3.76/2.69 ((~hskp3) | c0_1(a603)),
% 3.76/2.69 inference(modus_ponens,[status(thm)],[1674, 1673])).
% 3.76/2.69 tff(1676,plain,
% 3.76/2.69 ((~hskp3) | c0_1(a603)),
% 3.76/2.69 inference(modus_ponens,[status(thm)],[1675, 1673])).
% 3.76/2.69 tff(1677,plain,
% 3.76/2.69 ((~hskp3) | c0_1(a603)),
% 3.76/2.69 inference(modus_ponens,[status(thm)],[1676, 1673])).
% 3.76/2.69 tff(1678,plain,
% 3.76/2.69 ((~hskp3) | c0_1(a603)),
% 3.76/2.69 inference(modus_ponens,[status(thm)],[1677, 1673])).
% 3.76/2.69 tff(1679,plain,
% 3.76/2.69 ((~hskp3) | c0_1(a603)),
% 3.76/2.69 inference(modus_ponens,[status(thm)],[1678, 1673])).
% 3.76/2.69 tff(1680,plain,
% 3.76/2.69 ((~hskp3) | c0_1(a603)),
% 3.76/2.69 inference(modus_ponens,[status(thm)],[1679, 1673])).
% 3.76/2.69 tff(1681,plain,
% 3.76/2.69 ((~hskp3) | c0_1(a603)),
% 3.76/2.69 inference(modus_ponens,[status(thm)],[1680, 1673])).
% 3.76/2.69 tff(1682,plain,
% 3.76/2.69 ((~hskp3) | c0_1(a603)),
% 3.76/2.69 inference(modus_ponens,[status(thm)],[1681, 1673])).
% 3.76/2.69 tff(1683,plain,
% 3.76/2.69 (c0_1(a603)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1682, 1658])).
% 3.76/2.69 tff(1684,plain,
% 3.76/2.69 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a617) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a617) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a617) | (~c3_1(a617)))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1685,plain,
% 3.76/2.69 ((hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617))) <=> (hskp42 | c1_1(a617) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a617) | (~c3_1(a617)))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1686,plain,
% 3.76/2.69 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a617) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a617) | (~c3_1(a617))))),
% 3.76/2.69 inference(monotonicity,[status(thm)],[1685])).
% 3.76/2.69 tff(1687,plain,
% 3.76/2.69 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a617) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a617) | (~c3_1(a617)))),
% 3.76/2.69 inference(transitivity,[status(thm)],[1686, 1684])).
% 3.76/2.69 tff(1688,plain,
% 3.76/2.69 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))),
% 3.76/2.69 inference(quant_inst,[status(thm)],[])).
% 3.76/2.69 tff(1689,plain,
% 3.76/2.69 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a617) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a617) | (~c3_1(a617))),
% 3.76/2.69 inference(modus_ponens,[status(thm)],[1688, 1687])).
% 3.76/2.69 tff(1690,plain,
% 3.76/2.69 (hskp42),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1689, 96, 1043, 1683, 1042, 1665, 900, 1672, 1025])).
% 3.76/2.69 tff(1691,plain,
% 3.76/2.69 (~c3_1(a618)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1002, 1690])).
% 3.76/2.69 tff(1692,plain,
% 3.76/2.69 (~c2_1(a618)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[923, 1690])).
% 3.76/2.69 tff(1693,plain,
% 3.76/2.69 (c1_1(a618)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[957, 1690])).
% 3.76/2.69 tff(1694,plain,
% 3.76/2.69 (hskp45),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1081, 96, 1693, 1044, 1043, 1692, 1691, 1063, 1025])).
% 3.76/2.69 tff(1695,plain,
% 3.76/2.69 (~c0_1(a623)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1089, 1694])).
% 3.76/2.69 tff(1696,plain,
% 3.76/2.69 (c3_1(a623)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1100, 1694])).
% 3.76/2.69 tff(1697,plain,
% 3.76/2.69 (c2_1(a623)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1111, 1694])).
% 3.76/2.69 tff(1698,plain,
% 3.76/2.69 (~hskp9),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1152, 1697, 882, 881, 1696, 880, 1695])).
% 3.76/2.69 tff(1699,plain,
% 3.76/2.69 (hskp16),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1164, 1698, 12])).
% 3.76/2.69 tff(1700,plain,
% 3.76/2.69 (~c3_1(a627)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1170, 1699])).
% 3.76/2.69 tff(1701,plain,
% 3.76/2.69 (c2_1(a627)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1181, 1699])).
% 3.76/2.69 tff(1702,plain,
% 3.76/2.69 (~c1_1(a627)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1188, 96, 882, 881, 1696, 1697, 1701, 880, 1695, 1700, 1040])).
% 3.76/2.69 tff(1703,plain,
% 3.76/2.69 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c1_1(a618)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c1_1(a618)))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1704,plain,
% 3.76/2.69 ((hskp56 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c1_1(a625) | c2_1(a625) | (~c3_1(a625))) <=> (hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c1_1(a618)))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1705,plain,
% 3.76/2.69 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c1_1(a618))))),
% 3.76/2.69 inference(monotonicity,[status(thm)],[1704])).
% 3.76/2.69 tff(1706,plain,
% 3.76/2.69 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c1_1(a618)))),
% 3.76/2.69 inference(transitivity,[status(thm)],[1705, 1703])).
% 3.76/2.69 tff(1707,plain,
% 3.76/2.69 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)))),
% 3.76/2.69 inference(quant_inst,[status(thm)],[])).
% 3.76/2.69 tff(1708,plain,
% 3.76/2.69 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c1_1(a618))),
% 3.76/2.69 inference(modus_ponens,[status(thm)],[1707, 1706])).
% 3.76/2.69 tff(1709,plain,
% 3.76/2.69 (hskp56),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1708, 96, 1693, 1692, 1691, 1650, 1640, 1348, 1648])).
% 3.76/2.69 tff(1710,plain,
% 3.76/2.69 (~c1_1(a658)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1361, 1709])).
% 3.76/2.69 tff(1711,plain,
% 3.76/2.69 (c2_1(a658)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1400, 1709])).
% 3.76/2.69 tff(1712,plain,
% 3.76/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a658) | c0_1(a623) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a658)) | (~c2_1(a658)) | (~c2_1(a623)) | (~c3_1(a623)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a658) | c0_1(a623) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a658)) | (~c2_1(a658)) | (~c2_1(a623)) | (~c3_1(a623)))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1713,plain,
% 3.76/2.69 (((~ndr1_0) | c0_1(a623) | (~c3_1(a623)) | (~c2_1(a623)) | c1_1(a658) | (~c2_1(a658)) | (~c0_1(a658)) | c2_1(a625) | c1_1(a625) | (~c3_1(a625))) <=> (c1_1(a658) | c0_1(a623) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a658)) | (~c2_1(a658)) | (~c2_1(a623)) | (~c3_1(a623)))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1714,plain,
% 3.76/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a623) | (~c3_1(a623)) | (~c2_1(a623)) | c1_1(a658) | (~c2_1(a658)) | (~c0_1(a658)) | c2_1(a625) | c1_1(a625) | (~c3_1(a625)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a658) | c0_1(a623) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a658)) | (~c2_1(a658)) | (~c2_1(a623)) | (~c3_1(a623))))),
% 3.76/2.69 inference(monotonicity,[status(thm)],[1713])).
% 3.76/2.69 tff(1715,plain,
% 3.76/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a623) | (~c3_1(a623)) | (~c2_1(a623)) | c1_1(a658) | (~c2_1(a658)) | (~c0_1(a658)) | c2_1(a625) | c1_1(a625) | (~c3_1(a625)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a658) | c0_1(a623) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a658)) | (~c2_1(a658)) | (~c2_1(a623)) | (~c3_1(a623)))),
% 3.76/2.69 inference(transitivity,[status(thm)],[1714, 1712])).
% 3.76/2.69 tff(1716,plain,
% 3.76/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a623) | (~c3_1(a623)) | (~c2_1(a623)) | c1_1(a658) | (~c2_1(a658)) | (~c0_1(a658)) | c2_1(a625) | c1_1(a625) | (~c3_1(a625)))),
% 3.76/2.69 inference(quant_inst,[status(thm)],[])).
% 3.76/2.69 tff(1717,plain,
% 3.76/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a658) | c0_1(a623) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a658)) | (~c2_1(a658)) | (~c2_1(a623)) | (~c3_1(a623))),
% 3.76/2.69 inference(modus_ponens,[status(thm)],[1716, 1715])).
% 3.76/2.69 tff(1718,plain,
% 3.76/2.69 (~c0_1(a658)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1717, 96, 1711, 1696, 1697, 1710, 1695, 1650, 1640, 708, 1648])).
% 3.76/2.69 tff(1719,plain,
% 3.76/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a658) | c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a658) | c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1720,plain,
% 3.76/2.69 (((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a625) | c1_1(a625) | c0_1(a625)) <=> (c1_1(a658) | c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627))),
% 3.76/2.69 inference(rewrite,[status(thm)],[])).
% 3.76/2.69 tff(1721,plain,
% 3.76/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a625) | c1_1(a625) | c0_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a658) | c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627)))),
% 3.76/2.69 inference(monotonicity,[status(thm)],[1720])).
% 3.76/2.69 tff(1722,plain,
% 3.76/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a625) | c1_1(a625) | c0_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a658) | c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627))),
% 3.76/2.69 inference(transitivity,[status(thm)],[1721, 1719])).
% 3.76/2.69 tff(1723,plain,
% 3.76/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a625) | c1_1(a625) | c0_1(a625))),
% 3.76/2.69 inference(quant_inst,[status(thm)],[])).
% 3.76/2.69 tff(1724,plain,
% 3.76/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a658) | c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627)),
% 3.76/2.69 inference(modus_ponens,[status(thm)],[1723, 1722])).
% 3.76/2.69 tff(1725,plain,
% 3.76/2.69 ($false),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1724, 96, 1711, 1701, 1710, 1700, 1650, 1640, 1639, 1390, 1718, 1702])).
% 3.76/2.69 tff(1726,plain,(c0_1(a617) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | hskp17), inference(lemma,lemma(discharge,[]))).
% 3.76/2.69 tff(1727,plain,
% 3.76/2.69 (c0_1(a617)),
% 3.76/2.69 inference(unit_resolution,[status(thm)],[1726, 1638, 1637, 1636, 879, 868, 857, 12])).
% 3.76/2.69 tff(1728,plain,
% 3.76/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a648) | c1_1(a617) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a648) | c1_1(a617) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1729,plain,
% 3.76/2.70 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a625) | c0_1(a625) | c3_1(a625)) <=> (c2_1(a648) | c1_1(a617) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1730,plain,
% 3.76/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a625) | c0_1(a625) | c3_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a648) | c1_1(a617) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648))))),
% 3.76/2.70 inference(monotonicity,[status(thm)],[1729])).
% 3.76/2.70 tff(1731,plain,
% 3.76/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a625) | c0_1(a625) | c3_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a648) | c1_1(a617) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.76/2.70 inference(transitivity,[status(thm)],[1730, 1728])).
% 3.76/2.70 tff(1732,plain,
% 3.76/2.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a625) | c0_1(a625) | c3_1(a625))),
% 3.76/2.70 inference(quant_inst,[status(thm)],[])).
% 3.76/2.70 tff(1733,plain,
% 3.76/2.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a648) | c1_1(a617) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648))),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1732, 1731])).
% 3.76/2.70 tff(1734,plain,
% 3.76/2.70 (c3_1(a625) | (~c0_1(a617))),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[1733, 96, 879, 868, 1014, 857, 1460, 1638, 1636, 997])).
% 3.76/2.70 tff(1735,plain,
% 3.76/2.70 (c3_1(a625)),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[1734, 1727])).
% 3.76/2.70 tff(1736,assumption,(c3_1(a625)), introduced(assumption)).
% 3.76/2.70 tff(1737,plain,
% 3.76/2.70 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a648) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a648)) | (~c1_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a648) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a648)) | (~c1_1(a648)))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1738,plain,
% 3.76/2.70 ((hskp5 | (~ndr1_0) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648))) <=> (hskp5 | c2_1(a648) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a648)) | (~c1_1(a648)))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1739,plain,
% 3.76/2.70 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a648) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a648)) | (~c1_1(a648))))),
% 3.76/2.70 inference(monotonicity,[status(thm)],[1738])).
% 3.76/2.70 tff(1740,plain,
% 3.76/2.70 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a648) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a648)) | (~c1_1(a648)))),
% 3.76/2.70 inference(transitivity,[status(thm)],[1739, 1737])).
% 3.76/2.70 tff(1741,plain,
% 3.76/2.70 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)))),
% 3.76/2.70 inference(quant_inst,[status(thm)],[])).
% 3.76/2.70 tff(1742,plain,
% 3.76/2.70 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a648) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a648)) | (~c1_1(a648))),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1741, 1740])).
% 3.76/2.70 tff(1743,plain,
% 3.76/2.70 (hskp5 | (~c3_1(a625)) | (~c1_1(a648))),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[1742, 96, 881, 880, 1650, 1640, 567])).
% 3.76/2.70 tff(1744,plain,
% 3.76/2.70 (~c1_1(a648)),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[1743, 583, 1736])).
% 3.76/2.70 tff(1745,plain,
% 3.76/2.70 (hskp37 | hskp5 | (~c0_1(a617))),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[589, 96, 1044, 1043, 581])).
% 3.76/2.70 tff(1746,plain,
% 3.76/2.70 (hskp37),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[1745, 583, 698])).
% 3.76/2.70 tff(1747,plain,
% 3.76/2.70 (~c2_1(a607)),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[428, 1746])).
% 3.76/2.70 tff(1748,plain,
% 3.76/2.70 (c0_1(a607)),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[439, 1746])).
% 3.76/2.70 tff(1749,plain,
% 3.76/2.70 (c1_1(a607)),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[450, 1746])).
% 3.76/2.70 tff(1750,plain,
% 3.76/2.70 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a648) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a607)) | (~c3_1(a648)) | c1_1(a648))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a648) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a607)) | (~c3_1(a648)) | c1_1(a648))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1751,plain,
% 3.76/2.70 ((hskp5 | (~ndr1_0) | c1_1(a648) | c2_1(a648) | (~c3_1(a648)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp5 | c2_1(a648) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a607)) | (~c3_1(a648)) | c1_1(a648))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1752,plain,
% 3.76/2.70 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a648) | c2_1(a648) | (~c3_1(a648)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a648) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a607)) | (~c3_1(a648)) | c1_1(a648)))),
% 3.76/2.70 inference(monotonicity,[status(thm)],[1751])).
% 3.76/2.70 tff(1753,plain,
% 3.76/2.70 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a648) | c2_1(a648) | (~c3_1(a648)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a648) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a607)) | (~c3_1(a648)) | c1_1(a648))),
% 3.76/2.70 inference(transitivity,[status(thm)],[1752, 1750])).
% 3.76/2.70 tff(1754,plain,
% 3.76/2.70 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a648) | c2_1(a648) | (~c3_1(a648)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 3.76/2.70 inference(quant_inst,[status(thm)],[])).
% 3.76/2.70 tff(1755,plain,
% 3.76/2.70 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a648) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a607)) | (~c3_1(a648)) | c1_1(a648)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1754, 1753])).
% 3.76/2.70 tff(1756,plain,
% 3.76/2.70 ($false),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[1755, 96, 583, 882, 1749, 1748, 880, 1747, 567, 1744])).
% 3.76/2.70 tff(1757,plain,(hskp5 | (~c3_1(a648)) | c2_1(a648) | (~c3_1(a625)) | (~c0_1(a648)) | c2_1(a625) | c1_1(a625) | (~c0_1(a617))), inference(lemma,lemma(discharge,[]))).
% 3.76/2.70 tff(1758,plain,
% 3.76/2.70 (hskp5),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[1757, 879, 857, 1735, 868, 1638, 1637, 1727])).
% 3.76/2.70 tff(1759,plain,
% 3.76/2.70 (~c3_1(a606)),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[634, 1758])).
% 3.76/2.70 tff(1760,plain,
% 3.76/2.70 (~c0_1(a606)),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[640, 1758])).
% 3.76/2.70 tff(1761,plain,
% 3.76/2.70 (c2_1(a606)),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[651, 1758])).
% 3.76/2.70 tff(1762,plain,
% 3.76/2.70 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)) | (~c1_1(a606)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)) | (~c1_1(a606)))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1763,plain,
% 3.76/2.70 (((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c0_1(a606) | (~c2_1(a606)) | (~c1_1(a606))) <=> (c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)) | (~c1_1(a606)))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1764,plain,
% 3.76/2.70 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c0_1(a606) | (~c2_1(a606)) | (~c1_1(a606)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)) | (~c1_1(a606))))),
% 3.76/2.70 inference(monotonicity,[status(thm)],[1763])).
% 3.76/2.70 tff(1765,plain,
% 3.76/2.70 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c0_1(a606) | (~c2_1(a606)) | (~c1_1(a606)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)) | (~c1_1(a606)))),
% 3.76/2.70 inference(transitivity,[status(thm)],[1764, 1762])).
% 3.76/2.70 tff(1766,plain,
% 3.76/2.70 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c0_1(a606) | (~c2_1(a606)) | (~c1_1(a606)))),
% 3.76/2.70 inference(quant_inst,[status(thm)],[])).
% 3.76/2.70 tff(1767,plain,
% 3.76/2.70 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)) | (~c1_1(a606))),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1766, 1765])).
% 3.76/2.70 tff(1768,plain,
% 3.76/2.70 (~c1_1(a606)),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[1767, 96, 1761, 1760, 1759, 23])).
% 3.76/2.70 tff(1769,plain,
% 3.76/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c1_1(a625) | c0_1(a625) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c3_1(a625)) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a625) | c0_1(a625) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c3_1(a625)) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1770,plain,
% 3.76/2.70 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)) | c1_1(a606) | c0_1(a606) | c3_1(a606)) <=> (c1_1(a617) | c1_1(a625) | c0_1(a625) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c3_1(a625)) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1771,plain,
% 3.76/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)) | c1_1(a606) | c0_1(a606) | c3_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c1_1(a625) | c0_1(a625) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c3_1(a625)) | (~c2_1(a617)) | (~c3_1(a617))))),
% 3.76/2.70 inference(monotonicity,[status(thm)],[1770])).
% 3.76/2.70 tff(1772,plain,
% 3.76/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)) | c1_1(a606) | c0_1(a606) | c3_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a625) | c0_1(a625) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c3_1(a625)) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.76/2.70 inference(transitivity,[status(thm)],[1771, 1769])).
% 3.76/2.70 tff(1773,plain,
% 3.76/2.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)) | c1_1(a606) | c0_1(a606) | c3_1(a606))),
% 3.76/2.70 inference(quant_inst,[status(thm)],[])).
% 3.76/2.70 tff(1774,plain,
% 3.76/2.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a625) | c0_1(a625) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c3_1(a625)) | (~c2_1(a617)) | (~c3_1(a617))),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1773, 1772])).
% 3.76/2.70 tff(1775,plain,
% 3.76/2.70 ($false),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[1774, 96, 1013, 1014, 1460, 1637, 1636, 1760, 1759, 1221, 1735, 1768])).
% 3.76/2.70 tff(1776,plain,(hskp64 | hskp17), inference(lemma,lemma(discharge,[]))).
% 3.76/2.70 tff(1777,plain,
% 3.76/2.70 (hskp64),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[1776, 12])).
% 3.76/2.70 tff(1778,plain,
% 3.76/2.70 (((~hskp64) | c3_1(a673)) <=> ((~hskp64) | c3_1(a673))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1779,axiom,((~hskp64) | c3_1(a673)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 3.76/2.70 tff(1780,plain,
% 3.76/2.70 ((~hskp64) | c3_1(a673)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1779, 1778])).
% 3.76/2.70 tff(1781,plain,
% 3.76/2.70 ((~hskp64) | c3_1(a673)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1780, 1778])).
% 3.76/2.70 tff(1782,plain,
% 3.76/2.70 ((~hskp64) | c3_1(a673)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1781, 1778])).
% 3.76/2.70 tff(1783,plain,
% 3.76/2.70 ((~hskp64) | c3_1(a673)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1782, 1778])).
% 3.76/2.70 tff(1784,plain,
% 3.76/2.70 ((~hskp64) | c3_1(a673)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1783, 1778])).
% 3.76/2.70 tff(1785,plain,
% 3.76/2.70 ((~hskp64) | c3_1(a673)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1784, 1778])).
% 3.76/2.70 tff(1786,plain,
% 3.76/2.70 ((~hskp64) | c3_1(a673)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1785, 1778])).
% 3.76/2.70 tff(1787,plain,
% 3.76/2.70 ((~hskp64) | c3_1(a673)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1786, 1778])).
% 3.76/2.70 tff(1788,plain,
% 3.76/2.70 (c3_1(a673)),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[1787, 1777])).
% 3.76/2.70 tff(1789,plain,
% 3.76/2.70 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 3.76/2.70 inference(bind,[status(th)],[])).
% 3.76/2.70 tff(1790,plain,
% 3.76/2.70 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.76/2.70 inference(quant_intro,[status(thm)],[1789])).
% 3.76/2.70 tff(1791,plain,
% 3.76/2.70 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1792,plain,
% 3.76/2.70 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c0_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 3.76/2.70 inference(bind,[status(th)],[])).
% 3.76/2.70 tff(1793,plain,
% 3.76/2.70 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.76/2.70 inference(quant_intro,[status(thm)],[1792])).
% 3.76/2.70 tff(1794,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause310')).
% 3.76/2.70 tff(1795,plain,
% 3.76/2.70 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1794, 1793])).
% 3.76/2.70 tff(1796,plain,
% 3.76/2.70 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1795, 1791])).
% 3.76/2.70 tff(1797,plain,(
% 3.76/2.70 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.76/2.70 inference(skolemize,[status(sab)],[1796])).
% 3.76/2.70 tff(1798,plain,
% 3.76/2.70 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1797, 1790])).
% 3.76/2.70 tff(1799,plain,
% 3.76/2.70 (^[V: $i, U: $i] : refl((hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) <=> (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)))),
% 3.76/2.70 inference(bind,[status(th)],[])).
% 3.76/2.70 tff(1800,plain,
% 3.76/2.70 (![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.76/2.70 inference(quant_intro,[status(thm)],[1799])).
% 3.76/2.70 tff(1801,plain,
% 3.76/2.70 (![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1802,plain,
% 3.76/2.70 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) | c3_1(V)) | hskp51) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) | hskp51))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) | hskp51) <=> (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) | c3_1(V)) | hskp51) <=> (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))))),
% 3.76/2.70 inference(bind,[status(th)],[])).
% 3.76/2.70 tff(1803,plain,
% 3.76/2.70 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) | c3_1(V)) | hskp51) <=> ![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.76/2.70 inference(quant_intro,[status(thm)],[1802])).
% 3.76/2.70 tff(1804,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) | c3_1(V)) | hskp51)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause304')).
% 3.76/2.70 tff(1805,plain,
% 3.76/2.70 (![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1804, 1803])).
% 3.76/2.70 tff(1806,plain,
% 3.76/2.70 (![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1805, 1801])).
% 3.76/2.70 tff(1807,plain,(
% 3.76/2.70 ![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.76/2.70 inference(skolemize,[status(sab)],[1806])).
% 3.76/2.70 tff(1808,plain,
% 3.76/2.70 (![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1807, 1800])).
% 3.76/2.70 tff(1809,plain,
% 3.76/2.70 (((~hskp64) | (~c0_1(a673))) <=> ((~hskp64) | (~c0_1(a673)))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1810,plain,
% 3.76/2.70 (((~c0_1(a673)) | (~hskp64)) <=> ((~hskp64) | (~c0_1(a673)))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1811,axiom,((~c0_1(a673)) | (~hskp64)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 3.76/2.70 tff(1812,plain,
% 3.76/2.70 ((~hskp64) | (~c0_1(a673))),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1811, 1810])).
% 3.76/2.70 tff(1813,plain,
% 3.76/2.70 ((~hskp64) | (~c0_1(a673))),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1812, 1809])).
% 3.76/2.70 tff(1814,plain,
% 3.76/2.70 (~c0_1(a673)),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[1813, 1777])).
% 3.76/2.70 tff(1815,plain,
% 3.76/2.70 (((~hskp64) | c1_1(a673)) <=> ((~hskp64) | c1_1(a673))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1816,axiom,((~hskp64) | c1_1(a673)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 3.76/2.70 tff(1817,plain,
% 3.76/2.70 ((~hskp64) | c1_1(a673)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1816, 1815])).
% 3.76/2.70 tff(1818,plain,
% 3.76/2.70 ((~hskp64) | c1_1(a673)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1817, 1815])).
% 3.76/2.70 tff(1819,plain,
% 3.76/2.70 ((~hskp64) | c1_1(a673)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1818, 1815])).
% 3.76/2.70 tff(1820,plain,
% 3.76/2.70 ((~hskp64) | c1_1(a673)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1819, 1815])).
% 3.76/2.70 tff(1821,plain,
% 3.76/2.70 ((~hskp64) | c1_1(a673)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1820, 1815])).
% 3.76/2.70 tff(1822,plain,
% 3.76/2.70 ((~hskp64) | c1_1(a673)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1821, 1815])).
% 3.76/2.70 tff(1823,plain,
% 3.76/2.70 ((~hskp64) | c1_1(a673)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1822, 1815])).
% 3.76/2.70 tff(1824,plain,
% 3.76/2.70 ((~hskp64) | c1_1(a673)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1823, 1815])).
% 3.76/2.70 tff(1825,plain,
% 3.76/2.70 (c1_1(a673)),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[1824, 1777])).
% 3.76/2.70 tff(1826,plain,
% 3.76/2.70 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp51 | c0_1(a673) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp51 | c0_1(a673) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1827,plain,
% 3.76/2.70 ((hskp51 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a660) | c3_1(a660) | c0_1(a660)) <=> (hskp51 | c0_1(a673) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1828,plain,
% 3.76/2.70 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp51 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a660) | c3_1(a660) | c0_1(a660))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp51 | c0_1(a673) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673))))),
% 3.76/2.70 inference(monotonicity,[status(thm)],[1827])).
% 3.76/2.70 tff(1829,plain,
% 3.76/2.70 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp51 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a660) | c3_1(a660) | c0_1(a660))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp51 | c0_1(a673) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)))),
% 3.76/2.70 inference(transitivity,[status(thm)],[1828, 1826])).
% 3.76/2.70 tff(1830,plain,
% 3.76/2.70 ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp51 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a660) | c3_1(a660) | c0_1(a660))),
% 3.76/2.70 inference(quant_inst,[status(thm)],[])).
% 3.76/2.70 tff(1831,plain,
% 3.76/2.70 ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp51 | c0_1(a673) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673))),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1830, 1829])).
% 3.76/2.70 tff(1832,plain,
% 3.76/2.70 (hskp51),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[1831, 96, 1788, 1825, 1814, 1479, 1473, 1467, 1808])).
% 3.76/2.70 tff(1833,plain,
% 3.76/2.70 (((~hskp51) | (~c3_1(a644))) <=> ((~hskp51) | (~c3_1(a644)))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1834,plain,
% 3.76/2.70 (((~c3_1(a644)) | (~hskp51)) <=> ((~hskp51) | (~c3_1(a644)))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1835,axiom,((~c3_1(a644)) | (~hskp51)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 3.76/2.70 tff(1836,plain,
% 3.76/2.70 ((~hskp51) | (~c3_1(a644))),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1835, 1834])).
% 3.76/2.70 tff(1837,plain,
% 3.76/2.70 ((~hskp51) | (~c3_1(a644))),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1836, 1833])).
% 3.76/2.70 tff(1838,plain,
% 3.76/2.70 (~c3_1(a644)),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[1837, 1832])).
% 3.76/2.70 tff(1839,plain,
% 3.76/2.70 (((~hskp51) | c0_1(a644)) <=> ((~hskp51) | c0_1(a644))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1840,axiom,((~hskp51) | c0_1(a644)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 3.76/2.70 tff(1841,plain,
% 3.76/2.70 ((~hskp51) | c0_1(a644)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1840, 1839])).
% 3.76/2.70 tff(1842,plain,
% 3.76/2.70 ((~hskp51) | c0_1(a644)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1841, 1839])).
% 3.76/2.70 tff(1843,plain,
% 3.76/2.70 ((~hskp51) | c0_1(a644)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1842, 1839])).
% 3.76/2.70 tff(1844,plain,
% 3.76/2.70 ((~hskp51) | c0_1(a644)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1843, 1839])).
% 3.76/2.70 tff(1845,plain,
% 3.76/2.70 ((~hskp51) | c0_1(a644)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1844, 1839])).
% 3.76/2.70 tff(1846,plain,
% 3.76/2.70 ((~hskp51) | c0_1(a644)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1845, 1839])).
% 3.76/2.70 tff(1847,plain,
% 3.76/2.70 ((~hskp51) | c0_1(a644)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1846, 1839])).
% 3.76/2.70 tff(1848,plain,
% 3.76/2.70 ((~hskp51) | c0_1(a644)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1847, 1839])).
% 3.76/2.70 tff(1849,plain,
% 3.76/2.70 (c0_1(a644)),
% 3.76/2.70 inference(unit_resolution,[status(thm)],[1848, 1832])).
% 3.76/2.70 tff(1850,plain,
% 3.76/2.70 (((~hskp51) | c2_1(a644)) <=> ((~hskp51) | c2_1(a644))),
% 3.76/2.70 inference(rewrite,[status(thm)],[])).
% 3.76/2.70 tff(1851,axiom,((~hskp51) | c2_1(a644)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 3.76/2.70 tff(1852,plain,
% 3.76/2.70 ((~hskp51) | c2_1(a644)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1851, 1850])).
% 3.76/2.70 tff(1853,plain,
% 3.76/2.70 ((~hskp51) | c2_1(a644)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1852, 1850])).
% 3.76/2.70 tff(1854,plain,
% 3.76/2.70 ((~hskp51) | c2_1(a644)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1853, 1850])).
% 3.76/2.70 tff(1855,plain,
% 3.76/2.70 ((~hskp51) | c2_1(a644)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1854, 1850])).
% 3.76/2.70 tff(1856,plain,
% 3.76/2.70 ((~hskp51) | c2_1(a644)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1855, 1850])).
% 3.76/2.70 tff(1857,plain,
% 3.76/2.70 ((~hskp51) | c2_1(a644)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1856, 1850])).
% 3.76/2.70 tff(1858,plain,
% 3.76/2.70 ((~hskp51) | c2_1(a644)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1857, 1850])).
% 3.76/2.70 tff(1859,plain,
% 3.76/2.70 ((~hskp51) | c2_1(a644)),
% 3.76/2.70 inference(modus_ponens,[status(thm)],[1858, 1850])).
% 3.76/2.71 tff(1860,plain,
% 3.76/2.71 (c2_1(a644)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1859, 1832])).
% 3.76/2.71 tff(1861,plain,
% 3.76/2.71 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | c0_1(a673) | c3_1(a644) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a644)) | (~c0_1(a644)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a673) | c3_1(a644) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a644)) | (~c0_1(a644)))),
% 3.76/2.71 inference(rewrite,[status(thm)],[])).
% 3.76/2.71 tff(1862,plain,
% 3.76/2.71 ((hskp16 | (~ndr1_0) | c3_1(a644) | (~c0_1(a644)) | (~c2_1(a644)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673))) <=> (hskp16 | c0_1(a673) | c3_1(a644) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a644)) | (~c0_1(a644)))),
% 3.76/2.71 inference(rewrite,[status(thm)],[])).
% 3.76/2.71 tff(1863,plain,
% 3.76/2.71 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a644) | (~c0_1(a644)) | (~c2_1(a644)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | c0_1(a673) | c3_1(a644) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a644)) | (~c0_1(a644))))),
% 3.76/2.71 inference(monotonicity,[status(thm)],[1862])).
% 3.76/2.71 tff(1864,plain,
% 3.76/2.71 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a644) | (~c0_1(a644)) | (~c2_1(a644)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a673) | c3_1(a644) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a644)) | (~c0_1(a644)))),
% 3.76/2.71 inference(transitivity,[status(thm)],[1863, 1861])).
% 3.76/2.71 tff(1865,plain,
% 3.76/2.71 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a644) | (~c0_1(a644)) | (~c2_1(a644)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673)))),
% 3.76/2.71 inference(quant_inst,[status(thm)],[])).
% 3.76/2.71 tff(1866,plain,
% 3.76/2.71 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a673) | c3_1(a644) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a644)) | (~c0_1(a644))),
% 3.76/2.71 inference(modus_ponens,[status(thm)],[1865, 1864])).
% 3.76/2.71 tff(1867,plain,
% 3.76/2.71 (hskp16),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1866, 96, 1788, 1860, 1849, 1814, 1838, 1798, 13])).
% 3.76/2.71 tff(1868,assumption,(hskp53), introduced(assumption)).
% 3.76/2.71 tff(1869,plain,
% 3.76/2.71 (~c2_1(a648)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[856, 1868])).
% 3.76/2.71 tff(1870,plain,
% 3.76/2.71 (c3_1(a648)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[878, 1868])).
% 3.76/2.71 tff(1871,plain,
% 3.76/2.71 (c0_1(a648)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[867, 1868])).
% 3.76/2.71 tff(1872,plain,
% 3.76/2.71 ($false),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1011, 1871, 1870, 106, 1869])).
% 3.76/2.71 tff(1873,plain,((~hskp53) | hskp41), inference(lemma,lemma(discharge,[]))).
% 3.76/2.71 tff(1874,plain,
% 3.76/2.71 (~hskp53),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1873, 106])).
% 3.76/2.71 tff(1875,plain,
% 3.76/2.71 (~hskp58),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[104, 1874, 12])).
% 3.76/2.71 tff(1876,plain,
% 3.76/2.71 (~hskp33),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[154, 1875, 106])).
% 3.76/2.71 tff(1877,plain,
% 3.76/2.71 (~hskp15),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[199, 1874, 12])).
% 3.76/2.71 tff(1878,plain,
% 3.76/2.71 (~hskp33),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[154, 105, 106])).
% 3.76/2.71 tff(1879,assumption,(~hskp61), introduced(assumption)).
% 3.76/2.71 tff(1880,assumption,(c1_1(a673)), introduced(assumption)).
% 3.76/2.71 tff(1881,assumption,(c3_1(a673)), introduced(assumption)).
% 3.76/2.71 tff(1882,plain,
% 3.76/2.71 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a669) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a669)) | (~c1_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a669) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a669)) | (~c1_1(a669)))),
% 3.76/2.71 inference(rewrite,[status(thm)],[])).
% 3.76/2.71 tff(1883,plain,
% 3.76/2.71 ((hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669))) <=> (hskp41 | c2_1(a669) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a669)) | (~c1_1(a669)))),
% 3.76/2.71 inference(rewrite,[status(thm)],[])).
% 3.76/2.71 tff(1884,plain,
% 3.76/2.71 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a669) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a669)) | (~c1_1(a669))))),
% 3.76/2.71 inference(monotonicity,[status(thm)],[1883])).
% 3.76/2.71 tff(1885,plain,
% 3.76/2.71 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a669) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a669)) | (~c1_1(a669)))),
% 3.76/2.71 inference(transitivity,[status(thm)],[1884, 1882])).
% 3.76/2.71 tff(1886,plain,
% 3.76/2.71 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))),
% 3.76/2.71 inference(quant_inst,[status(thm)],[])).
% 3.76/2.71 tff(1887,plain,
% 3.76/2.71 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a669) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a669)) | (~c1_1(a669))),
% 3.76/2.71 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 3.76/2.71 tff(1888,plain,
% 3.76/2.71 ($false),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1887, 96, 106, 1881, 1880, 359, 348, 336, 329, 13])).
% 3.76/2.71 tff(1889,plain,((~hskp60) | hskp41 | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a673)), inference(lemma,lemma(discharge,[]))).
% 3.76/2.71 tff(1890,plain,
% 3.76/2.71 (~hskp60),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1889, 106, 1881, 1880, 13])).
% 3.76/2.71 tff(1891,plain,
% 3.76/2.71 (hskp33),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[381, 1890, 1879])).
% 3.76/2.71 tff(1892,plain,
% 3.76/2.71 (~c2_1(a599)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[122, 1891])).
% 3.76/2.71 tff(1893,plain,
% 3.76/2.71 (c3_1(a599)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[133, 1891])).
% 3.76/2.71 tff(1894,plain,
% 3.76/2.71 (c0_1(a599)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[144, 1891])).
% 3.76/2.71 tff(1895,plain,
% 3.76/2.71 ($false),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[152, 96, 146, 106, 1894, 1893, 1892, 116])).
% 3.76/2.71 tff(1896,plain,(hskp41 | hskp58 | hskp61 | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a673)), inference(lemma,lemma(discharge,[]))).
% 3.76/2.71 tff(1897,plain,
% 3.76/2.71 (hskp61),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1896, 13, 1788, 106, 1825, 105])).
% 3.76/2.71 tff(1898,plain,
% 3.76/2.71 (~c0_1(a670)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[387, 1897])).
% 3.76/2.71 tff(1899,plain,
% 3.76/2.71 (~c1_1(a670)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[393, 1897])).
% 3.76/2.71 tff(1900,plain,
% 3.76/2.71 (~c3_1(a670)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[400, 96, 35, 12, 1899, 1898, 34])).
% 3.76/2.71 tff(1901,assumption,(hskp3), introduced(assumption)).
% 3.76/2.71 tff(1902,plain,
% 3.76/2.71 (c0_1(a603)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1682, 1901])).
% 3.76/2.71 tff(1903,assumption,(~c2_1(a603)), introduced(assumption)).
% 3.76/2.71 tff(1904,assumption,(hskp61), introduced(assumption)).
% 3.76/2.71 tff(1905,plain,
% 3.76/2.71 (~c0_1(a670)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[387, 1904])).
% 3.76/2.71 tff(1906,plain,
% 3.76/2.71 (~c1_1(a670)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[393, 1904])).
% 3.76/2.71 tff(1907,plain,
% 3.76/2.71 (~c3_1(a670)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[400, 96, 35, 12, 1906, 1905, 34])).
% 3.76/2.71 tff(1908,plain,
% 3.76/2.71 (c2_1(a670)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[421, 1904])).
% 3.76/2.71 tff(1909,plain,
% 3.76/2.71 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c0_1(a670) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a670)) | c3_1(a670))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c0_1(a670) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a670)) | c3_1(a670))),
% 3.76/2.71 inference(rewrite,[status(thm)],[])).
% 3.76/2.71 tff(1910,plain,
% 3.76/2.71 (((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c1_1(a603) | c3_1(a603) | c2_1(a603)) <=> (c0_1(a670) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a670)) | c3_1(a670))),
% 3.76/2.71 inference(rewrite,[status(thm)],[])).
% 3.76/2.71 tff(1911,plain,
% 3.76/2.71 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c1_1(a603) | c3_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c0_1(a670) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a670)) | c3_1(a670)))),
% 3.76/2.71 inference(monotonicity,[status(thm)],[1910])).
% 3.76/2.71 tff(1912,plain,
% 3.76/2.71 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c1_1(a603) | c3_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c0_1(a670) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a670)) | c3_1(a670))),
% 3.76/2.71 inference(transitivity,[status(thm)],[1911, 1909])).
% 3.76/2.71 tff(1913,plain,
% 3.76/2.71 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c1_1(a603) | c3_1(a603) | c2_1(a603))),
% 3.76/2.71 inference(quant_inst,[status(thm)],[])).
% 3.76/2.71 tff(1914,plain,
% 3.76/2.71 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c0_1(a670) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a670)) | c3_1(a670)),
% 3.76/2.71 inference(modus_ponens,[status(thm)],[1913, 1912])).
% 3.76/2.71 tff(1915,plain,
% 3.76/2.71 ($false),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1914, 96, 1908, 1905, 1233, 1030, 662, 1903, 1907])).
% 3.76/2.71 tff(1916,plain,((~hskp61) | c1_1(a603) | c3_1(a603) | c2_1(a603) | hskp53 | hskp17), inference(lemma,lemma(discharge,[]))).
% 3.76/2.71 tff(1917,plain,
% 3.76/2.71 (c1_1(a603)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1916, 1897, 12, 1030, 35, 1903])).
% 3.76/2.71 tff(1918,assumption,(c0_1(a603)), introduced(assumption)).
% 3.76/2.71 tff(1919,plain,
% 3.76/2.71 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~c1_1(a603)) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | (~c1_1(a603)) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c0_1(a603)))),
% 3.76/2.71 inference(rewrite,[status(thm)],[])).
% 3.76/2.71 tff(1920,plain,
% 3.76/2.71 ((hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c1_1(a603)) | (~c0_1(a603))) <=> (hskp41 | (~c1_1(a603)) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c0_1(a603)))),
% 3.76/2.71 inference(rewrite,[status(thm)],[])).
% 3.76/2.71 tff(1921,plain,
% 3.76/2.71 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c1_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~c1_1(a603)) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c0_1(a603))))),
% 3.76/2.71 inference(monotonicity,[status(thm)],[1920])).
% 3.76/2.71 tff(1922,plain,
% 3.76/2.71 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c1_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | (~c1_1(a603)) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c0_1(a603)))),
% 3.76/2.71 inference(transitivity,[status(thm)],[1921, 1919])).
% 3.76/2.71 tff(1923,plain,
% 3.76/2.71 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c1_1(a603)) | (~c0_1(a603)))),
% 3.76/2.71 inference(quant_inst,[status(thm)],[])).
% 3.76/2.71 tff(1924,plain,
% 3.76/2.71 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | (~c1_1(a603)) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c0_1(a603))),
% 3.76/2.71 inference(modus_ponens,[status(thm)],[1923, 1922])).
% 3.76/2.71 tff(1925,plain,
% 3.76/2.71 ($false),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1924, 96, 106, 1788, 1825, 1918, 1917, 329, 13, 1903])).
% 3.76/2.71 tff(1926,plain,(c2_1(a673) | hskp41 | (~c0_1(a603)) | c2_1(a603) | hskp17 | c3_1(a603) | hskp53), inference(lemma,lemma(discharge,[]))).
% 3.76/2.71 tff(1927,plain,
% 3.76/2.71 (c2_1(a603)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1926, 1902, 106, 13, 12, 1030, 35])).
% 3.76/2.71 tff(1928,plain,
% 3.76/2.71 (~c1_1(a603)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1664, 1901])).
% 3.76/2.71 tff(1929,plain,
% 3.76/2.71 (~hskp14),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[239, 35, 12, 106])).
% 3.76/2.71 tff(1930,plain,
% 3.76/2.71 ($false),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1246, 96, 281, 1929, 1902, 1928, 250, 1927])).
% 3.76/2.71 tff(1931,plain,((~hskp3) | hskp15 | hskp41 | c2_1(a673) | hskp17 | c3_1(a603) | hskp53), inference(lemma,lemma(discharge,[]))).
% 3.76/2.71 tff(1932,plain,
% 3.76/2.71 (~hskp3),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1931, 13, 106, 281, 12, 1030, 35])).
% 3.76/2.71 tff(1933,plain,
% 3.76/2.71 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c0_1(a673) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c0_1(a673) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)))),
% 3.76/2.71 inference(rewrite,[status(thm)],[])).
% 3.76/2.71 tff(1934,plain,
% 3.76/2.71 ((hskp29 | hskp3 | (~ndr1_0) | c2_1(a673) | c0_1(a673) | (~c3_1(a673))) <=> (hskp29 | hskp3 | c0_1(a673) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)))),
% 3.76/2.71 inference(rewrite,[status(thm)],[])).
% 3.76/2.71 tff(1935,plain,
% 3.76/2.71 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a673) | c0_1(a673) | (~c3_1(a673)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c0_1(a673) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673))))),
% 3.76/2.71 inference(monotonicity,[status(thm)],[1934])).
% 3.76/2.71 tff(1936,plain,
% 3.76/2.71 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a673) | c0_1(a673) | (~c3_1(a673)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c0_1(a673) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)))),
% 3.76/2.71 inference(transitivity,[status(thm)],[1935, 1933])).
% 3.76/2.71 tff(1937,plain,
% 3.76/2.71 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a673) | c0_1(a673) | (~c3_1(a673)))),
% 3.76/2.71 inference(quant_inst,[status(thm)],[])).
% 3.76/2.71 tff(1938,plain,
% 3.76/2.71 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c0_1(a673) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673))),
% 3.76/2.71 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 3.76/2.71 tff(1939,plain,
% 3.76/2.71 (hskp29 | hskp3 | c2_1(a673)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1938, 96, 1788, 1814, 1024])).
% 3.76/2.71 tff(1940,plain,
% 3.76/2.71 (hskp29),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1939, 1932, 13])).
% 3.76/2.71 tff(1941,plain,
% 3.76/2.71 (~c3_1(a660)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1472, 1940])).
% 3.76/2.71 tff(1942,plain,
% 3.76/2.71 (~c0_1(a660)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1466, 1940])).
% 3.76/2.71 tff(1943,plain,
% 3.76/2.71 (~c1_1(a660)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1478, 1940])).
% 3.76/2.71 tff(1944,plain,
% 3.76/2.71 (c2_1(a670)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[421, 1897])).
% 3.76/2.71 tff(1945,plain,
% 3.76/2.71 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c0_1(a670) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c2_1(a660) | (~c2_1(a670)) | c3_1(a670))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c0_1(a670) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c2_1(a660) | (~c2_1(a670)) | c3_1(a670))),
% 3.76/2.71 inference(rewrite,[status(thm)],[])).
% 3.76/2.71 tff(1946,plain,
% 3.76/2.71 (((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c1_1(a660) | c3_1(a660) | c2_1(a660)) <=> (c0_1(a670) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c2_1(a660) | (~c2_1(a670)) | c3_1(a670))),
% 3.76/2.71 inference(rewrite,[status(thm)],[])).
% 3.76/2.71 tff(1947,plain,
% 3.76/2.71 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c1_1(a660) | c3_1(a660) | c2_1(a660))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c0_1(a670) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c2_1(a660) | (~c2_1(a670)) | c3_1(a670)))),
% 3.76/2.71 inference(monotonicity,[status(thm)],[1946])).
% 3.76/2.71 tff(1948,plain,
% 3.76/2.71 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c1_1(a660) | c3_1(a660) | c2_1(a660))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c0_1(a670) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c2_1(a660) | (~c2_1(a670)) | c3_1(a670))),
% 3.76/2.71 inference(transitivity,[status(thm)],[1947, 1945])).
% 3.76/2.71 tff(1949,plain,
% 3.76/2.71 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c1_1(a660) | c3_1(a660) | c2_1(a660))),
% 3.76/2.71 inference(quant_inst,[status(thm)],[])).
% 3.76/2.71 tff(1950,plain,
% 3.76/2.71 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c0_1(a670) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c2_1(a660) | (~c2_1(a670)) | c3_1(a670)),
% 3.76/2.71 inference(modus_ponens,[status(thm)],[1949, 1948])).
% 3.76/2.71 tff(1951,plain,
% 3.76/2.71 (c2_1(a660)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[1950, 96, 1944, 1898, 1943, 1941, 662, 1900])).
% 3.76/2.71 tff(1952,assumption,(hskp54), introduced(assumption)).
% 3.76/2.71 tff(1953,plain,
% 3.76/2.71 (~c0_1(a651)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[473, 1952])).
% 3.76/2.71 tff(1954,plain,
% 3.76/2.71 (c3_1(a651)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[502, 1952])).
% 3.76/2.71 tff(1955,plain,
% 3.76/2.71 (c1_1(a651)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[509, 96, 35, 12, 1954, 1953, 34])).
% 3.76/2.71 tff(1956,assumption,(c2_1(a660)), introduced(assumption)).
% 3.76/2.71 tff(1957,assumption,(~c0_1(a660)), introduced(assumption)).
% 3.76/2.71 tff(1958,assumption,(~c3_1(a660)), introduced(assumption)).
% 3.76/2.71 tff(1959,plain,
% 3.76/2.71 (c2_1(a651)),
% 3.76/2.71 inference(unit_resolution,[status(thm)],[484, 1952])).
% 3.76/2.71 tff(1960,plain,
% 3.76/2.71 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a651) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a660)) | (~c2_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a651) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a660)) | (~c2_1(a651)) | (~c1_1(a651)))),
% 3.76/2.71 inference(rewrite,[status(thm)],[])).
% 3.76/2.71 tff(1961,plain,
% 3.76/2.71 (((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c0_1(a651) | (~c2_1(a651)) | (~c1_1(a651))) <=> (c0_1(a651) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a660)) | (~c2_1(a651)) | (~c1_1(a651)))),
% 3.76/2.71 inference(rewrite,[status(thm)],[])).
% 3.76/2.71 tff(1962,plain,
% 3.80/2.71 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c0_1(a651) | (~c2_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a651) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a660)) | (~c2_1(a651)) | (~c1_1(a651))))),
% 3.80/2.71 inference(monotonicity,[status(thm)],[1961])).
% 3.80/2.71 tff(1963,plain,
% 3.80/2.71 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c0_1(a651) | (~c2_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a651) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a660)) | (~c2_1(a651)) | (~c1_1(a651)))),
% 3.80/2.71 inference(transitivity,[status(thm)],[1962, 1960])).
% 3.80/2.71 tff(1964,plain,
% 3.80/2.71 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c0_1(a651) | (~c2_1(a651)) | (~c1_1(a651)))),
% 3.80/2.71 inference(quant_inst,[status(thm)],[])).
% 3.80/2.71 tff(1965,plain,
% 3.80/2.71 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a651) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a660)) | (~c2_1(a651)) | (~c1_1(a651))),
% 3.80/2.71 inference(modus_ponens,[status(thm)],[1964, 1963])).
% 3.80/2.71 tff(1966,plain,
% 3.80/2.71 ($false),
% 3.80/2.71 inference(unit_resolution,[status(thm)],[1965, 96, 1959, 1953, 1958, 1957, 23, 1956, 1955])).
% 3.80/2.71 tff(1967,plain,((~hskp54) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | hskp53 | hskp17), inference(lemma,lemma(discharge,[]))).
% 3.80/2.71 tff(1968,plain,
% 3.80/2.71 (~hskp54),
% 3.80/2.71 inference(unit_resolution,[status(thm)],[1967, 1951, 35, 1942, 1941, 12])).
% 3.80/2.71 tff(1969,plain,
% 3.80/2.71 (hskp54 | hskp37 | c3_1(a670)),
% 3.80/2.71 inference(unit_resolution,[status(thm)],[466, 96, 1944, 1898, 411])).
% 3.80/2.71 tff(1970,plain,
% 3.80/2.71 (hskp37),
% 3.80/2.71 inference(unit_resolution,[status(thm)],[1969, 1968, 1900])).
% 3.80/2.71 tff(1971,plain,
% 3.80/2.71 (~c2_1(a607)),
% 3.80/2.71 inference(unit_resolution,[status(thm)],[428, 1970])).
% 3.80/2.71 tff(1972,plain,
% 3.80/2.71 (c0_1(a607)),
% 3.80/2.71 inference(unit_resolution,[status(thm)],[439, 1970])).
% 3.80/2.71 tff(1973,plain,
% 3.80/2.71 (c1_1(a607)),
% 3.80/2.71 inference(unit_resolution,[status(thm)],[450, 1970])).
% 3.80/2.71 tff(1974,plain,
% 3.80/2.71 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a607) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a607)) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a607) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 3.80/2.71 inference(rewrite,[status(thm)],[])).
% 3.80/2.71 tff(1975,plain,
% 3.80/2.71 ((hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp41 | c2_1(a607) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 3.80/2.71 inference(rewrite,[status(thm)],[])).
% 3.80/2.71 tff(1976,plain,
% 3.80/2.71 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a607) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a607)) | (~c1_1(a607))))),
% 3.80/2.71 inference(monotonicity,[status(thm)],[1975])).
% 3.80/2.71 tff(1977,plain,
% 3.80/2.71 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a607) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 3.80/2.71 inference(transitivity,[status(thm)],[1976, 1974])).
% 3.80/2.71 tff(1978,plain,
% 3.80/2.71 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 3.80/2.71 inference(quant_inst,[status(thm)],[])).
% 3.80/2.71 tff(1979,plain,
% 3.80/2.71 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a607) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a607)) | (~c1_1(a607))),
% 3.80/2.71 inference(modus_ponens,[status(thm)],[1978, 1977])).
% 3.80/2.71 tff(1980,plain,
% 3.80/2.71 ($false),
% 3.80/2.71 inference(unit_resolution,[status(thm)],[1979, 96, 106, 1788, 1825, 1973, 1972, 1971, 329, 13])).
% 3.80/2.71 tff(1981,plain,(c2_1(a673) | hskp41 | hskp53 | hskp17 | hskp15 | c3_1(a603)), inference(lemma,lemma(discharge,[]))).
% 3.80/2.71 tff(1982,plain,
% 3.80/2.71 (c2_1(a673)),
% 3.80/2.71 inference(unit_resolution,[status(thm)],[1981, 35, 106, 12, 281, 1030])).
% 3.80/2.71 tff(1983,assumption,(c2_1(a673)), introduced(assumption)).
% 3.80/2.71 tff(1984,assumption,(~c0_1(a673)), introduced(assumption)).
% 3.80/2.71 tff(1985,plain,
% 3.80/2.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a673) | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a673) | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | (~c3_1(a670)))),
% 3.80/2.71 inference(rewrite,[status(thm)],[])).
% 3.80/2.71 tff(1986,plain,
% 3.80/2.71 (((~ndr1_0) | c1_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a673) | (~c1_1(a673)) | (~c2_1(a673))) <=> (c0_1(a673) | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | (~c3_1(a670)))),
% 3.80/2.71 inference(rewrite,[status(thm)],[])).
% 3.80/2.71 tff(1987,plain,
% 3.80/2.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a673) | (~c1_1(a673)) | (~c2_1(a673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a673) | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | (~c3_1(a670))))),
% 3.80/2.71 inference(monotonicity,[status(thm)],[1986])).
% 3.80/2.71 tff(1988,plain,
% 3.80/2.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a673) | (~c1_1(a673)) | (~c2_1(a673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a673) | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | (~c3_1(a670)))),
% 3.80/2.71 inference(transitivity,[status(thm)],[1987, 1985])).
% 3.80/2.71 tff(1989,plain,
% 3.80/2.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a673) | (~c1_1(a673)) | (~c2_1(a673)))),
% 3.80/2.71 inference(quant_inst,[status(thm)],[])).
% 3.80/2.71 tff(1990,plain,
% 3.80/2.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a673) | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | (~c3_1(a670))),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[1989, 1988])).
% 3.80/2.72 tff(1991,plain,
% 3.80/2.72 (~c3_1(a670)),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[1990, 96, 1880, 1908, 1984, 1906, 1905, 1566, 1983])).
% 3.80/2.72 tff(1992,plain,
% 3.80/2.72 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a673) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | c3_1(a670))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a673) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | c3_1(a670))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(1993,plain,
% 3.80/2.72 (((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673))) <=> (c0_1(a673) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | c3_1(a670))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(1994,plain,
% 3.80/2.72 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a673) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | c3_1(a670)))),
% 3.80/2.72 inference(monotonicity,[status(thm)],[1993])).
% 3.80/2.72 tff(1995,plain,
% 3.80/2.72 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a673) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | c3_1(a670))),
% 3.80/2.72 inference(transitivity,[status(thm)],[1994, 1992])).
% 3.80/2.72 tff(1996,plain,
% 3.80/2.72 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673)))),
% 3.80/2.72 inference(quant_inst,[status(thm)],[])).
% 3.80/2.72 tff(1997,plain,
% 3.80/2.72 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a673) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | c3_1(a670)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[1996, 1995])).
% 3.80/2.72 tff(1998,plain,
% 3.80/2.72 ($false),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[1997, 96, 1880, 1908, 1984, 1905, 23, 1983, 1991])).
% 3.80/2.72 tff(1999,plain,((~hskp61) | (~c1_1(a673)) | c0_1(a673) | (~c2_1(a673))), inference(lemma,lemma(discharge,[]))).
% 3.80/2.72 tff(2000,plain,
% 3.80/2.72 (~hskp61),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[1999, 1982, 1814, 1825])).
% 3.80/2.72 tff(2001,plain,
% 3.80/2.72 (hskp60),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[381, 2000, 1878])).
% 3.80/2.72 tff(2002,plain,
% 3.80/2.72 (~c2_1(a669)),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[335, 2001])).
% 3.80/2.72 tff(2003,plain,
% 3.80/2.72 (c0_1(a669)),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[358, 2001])).
% 3.80/2.72 tff(2004,assumption,(hskp62), introduced(assumption)).
% 3.80/2.72 tff(2005,plain,
% 3.80/2.72 (((~hskp62) | c0_1(a671)) <=> ((~hskp62) | c0_1(a671))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2006,axiom,((~hskp62) | c0_1(a671)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 3.80/2.72 tff(2007,plain,
% 3.80/2.72 ((~hskp62) | c0_1(a671)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2006, 2005])).
% 3.80/2.72 tff(2008,plain,
% 3.80/2.72 ((~hskp62) | c0_1(a671)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2007, 2005])).
% 3.80/2.72 tff(2009,plain,
% 3.80/2.72 ((~hskp62) | c0_1(a671)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2008, 2005])).
% 3.80/2.72 tff(2010,plain,
% 3.80/2.72 ((~hskp62) | c0_1(a671)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2009, 2005])).
% 3.80/2.72 tff(2011,plain,
% 3.80/2.72 ((~hskp62) | c0_1(a671)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2010, 2005])).
% 3.80/2.72 tff(2012,plain,
% 3.80/2.72 ((~hskp62) | c0_1(a671)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2011, 2005])).
% 3.80/2.72 tff(2013,plain,
% 3.80/2.72 ((~hskp62) | c0_1(a671)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2012, 2005])).
% 3.80/2.72 tff(2014,plain,
% 3.80/2.72 ((~hskp62) | c0_1(a671)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2013, 2005])).
% 3.80/2.72 tff(2015,plain,
% 3.80/2.72 (c0_1(a671)),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[2014, 2004])).
% 3.80/2.72 tff(2016,plain,
% 3.80/2.72 (((~hskp62) | c3_1(a671)) <=> ((~hskp62) | c3_1(a671))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2017,axiom,((~hskp62) | c3_1(a671)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 3.80/2.72 tff(2018,plain,
% 3.80/2.72 ((~hskp62) | c3_1(a671)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2017, 2016])).
% 3.80/2.72 tff(2019,plain,
% 3.80/2.72 ((~hskp62) | c3_1(a671)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2018, 2016])).
% 3.80/2.72 tff(2020,plain,
% 3.80/2.72 ((~hskp62) | c3_1(a671)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2019, 2016])).
% 3.80/2.72 tff(2021,plain,
% 3.80/2.72 ((~hskp62) | c3_1(a671)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2020, 2016])).
% 3.80/2.72 tff(2022,plain,
% 3.80/2.72 ((~hskp62) | c3_1(a671)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2021, 2016])).
% 3.80/2.72 tff(2023,plain,
% 3.80/2.72 ((~hskp62) | c3_1(a671)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2022, 2016])).
% 3.80/2.72 tff(2024,plain,
% 3.80/2.72 ((~hskp62) | c3_1(a671)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2023, 2016])).
% 3.80/2.72 tff(2025,plain,
% 3.80/2.72 ((~hskp62) | c3_1(a671)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2024, 2016])).
% 3.80/2.72 tff(2026,plain,
% 3.80/2.72 (c3_1(a671)),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[2025, 2004])).
% 3.80/2.72 tff(2027,plain,
% 3.80/2.72 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | (~c3_1(a671)) | c2_1(a671) | (~c0_1(a671)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | (~ndr1_0) | (~c3_1(a671)) | c2_1(a671) | (~c0_1(a671)))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2028,plain,
% 3.80/2.72 ((hskp58 | hskp41 | (~ndr1_0) | c2_1(a671) | (~c3_1(a671)) | (~c0_1(a671))) <=> (hskp58 | hskp41 | (~ndr1_0) | (~c3_1(a671)) | c2_1(a671) | (~c0_1(a671)))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2029,plain,
% 3.80/2.72 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a671) | (~c3_1(a671)) | (~c0_1(a671)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | (~c3_1(a671)) | c2_1(a671) | (~c0_1(a671))))),
% 3.80/2.72 inference(monotonicity,[status(thm)],[2028])).
% 3.80/2.72 tff(2030,plain,
% 3.80/2.72 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a671) | (~c3_1(a671)) | (~c0_1(a671)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | (~ndr1_0) | (~c3_1(a671)) | c2_1(a671) | (~c0_1(a671)))),
% 3.80/2.72 inference(transitivity,[status(thm)],[2029, 2027])).
% 3.80/2.72 tff(2031,plain,
% 3.80/2.72 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a671) | (~c3_1(a671)) | (~c0_1(a671)))),
% 3.80/2.72 inference(quant_inst,[status(thm)],[])).
% 3.80/2.72 tff(2032,plain,
% 3.80/2.72 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | (~ndr1_0) | (~c3_1(a671)) | c2_1(a671) | (~c0_1(a671))),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 3.80/2.72 tff(2033,plain,
% 3.80/2.72 (c2_1(a671)),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[2032, 96, 146, 106, 2026, 2015, 116])).
% 3.80/2.72 tff(2034,plain,
% 3.80/2.72 (((~hskp62) | (~c1_1(a671))) <=> ((~hskp62) | (~c1_1(a671)))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2035,plain,
% 3.80/2.72 (((~c1_1(a671)) | (~hskp62)) <=> ((~hskp62) | (~c1_1(a671)))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2036,axiom,((~c1_1(a671)) | (~hskp62)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 3.80/2.72 tff(2037,plain,
% 3.80/2.72 ((~hskp62) | (~c1_1(a671))),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2036, 2035])).
% 3.80/2.72 tff(2038,plain,
% 3.80/2.72 ((~hskp62) | (~c1_1(a671))),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2037, 2034])).
% 3.80/2.72 tff(2039,plain,
% 3.80/2.72 (~c1_1(a671)),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[2038, 2004])).
% 3.80/2.72 tff(2040,plain,
% 3.80/2.72 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | c1_1(a671) | (~ndr1_0) | (~c2_1(a671)) | (~c0_1(a671)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a671) | (~ndr1_0) | (~c2_1(a671)) | (~c0_1(a671)))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2041,plain,
% 3.80/2.72 ((hskp15 | hskp14 | (~ndr1_0) | c1_1(a671) | (~c0_1(a671)) | (~c2_1(a671))) <=> (hskp15 | hskp14 | c1_1(a671) | (~ndr1_0) | (~c2_1(a671)) | (~c0_1(a671)))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2042,plain,
% 3.80/2.72 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a671) | (~c0_1(a671)) | (~c2_1(a671)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | c1_1(a671) | (~ndr1_0) | (~c2_1(a671)) | (~c0_1(a671))))),
% 3.80/2.72 inference(monotonicity,[status(thm)],[2041])).
% 3.80/2.72 tff(2043,plain,
% 3.80/2.72 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a671) | (~c0_1(a671)) | (~c2_1(a671)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a671) | (~ndr1_0) | (~c2_1(a671)) | (~c0_1(a671)))),
% 3.80/2.72 inference(transitivity,[status(thm)],[2042, 2040])).
% 3.80/2.72 tff(2044,plain,
% 3.80/2.72 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a671) | (~c0_1(a671)) | (~c2_1(a671)))),
% 3.80/2.72 inference(quant_inst,[status(thm)],[])).
% 3.80/2.72 tff(2045,plain,
% 3.80/2.72 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a671) | (~ndr1_0) | (~c2_1(a671)) | (~c0_1(a671))),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2044, 2043])).
% 3.80/2.72 tff(2046,plain,
% 3.80/2.72 ($false),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[2045, 96, 281, 280, 2015, 2039, 250, 2033])).
% 3.80/2.72 tff(2047,plain,((~hskp62) | hskp15 | hskp14 | hskp58 | hskp41), inference(lemma,lemma(discharge,[]))).
% 3.80/2.72 tff(2048,plain,
% 3.80/2.72 (~hskp62),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[2047, 1929, 281, 105, 106])).
% 3.80/2.72 tff(2049,plain,
% 3.80/2.72 (~c2_1(a603)),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[1246, 96, 281, 1929, 1902, 1928, 250])).
% 3.80/2.72 tff(2050,assumption,(~hskp9), introduced(assumption)).
% 3.80/2.72 tff(2051,plain,
% 3.80/2.72 (hskp16),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[1164, 2050, 12])).
% 3.80/2.72 tff(2052,plain,
% 3.80/2.72 (c0_1(a627)),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[1199, 2051])).
% 3.80/2.72 tff(2053,plain,
% 3.80/2.72 (c2_1(a627)),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[1181, 2051])).
% 3.80/2.72 tff(2054,plain,
% 3.80/2.72 (c1_1(a627)),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[1206, 96, 281, 280, 2053, 2052, 250])).
% 3.80/2.72 tff(2055,plain,
% 3.80/2.72 (^[U: $i] : refl((hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))),
% 3.80/2.72 inference(bind,[status(th)],[])).
% 3.80/2.72 tff(2056,plain,
% 3.80/2.72 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 3.80/2.72 inference(quant_intro,[status(thm)],[2055])).
% 3.80/2.72 tff(2057,plain,
% 3.80/2.72 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2058,plain,
% 3.80/2.72 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U))), ((((~ndr1_0) | c2_1(U)) | 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))), ((((~ndr1_0) | c2_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U)))), (((((~ndr1_0) | c2_1(U)) | 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))), (((((~ndr1_0) | c2_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), ((((((~ndr1_0) | c2_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp8))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), ((((((~ndr1_0) | c2_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), (((((((~ndr1_0) | c2_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp9) <=> ((hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp9))), rewrite(((hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), (((((((~ndr1_0) | c2_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))))),
% 3.80/2.72 inference(bind,[status(th)],[])).
% 3.80/2.72 tff(2059,plain,
% 3.80/2.72 (![U: $i] : ((((((~ndr1_0) | c2_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp9) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 3.80/2.72 inference(quant_intro,[status(thm)],[2058])).
% 3.80/2.72 tff(2060,axiom,(![U: $i] : ((((((~ndr1_0) | c2_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause277')).
% 3.80/2.72 tff(2061,plain,
% 3.80/2.72 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2060, 2059])).
% 3.80/2.72 tff(2062,plain,
% 3.80/2.72 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2061, 2057])).
% 3.80/2.72 tff(2063,plain,(
% 3.80/2.72 ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 3.80/2.72 inference(skolemize,[status(sab)],[2062])).
% 3.80/2.72 tff(2064,plain,
% 3.80/2.72 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2063, 2056])).
% 3.80/2.72 tff(2065,plain,
% 3.80/2.72 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp9 | hskp8 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp9 | hskp8 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2066,plain,
% 3.80/2.72 ((hskp9 | hskp8 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | c2_1(a603)) <=> (hskp9 | hskp8 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2067,plain,
% 3.80/2.72 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp9 | hskp8 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp9 | hskp8 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603)))),
% 3.80/2.72 inference(monotonicity,[status(thm)],[2066])).
% 3.80/2.72 tff(2068,plain,
% 3.80/2.72 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp9 | hskp8 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp9 | hskp8 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 3.80/2.72 inference(transitivity,[status(thm)],[2067, 2065])).
% 3.80/2.72 tff(2069,plain,
% 3.80/2.72 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp9 | hskp8 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | c2_1(a603))),
% 3.80/2.72 inference(quant_inst,[status(thm)],[])).
% 3.80/2.72 tff(2070,plain,
% 3.80/2.72 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp9 | hskp8 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2069, 2068])).
% 3.80/2.72 tff(2071,plain,
% 3.80/2.72 (hskp9 | hskp8 | c1_1(a603) | c2_1(a603)),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[2070, 96, 1030, 2064])).
% 3.80/2.72 tff(2072,plain,
% 3.80/2.72 (hskp8),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[2071, 2050, 1233, 1903])).
% 3.80/2.72 tff(2073,plain,
% 3.80/2.72 (((~hskp8) | (~c2_1(a612))) <=> ((~hskp8) | (~c2_1(a612)))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2074,plain,
% 3.80/2.72 (((~c2_1(a612)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a612)))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2075,axiom,((~c2_1(a612)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause259')).
% 3.80/2.72 tff(2076,plain,
% 3.80/2.72 ((~hskp8) | (~c2_1(a612))),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2075, 2074])).
% 3.80/2.72 tff(2077,plain,
% 3.80/2.72 ((~hskp8) | (~c2_1(a612))),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2076, 2073])).
% 3.80/2.72 tff(2078,plain,
% 3.80/2.72 (~c2_1(a612)),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[2077, 2072])).
% 3.80/2.72 tff(2079,plain,
% 3.80/2.72 (~c3_1(a627)),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[1170, 2051])).
% 3.80/2.72 tff(2080,plain,
% 3.80/2.72 (((~hskp8) | c3_1(a612)) <=> ((~hskp8) | c3_1(a612))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2081,axiom,((~hskp8) | c3_1(a612)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 3.80/2.72 tff(2082,plain,
% 3.80/2.72 ((~hskp8) | c3_1(a612)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2081, 2080])).
% 3.80/2.72 tff(2083,plain,
% 3.80/2.72 ((~hskp8) | c3_1(a612)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2082, 2080])).
% 3.80/2.72 tff(2084,plain,
% 3.80/2.72 ((~hskp8) | c3_1(a612)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2083, 2080])).
% 3.80/2.72 tff(2085,plain,
% 3.80/2.72 ((~hskp8) | c3_1(a612)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2084, 2080])).
% 3.80/2.72 tff(2086,plain,
% 3.80/2.72 ((~hskp8) | c3_1(a612)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2085, 2080])).
% 3.80/2.72 tff(2087,plain,
% 3.80/2.72 ((~hskp8) | c3_1(a612)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2086, 2080])).
% 3.80/2.72 tff(2088,plain,
% 3.80/2.72 ((~hskp8) | c3_1(a612)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2087, 2080])).
% 3.80/2.72 tff(2089,plain,
% 3.80/2.72 ((~hskp8) | c3_1(a612)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2088, 2080])).
% 3.80/2.72 tff(2090,plain,
% 3.80/2.72 (c3_1(a612)),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[2089, 2072])).
% 3.80/2.72 tff(2091,plain,
% 3.80/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c0_1(a673) | c3_1(a627) | c2_1(a612) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c3_1(a612)) | (~c0_1(a612)) | (~c2_1(a627)) | (~c1_1(a627)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c0_1(a673) | c3_1(a627) | c2_1(a612) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c3_1(a612)) | (~c0_1(a612)) | (~c2_1(a627)) | (~c1_1(a627)))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2092,plain,
% 3.80/2.72 (((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a673) | (~c2_1(a673)) | (~c3_1(a673)) | c2_1(a612) | (~c0_1(a612)) | (~c3_1(a612))) <=> (c0_1(a673) | c3_1(a627) | c2_1(a612) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c3_1(a612)) | (~c0_1(a612)) | (~c2_1(a627)) | (~c1_1(a627)))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2093,plain,
% 3.80/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a673) | (~c2_1(a673)) | (~c3_1(a673)) | c2_1(a612) | (~c0_1(a612)) | (~c3_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c0_1(a673) | c3_1(a627) | c2_1(a612) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c3_1(a612)) | (~c0_1(a612)) | (~c2_1(a627)) | (~c1_1(a627))))),
% 3.80/2.72 inference(monotonicity,[status(thm)],[2092])).
% 3.80/2.72 tff(2094,plain,
% 3.80/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a673) | (~c2_1(a673)) | (~c3_1(a673)) | c2_1(a612) | (~c0_1(a612)) | (~c3_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c0_1(a673) | c3_1(a627) | c2_1(a612) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c3_1(a612)) | (~c0_1(a612)) | (~c2_1(a627)) | (~c1_1(a627)))),
% 3.80/2.72 inference(transitivity,[status(thm)],[2093, 2091])).
% 3.80/2.72 tff(2095,plain,
% 3.80/2.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a673) | (~c2_1(a673)) | (~c3_1(a673)) | c2_1(a612) | (~c0_1(a612)) | (~c3_1(a612)))),
% 3.80/2.72 inference(quant_inst,[status(thm)],[])).
% 3.80/2.72 tff(2096,plain,
% 3.80/2.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c0_1(a673) | c3_1(a627) | c2_1(a612) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c3_1(a612)) | (~c0_1(a612)) | (~c2_1(a627)) | (~c1_1(a627))),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2095, 2094])).
% 3.80/2.72 tff(2097,plain,
% 3.80/2.72 (~c0_1(a612)),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[2096, 96, 1881, 2053, 2090, 1984, 2079, 2078, 1040, 1983, 2054])).
% 3.80/2.72 tff(2098,plain,
% 3.80/2.72 (((~hskp8) | (~c1_1(a612))) <=> ((~hskp8) | (~c1_1(a612)))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2099,plain,
% 3.80/2.72 (((~c1_1(a612)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a612)))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2100,axiom,((~c1_1(a612)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause260')).
% 3.80/2.72 tff(2101,plain,
% 3.80/2.72 ((~hskp8) | (~c1_1(a612))),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2100, 2099])).
% 3.80/2.72 tff(2102,plain,
% 3.80/2.72 ((~hskp8) | (~c1_1(a612))),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2101, 2098])).
% 3.80/2.72 tff(2103,plain,
% 3.80/2.72 (~c1_1(a612)),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[2102, 2072])).
% 3.80/2.72 tff(2104,plain,
% 3.80/2.72 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a612) | (~ndr1_0) | (~c3_1(a612)) | c0_1(a612))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a612) | (~ndr1_0) | (~c3_1(a612)) | c0_1(a612))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2105,plain,
% 3.80/2.72 ((hskp53 | hskp17 | (~ndr1_0) | c1_1(a612) | c0_1(a612) | (~c3_1(a612))) <=> (hskp53 | hskp17 | c1_1(a612) | (~ndr1_0) | (~c3_1(a612)) | c0_1(a612))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2106,plain,
% 3.80/2.72 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a612) | c0_1(a612) | (~c3_1(a612)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a612) | (~ndr1_0) | (~c3_1(a612)) | c0_1(a612)))),
% 3.80/2.72 inference(monotonicity,[status(thm)],[2105])).
% 3.80/2.72 tff(2107,plain,
% 3.80/2.72 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a612) | c0_1(a612) | (~c3_1(a612)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a612) | (~ndr1_0) | (~c3_1(a612)) | c0_1(a612))),
% 3.80/2.72 inference(transitivity,[status(thm)],[2106, 2104])).
% 3.80/2.72 tff(2108,plain,
% 3.80/2.72 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a612) | c0_1(a612) | (~c3_1(a612)))),
% 3.80/2.72 inference(quant_inst,[status(thm)],[])).
% 3.80/2.72 tff(2109,plain,
% 3.80/2.72 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a612) | (~ndr1_0) | (~c3_1(a612)) | c0_1(a612)),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2108, 2107])).
% 3.80/2.72 tff(2110,plain,
% 3.80/2.72 ($false),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[2109, 96, 35, 12, 2090, 2103, 34, 2097])).
% 3.80/2.72 tff(2111,plain,(hskp9 | hskp53 | hskp17 | (~c3_1(a673)) | c0_1(a673) | (~c2_1(a673)) | hskp15 | hskp14 | c1_1(a603) | c2_1(a603) | c3_1(a603)), inference(lemma,lemma(discharge,[]))).
% 3.80/2.72 tff(2112,plain,
% 3.80/2.72 (hskp9),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[2111, 2049, 12, 1788, 1814, 1030, 281, 1929, 1982, 1928, 35])).
% 3.80/2.72 tff(2113,plain,
% 3.80/2.72 (~hskp41),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[628, 35, 12, 583])).
% 3.80/2.72 tff(2114,plain,
% 3.80/2.72 (~hskp61),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[1916, 1903, 1030, 1233, 35, 12])).
% 3.80/2.72 tff(2115,plain,
% 3.80/2.72 (c2_1(a673)),
% 3.80/2.72 inference(unit_resolution,[status(thm)],[1896, 2114, 2113, 1881, 1880, 105])).
% 3.80/2.72 tff(2116,assumption,(c0_1(a613)), introduced(assumption)).
% 3.80/2.72 tff(2117,assumption,(~c3_1(a613)), introduced(assumption)).
% 3.80/2.72 tff(2118,assumption,(c2_1(a613)), introduced(assumption)).
% 3.80/2.72 tff(2119,assumption,(c1_1(a613)), introduced(assumption)).
% 3.80/2.72 tff(2120,plain,
% 3.80/2.72 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W))))),
% 3.80/2.72 inference(bind,[status(th)],[])).
% 3.80/2.72 tff(2121,plain,
% 3.80/2.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))),
% 3.80/2.72 inference(quant_intro,[status(thm)],[2120])).
% 3.80/2.72 tff(2122,plain,
% 3.80/2.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2123,plain,
% 3.80/2.72 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c0_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) <=> (((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))))), rewrite((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), (((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W)))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))))), ((((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) | (~c0_1(W))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))))),
% 3.80/2.72 inference(bind,[status(th)],[])).
% 3.80/2.72 tff(2124,plain,
% 3.80/2.72 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))),
% 3.80/2.72 inference(quant_intro,[status(thm)],[2123])).
% 3.80/2.72 tff(2125,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause328')).
% 3.80/2.72 tff(2126,plain,
% 3.80/2.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2125, 2124])).
% 3.80/2.72 tff(2127,plain,
% 3.80/2.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2126, 2122])).
% 3.80/2.72 tff(2128,plain,(
% 3.80/2.72 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))),
% 3.80/2.72 inference(skolemize,[status(sab)],[2127])).
% 3.80/2.72 tff(2129,plain,
% 3.80/2.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))),
% 3.80/2.72 inference(modus_ponens,[status(thm)],[2128, 2121])).
% 3.80/2.72 tff(2130,plain,
% 3.80/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | (c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a613)) | (~c3_1(a671)) | (~c2_1(a671)) | (~c0_1(a671)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a613)) | (~c3_1(a671)) | (~c2_1(a671)) | (~c0_1(a671)))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(2131,plain,
% 3.80/2.72 (((~ndr1_0) | (~c3_1(a671)) | (~c0_1(a671)) | (~c2_1(a671)) | c3_1(a613) | (~c2_1(a613)) | (~c0_1(a613)) | (~c0_1(a613)) | (~c1_1(a613)) | (~c2_1(a613))) <=> (c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a613)) | (~c3_1(a671)) | (~c2_1(a671)) | (~c0_1(a671)))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2132,plain,
% 3.80/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a671)) | (~c0_1(a671)) | (~c2_1(a671)) | c3_1(a613) | (~c2_1(a613)) | (~c0_1(a613)) | (~c0_1(a613)) | (~c1_1(a613)) | (~c2_1(a613)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | (c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a613)) | (~c3_1(a671)) | (~c2_1(a671)) | (~c0_1(a671))))),
% 3.80/2.73 inference(monotonicity,[status(thm)],[2131])).
% 3.80/2.73 tff(2133,plain,
% 3.80/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a671)) | (~c0_1(a671)) | (~c2_1(a671)) | c3_1(a613) | (~c2_1(a613)) | (~c0_1(a613)) | (~c0_1(a613)) | (~c1_1(a613)) | (~c2_1(a613)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a613)) | (~c3_1(a671)) | (~c2_1(a671)) | (~c0_1(a671)))),
% 3.80/2.73 inference(transitivity,[status(thm)],[2132, 2130])).
% 3.80/2.73 tff(2134,plain,
% 3.80/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a671)) | (~c0_1(a671)) | (~c2_1(a671)) | c3_1(a613) | (~c2_1(a613)) | (~c0_1(a613)) | (~c0_1(a613)) | (~c1_1(a613)) | (~c2_1(a613)))),
% 3.80/2.73 inference(quant_inst,[status(thm)],[])).
% 3.80/2.73 tff(2135,plain,
% 3.80/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a613)) | (~c3_1(a671)) | (~c2_1(a671)) | (~c0_1(a671))),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2134, 2133])).
% 3.80/2.73 tff(2136,plain,
% 3.80/2.73 (~c2_1(a671)),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2135, 96, 2026, 2015, 2119, 2118, 2117, 2129, 2116])).
% 3.80/2.73 tff(2137,assumption,(~c2_1(a669)), introduced(assumption)).
% 3.80/2.73 tff(2138,assumption,(c1_1(a669)), introduced(assumption)).
% 3.80/2.73 tff(2139,assumption,(c0_1(a669)), introduced(assumption)).
% 3.80/2.73 tff(2140,plain,
% 3.80/2.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c1_1(a671) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a671)) | c2_1(a671))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c1_1(a671) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a671)) | c2_1(a671))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2141,plain,
% 3.80/2.73 ((hskp5 | (~ndr1_0) | c1_1(a671) | c2_1(a671) | (~c3_1(a671)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669))) <=> (hskp5 | c1_1(a671) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a671)) | c2_1(a671))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2142,plain,
% 3.80/2.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a671) | c2_1(a671) | (~c3_1(a671)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c1_1(a671) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a671)) | c2_1(a671)))),
% 3.80/2.73 inference(monotonicity,[status(thm)],[2141])).
% 3.80/2.73 tff(2143,plain,
% 3.80/2.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a671) | c2_1(a671) | (~c3_1(a671)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c1_1(a671) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a671)) | c2_1(a671))),
% 3.80/2.73 inference(transitivity,[status(thm)],[2142, 2140])).
% 3.80/2.73 tff(2144,plain,
% 3.80/2.73 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a671) | c2_1(a671) | (~c3_1(a671)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))),
% 3.80/2.73 inference(quant_inst,[status(thm)],[])).
% 3.80/2.73 tff(2145,plain,
% 3.80/2.73 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c1_1(a671) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a671)) | c2_1(a671)),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2144, 2143])).
% 3.80/2.73 tff(2146,plain,
% 3.80/2.73 ($false),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2145, 96, 583, 2026, 2139, 2138, 2039, 2137, 567, 2136])).
% 3.80/2.73 tff(2147,plain,((~hskp62) | hskp5 | (~c0_1(a669)) | (~c1_1(a669)) | c2_1(a669) | (~c1_1(a613)) | (~c2_1(a613)) | c3_1(a613) | (~c0_1(a613))), inference(lemma,lemma(discharge,[]))).
% 3.80/2.73 tff(2148,plain,
% 3.80/2.73 (~hskp62),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2147, 359, 583, 348, 336, 2119, 2118, 2117, 2116])).
% 3.80/2.73 tff(2149,plain,
% 3.80/2.73 (^[U: $i] : refl((hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))),
% 3.80/2.73 inference(bind,[status(th)],[])).
% 3.80/2.73 tff(2150,plain,
% 3.80/2.73 (![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 3.80/2.73 inference(quant_intro,[status(thm)],[2149])).
% 3.80/2.73 tff(2151,plain,
% 3.80/2.73 (![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2152,plain,
% 3.80/2.73 (^[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)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c3_1(U)) | 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) | c3_1(U) | c1_1(U) | c2_1(U))), (((((~ndr1_0) | c1_1(U)) | c3_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c3_1(U)) | c2_1(U)) | hskp62) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp62))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp62) <=> (hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), ((((((~ndr1_0) | c1_1(U)) | c3_1(U)) | c2_1(U)) | hskp62) <=> (hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c3_1(U)) | c2_1(U)) | hskp62) | hskp63) <=> ((hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp63))), rewrite(((hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp63) <=> (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), (((((((~ndr1_0) | c1_1(U)) | c3_1(U)) | c2_1(U)) | hskp62) | hskp63) <=> (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))))),
% 3.80/2.73 inference(bind,[status(th)],[])).
% 3.80/2.73 tff(2153,plain,
% 3.80/2.73 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c3_1(U)) | c2_1(U)) | hskp62) | hskp63) <=> ![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 3.80/2.73 inference(quant_intro,[status(thm)],[2152])).
% 3.80/2.73 tff(2154,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c3_1(U)) | c2_1(U)) | hskp62) | hskp63)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause279')).
% 3.80/2.73 tff(2155,plain,
% 3.80/2.73 (![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2154, 2153])).
% 3.80/2.73 tff(2156,plain,
% 3.80/2.73 (![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2155, 2151])).
% 3.80/2.73 tff(2157,plain,(
% 3.80/2.73 ![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 3.80/2.73 inference(skolemize,[status(sab)],[2156])).
% 3.80/2.73 tff(2158,plain,
% 3.80/2.73 (![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2157, 2150])).
% 3.80/2.73 tff(2159,plain,
% 3.80/2.73 (((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))) <=> ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp63 | hskp62 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2160,plain,
% 3.80/2.73 ((hskp63 | hskp62 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | c2_1(a603)) <=> (hskp63 | hskp62 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2161,plain,
% 3.80/2.73 (((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603)))),
% 3.80/2.73 inference(monotonicity,[status(thm)],[2160])).
% 3.80/2.73 tff(2162,plain,
% 3.80/2.73 (((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp63 | hskp62 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 3.80/2.73 inference(transitivity,[status(thm)],[2161, 2159])).
% 3.80/2.73 tff(2163,plain,
% 3.80/2.73 ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | c2_1(a603))),
% 3.80/2.73 inference(quant_inst,[status(thm)],[])).
% 3.80/2.73 tff(2164,plain,
% 3.80/2.73 ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp63 | hskp62 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603)),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2163, 2162])).
% 3.80/2.73 tff(2165,plain,
% 3.80/2.73 (hskp63 | hskp62 | c1_1(a603) | c2_1(a603)),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2164, 96, 1030, 2158])).
% 3.80/2.73 tff(2166,plain,
% 3.80/2.73 (hskp63),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2165, 2148, 1233, 1903])).
% 3.80/2.73 tff(2167,plain,
% 3.80/2.73 (((~hskp63) | (~c0_1(a672))) <=> ((~hskp63) | (~c0_1(a672)))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2168,plain,
% 3.80/2.73 (((~c0_1(a672)) | (~hskp63)) <=> ((~hskp63) | (~c0_1(a672)))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2169,axiom,((~c0_1(a672)) | (~hskp63)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 3.80/2.73 tff(2170,plain,
% 3.80/2.73 ((~hskp63) | (~c0_1(a672))),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2169, 2168])).
% 3.80/2.73 tff(2171,plain,
% 3.80/2.73 ((~hskp63) | (~c0_1(a672))),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2170, 2167])).
% 3.80/2.73 tff(2172,plain,
% 3.80/2.73 (~c0_1(a672)),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2171, 2166])).
% 3.80/2.73 tff(2173,plain,
% 3.80/2.73 (((~hskp63) | c3_1(a672)) <=> ((~hskp63) | c3_1(a672))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2174,axiom,((~hskp63) | c3_1(a672)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 3.80/2.73 tff(2175,plain,
% 3.80/2.73 ((~hskp63) | c3_1(a672)),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2174, 2173])).
% 3.80/2.73 tff(2176,plain,
% 3.80/2.73 ((~hskp63) | c3_1(a672)),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2175, 2173])).
% 3.80/2.73 tff(2177,plain,
% 3.80/2.73 ((~hskp63) | c3_1(a672)),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2176, 2173])).
% 3.80/2.73 tff(2178,plain,
% 3.80/2.73 ((~hskp63) | c3_1(a672)),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2177, 2173])).
% 3.80/2.73 tff(2179,plain,
% 3.80/2.73 ((~hskp63) | c3_1(a672)),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2178, 2173])).
% 3.80/2.73 tff(2180,plain,
% 3.80/2.73 ((~hskp63) | c3_1(a672)),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2179, 2173])).
% 3.80/2.73 tff(2181,plain,
% 3.80/2.73 ((~hskp63) | c3_1(a672)),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2180, 2173])).
% 3.80/2.73 tff(2182,plain,
% 3.80/2.73 ((~hskp63) | c3_1(a672)),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2181, 2173])).
% 3.80/2.73 tff(2183,plain,
% 3.80/2.73 (c3_1(a672)),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2182, 2166])).
% 3.80/2.73 tff(2184,plain,
% 3.80/2.73 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c0_1(a672) | (~ndr1_0) | (~c3_1(a672)) | c1_1(a672))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c0_1(a672) | (~ndr1_0) | (~c3_1(a672)) | c1_1(a672))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2185,plain,
% 3.80/2.73 ((hskp53 | hskp17 | (~ndr1_0) | c1_1(a672) | c0_1(a672) | (~c3_1(a672))) <=> (hskp53 | hskp17 | c0_1(a672) | (~ndr1_0) | (~c3_1(a672)) | c1_1(a672))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2186,plain,
% 3.80/2.73 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a672) | c0_1(a672) | (~c3_1(a672)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c0_1(a672) | (~ndr1_0) | (~c3_1(a672)) | c1_1(a672)))),
% 3.80/2.73 inference(monotonicity,[status(thm)],[2185])).
% 3.80/2.73 tff(2187,plain,
% 3.80/2.73 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a672) | c0_1(a672) | (~c3_1(a672)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c0_1(a672) | (~ndr1_0) | (~c3_1(a672)) | c1_1(a672))),
% 3.80/2.73 inference(transitivity,[status(thm)],[2186, 2184])).
% 3.80/2.73 tff(2188,plain,
% 3.80/2.73 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a672) | c0_1(a672) | (~c3_1(a672)))),
% 3.80/2.73 inference(quant_inst,[status(thm)],[])).
% 3.80/2.73 tff(2189,plain,
% 3.80/2.73 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c0_1(a672) | (~ndr1_0) | (~c3_1(a672)) | c1_1(a672)),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2188, 2187])).
% 3.80/2.73 tff(2190,plain,
% 3.80/2.73 (c1_1(a672)),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2189, 96, 35, 12, 2183, 2172, 34])).
% 3.80/2.73 tff(2191,plain,
% 3.80/2.73 (((~hskp63) | (~c2_1(a672))) <=> ((~hskp63) | (~c2_1(a672)))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2192,plain,
% 3.80/2.73 (((~c2_1(a672)) | (~hskp63)) <=> ((~hskp63) | (~c2_1(a672)))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2193,axiom,((~c2_1(a672)) | (~hskp63)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 3.80/2.73 tff(2194,plain,
% 3.80/2.73 ((~hskp63) | (~c2_1(a672))),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2193, 2192])).
% 3.80/2.73 tff(2195,plain,
% 3.80/2.73 ((~hskp63) | (~c2_1(a672))),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2194, 2191])).
% 3.80/2.73 tff(2196,plain,
% 3.80/2.73 (~c2_1(a672)),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2195, 2166])).
% 3.80/2.73 tff(2197,plain,
% 3.80/2.73 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a672) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a672)) | (~c1_1(a672)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a672) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a672)) | (~c1_1(a672)))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2198,plain,
% 3.80/2.73 ((hskp41 | (~ndr1_0) | c2_1(a672) | (~c3_1(a672)) | (~c1_1(a672)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669))) <=> (hskp41 | c2_1(a672) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a672)) | (~c1_1(a672)))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2199,plain,
% 3.80/2.73 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a672) | (~c3_1(a672)) | (~c1_1(a672)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a672) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a672)) | (~c1_1(a672))))),
% 3.80/2.73 inference(monotonicity,[status(thm)],[2198])).
% 3.80/2.73 tff(2200,plain,
% 3.80/2.73 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a672) | (~c3_1(a672)) | (~c1_1(a672)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a672) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a672)) | (~c1_1(a672)))),
% 3.80/2.73 inference(transitivity,[status(thm)],[2199, 2197])).
% 3.80/2.73 tff(2201,plain,
% 3.80/2.73 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a672) | (~c3_1(a672)) | (~c1_1(a672)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))),
% 3.80/2.73 inference(quant_inst,[status(thm)],[])).
% 3.80/2.73 tff(2202,plain,
% 3.80/2.73 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a672) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a672)) | (~c1_1(a672))),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2201, 2200])).
% 3.80/2.73 tff(2203,plain,
% 3.80/2.73 ($false),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2202, 96, 106, 2183, 359, 348, 2196, 336, 329, 2190])).
% 3.80/2.73 tff(2204,plain,((~hskp60) | hskp41 | hskp53 | hskp17 | c1_1(a603) | c2_1(a603) | c3_1(a603) | hskp5 | (~c1_1(a613)) | (~c2_1(a613)) | c3_1(a613) | (~c0_1(a613))), inference(lemma,lemma(discharge,[]))).
% 3.80/2.73 tff(2205,plain,
% 3.80/2.73 (~c0_1(a613)),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2204, 1142, 35, 12, 1233, 1903, 1030, 583, 330, 1131, 1119, 106])).
% 3.80/2.73 tff(2206,plain,
% 3.80/2.73 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a673) | c3_1(a613) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a613)) | c0_1(a613))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a673) | c3_1(a613) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a613)) | c0_1(a613))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2207,plain,
% 3.80/2.73 (((~ndr1_0) | c3_1(a613) | c0_1(a613) | (~c2_1(a613)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673))) <=> (c0_1(a673) | c3_1(a613) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a613)) | c0_1(a613))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2208,plain,
% 3.80/2.73 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a613) | c0_1(a613) | (~c2_1(a613)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a673) | c3_1(a613) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a613)) | c0_1(a613)))),
% 3.80/2.73 inference(monotonicity,[status(thm)],[2207])).
% 3.80/2.73 tff(2209,plain,
% 3.80/2.73 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a613) | c0_1(a613) | (~c2_1(a613)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a673) | c3_1(a613) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a613)) | c0_1(a613))),
% 3.80/2.73 inference(transitivity,[status(thm)],[2208, 2206])).
% 3.80/2.73 tff(2210,plain,
% 3.80/2.73 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a613) | c0_1(a613) | (~c2_1(a613)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673)))),
% 3.80/2.73 inference(quant_inst,[status(thm)],[])).
% 3.80/2.73 tff(2211,plain,
% 3.80/2.73 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a673) | c3_1(a613) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a613)) | c0_1(a613)),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2210, 2209])).
% 3.80/2.73 tff(2212,plain,
% 3.80/2.73 ($false),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2211, 96, 1880, 1131, 1984, 1119, 23, 1983, 2205])).
% 3.80/2.73 tff(2213,plain,((~hskp9) | (~c1_1(a673)) | c0_1(a673) | (~c2_1(a673)) | hskp53 | hskp17 | c1_1(a603) | c2_1(a603) | c3_1(a603) | hskp5 | (~hskp60) | hskp41), inference(lemma,lemma(discharge,[]))).
% 3.80/2.73 tff(2214,plain,
% 3.80/2.73 (~hskp60),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2213, 1113, 1984, 2115, 35, 12, 1233, 1903, 1030, 583, 1880, 2113])).
% 3.80/2.73 tff(2215,plain,
% 3.80/2.73 (hskp33),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[381, 2214, 2114])).
% 3.80/2.73 tff(2216,plain,
% 3.80/2.73 (~c2_1(a599)),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[122, 2215])).
% 3.80/2.73 tff(2217,plain,
% 3.80/2.73 (c3_1(a599)),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[133, 2215])).
% 3.80/2.73 tff(2218,plain,
% 3.80/2.73 (c0_1(a599)),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[144, 2215])).
% 3.80/2.73 tff(2219,plain,
% 3.80/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c0_1(a673) | c2_1(a599) | c3_1(a613) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a599)) | (~c3_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c0_1(a673) | c2_1(a599) | c3_1(a613) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a599)) | (~c3_1(a599)))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2220,plain,
% 3.80/2.73 (((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a673) | (~c2_1(a673)) | (~c3_1(a673)) | c2_1(a599) | (~c0_1(a599)) | (~c3_1(a599))) <=> (c0_1(a673) | c2_1(a599) | c3_1(a613) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a599)) | (~c3_1(a599)))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2221,plain,
% 3.80/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a673) | (~c2_1(a673)) | (~c3_1(a673)) | c2_1(a599) | (~c0_1(a599)) | (~c3_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c0_1(a673) | c2_1(a599) | c3_1(a613) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a599)) | (~c3_1(a599))))),
% 3.80/2.73 inference(monotonicity,[status(thm)],[2220])).
% 3.80/2.73 tff(2222,plain,
% 3.80/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a673) | (~c2_1(a673)) | (~c3_1(a673)) | c2_1(a599) | (~c0_1(a599)) | (~c3_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c0_1(a673) | c2_1(a599) | c3_1(a613) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a599)) | (~c3_1(a599)))),
% 3.80/2.73 inference(transitivity,[status(thm)],[2221, 2219])).
% 3.80/2.73 tff(2223,plain,
% 3.80/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a673) | (~c2_1(a673)) | (~c3_1(a673)) | c2_1(a599) | (~c0_1(a599)) | (~c3_1(a599)))),
% 3.80/2.73 inference(quant_inst,[status(thm)],[])).
% 3.80/2.73 tff(2224,plain,
% 3.80/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c0_1(a673) | c2_1(a599) | c3_1(a613) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a599)) | (~c3_1(a599))),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2223, 2222])).
% 3.80/2.73 tff(2225,plain,
% 3.80/2.73 ($false),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2224, 96, 1881, 2218, 2217, 1142, 1131, 1984, 2216, 1119, 1040, 2115])).
% 3.80/2.73 tff(2226,plain,((~hskp9) | (~c3_1(a673)) | c0_1(a673) | hskp53 | hskp17 | c1_1(a603) | c2_1(a603) | c3_1(a603) | hskp5 | (~c1_1(a673))), inference(lemma,lemma(discharge,[]))).
% 3.80/2.73 tff(2227,plain,
% 3.80/2.73 (hskp5),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2226, 2049, 1825, 1814, 12, 35, 1928, 1030, 2112, 1788])).
% 3.80/2.73 tff(2228,plain,
% 3.80/2.73 (~c0_1(a606)),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[640, 2227])).
% 3.80/2.73 tff(2229,plain,
% 3.80/2.73 (~c3_1(a606)),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[634, 2227])).
% 3.80/2.73 tff(2230,plain,
% 3.80/2.73 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c0_1(a606) | c3_1(a606) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a606)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c0_1(a606) | c3_1(a606) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a606)))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2231,plain,
% 3.80/2.73 (((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c1_1(a603) | c3_1(a603) | c2_1(a603)) <=> (c0_1(a606) | c3_1(a606) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a606)))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2232,plain,
% 3.80/2.73 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c1_1(a603) | c3_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c0_1(a606) | c3_1(a606) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a606))))),
% 3.80/2.73 inference(monotonicity,[status(thm)],[2231])).
% 3.80/2.73 tff(2233,plain,
% 3.80/2.73 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c1_1(a603) | c3_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c0_1(a606) | c3_1(a606) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a606)))),
% 3.80/2.73 inference(transitivity,[status(thm)],[2232, 2230])).
% 3.80/2.73 tff(2234,plain,
% 3.80/2.73 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c1_1(a603) | c3_1(a603) | c2_1(a603))),
% 3.80/2.73 inference(quant_inst,[status(thm)],[])).
% 3.80/2.73 tff(2235,plain,
% 3.80/2.73 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c0_1(a606) | c3_1(a606) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a606))),
% 3.80/2.73 inference(modus_ponens,[status(thm)],[2234, 2233])).
% 3.80/2.73 tff(2236,plain,
% 3.80/2.73 (c0_1(a606) | c2_1(a603) | (~c2_1(a606))),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2235, 96, 663, 1233, 1030, 662])).
% 3.80/2.73 tff(2237,plain,
% 3.80/2.73 (~c2_1(a606)),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2236, 1903, 664])).
% 3.80/2.73 tff(2238,assumption,(hskp8), introduced(assumption)).
% 3.80/2.73 tff(2239,plain,
% 3.80/2.73 (~c1_1(a612)),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2102, 2238])).
% 3.80/2.73 tff(2240,plain,
% 3.80/2.73 (~c2_1(a612)),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2077, 2238])).
% 3.80/2.73 tff(2241,assumption,(~c2_1(a606)), introduced(assumption)).
% 3.80/2.73 tff(2242,plain,
% 3.80/2.73 (c3_1(a612)),
% 3.80/2.73 inference(unit_resolution,[status(thm)],[2089, 2238])).
% 3.80/2.73 tff(2243,plain,
% 3.80/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a606) | c2_1(a612) | c1_1(a612) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c3_1(a612)) | (~c0_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a606) | c2_1(a612) | c1_1(a612) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c3_1(a612)) | (~c0_1(a612)))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2244,plain,
% 3.80/2.73 (((~ndr1_0) | c1_1(a612) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a612) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | c0_1(a606) | c3_1(a606)) <=> (c2_1(a606) | c2_1(a612) | c1_1(a612) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c3_1(a612)) | (~c0_1(a612)))),
% 3.80/2.73 inference(rewrite,[status(thm)],[])).
% 3.80/2.73 tff(2245,plain,
% 3.80/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a612) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a612) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | c0_1(a606) | c3_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a606) | c2_1(a612) | c1_1(a612) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c3_1(a612)) | (~c0_1(a612))))),
% 3.82/2.73 inference(monotonicity,[status(thm)],[2244])).
% 3.82/2.73 tff(2246,plain,
% 3.82/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a612) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a612) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | c0_1(a606) | c3_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a606) | c2_1(a612) | c1_1(a612) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c3_1(a612)) | (~c0_1(a612)))),
% 3.82/2.73 inference(transitivity,[status(thm)],[2245, 2243])).
% 3.82/2.73 tff(2247,plain,
% 3.82/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a612) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a612) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | c0_1(a606) | c3_1(a606))),
% 3.82/2.73 inference(quant_inst,[status(thm)],[])).
% 3.82/2.73 tff(2248,plain,
% 3.82/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a606) | c2_1(a612) | c1_1(a612) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c3_1(a612)) | (~c0_1(a612))),
% 3.82/2.73 inference(modus_ponens,[status(thm)],[2247, 2246])).
% 3.82/2.73 tff(2249,plain,
% 3.82/2.73 (~c0_1(a612)),
% 3.82/2.73 inference(unit_resolution,[status(thm)],[2248, 96, 2242, 2241, 2240, 2239, 664, 663, 997])).
% 3.82/2.73 tff(2250,plain,
% 3.82/2.73 ($false),
% 3.82/2.73 inference(unit_resolution,[status(thm)],[2109, 96, 35, 12, 2242, 2239, 34, 2249])).
% 3.82/2.73 tff(2251,plain,((~hskp8) | hskp53 | hskp17 | c2_1(a606) | c0_1(a606) | c3_1(a606)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.73 tff(2252,plain,
% 3.82/2.73 (~hskp8),
% 3.82/2.73 inference(unit_resolution,[status(thm)],[2251, 35, 12, 2237, 664, 663])).
% 3.82/2.73 tff(2253,plain,
% 3.82/2.73 (hskp9),
% 3.82/2.73 inference(unit_resolution,[status(thm)],[2071, 2252, 1233, 1903])).
% 3.82/2.73 tff(2254,plain,
% 3.82/2.73 (~c3_1(a613)),
% 3.82/2.73 inference(unit_resolution,[status(thm)],[1118, 2253])).
% 3.82/2.73 tff(2255,plain,
% 3.82/2.73 (c2_1(a613)),
% 3.82/2.73 inference(unit_resolution,[status(thm)],[1130, 2253])).
% 3.82/2.73 tff(2256,plain,
% 3.82/2.73 (~hskp5),
% 3.82/2.73 inference(unit_resolution,[status(thm)],[651, 2237])).
% 3.82/2.73 tff(2257,plain,
% 3.82/2.73 (c1_1(a613)),
% 3.82/2.73 inference(unit_resolution,[status(thm)],[1141, 2253])).
% 3.82/2.73 tff(2258,plain,
% 3.82/2.73 (~c0_1(a613)),
% 3.82/2.73 inference(unit_resolution,[status(thm)],[2204, 2257, 330, 12, 1233, 1903, 1030, 2256, 35, 2255, 2254, 106])).
% 3.82/2.73 tff(2259,plain,
% 3.82/2.73 ($false),
% 3.82/2.73 inference(unit_resolution,[status(thm)],[2211, 96, 1880, 2255, 1984, 2254, 23, 1983, 2258])).
% 3.82/2.73 tff(2260,plain,(hskp53 | (~c1_1(a673)) | c0_1(a673) | (~c2_1(a673)) | (~hskp60) | hskp17 | c1_1(a603) | c2_1(a603) | c3_1(a603) | hskp41 | c0_1(a606) | c3_1(a606)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.73 tff(2261,plain,
% 3.82/2.73 ($false),
% 3.82/2.73 inference(unit_resolution,[status(thm)],[2260, 2229, 2228, 1814, 1825, 35, 12, 1982, 1928, 1030, 106, 2049, 2001])).
% 3.82/2.73 tff(2262,plain,((~hskp3) | hskp53 | hskp17 | c3_1(a603) | hskp41 | hskp15), inference(lemma,lemma(discharge,[]))).
% 3.82/2.73 tff(2263,plain,
% 3.82/2.73 (~hskp3),
% 3.82/2.73 inference(unit_resolution,[status(thm)],[2262, 35, 12, 1030, 106, 281])).
% 3.82/2.73 tff(2264,assumption,(~hskp3), introduced(assumption)).
% 3.82/2.73 tff(2265,assumption,(~hskp29), introduced(assumption)).
% 3.82/2.73 tff(2266,assumption,(hskp25), introduced(assumption)).
% 3.82/2.73 tff(2267,plain,
% 3.82/2.73 (((~hskp25) | (~c0_1(a646))) <=> ((~hskp25) | (~c0_1(a646)))),
% 3.82/2.73 inference(rewrite,[status(thm)],[])).
% 3.82/2.73 tff(2268,plain,
% 3.82/2.73 (((~c0_1(a646)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a646)))),
% 3.82/2.73 inference(rewrite,[status(thm)],[])).
% 3.82/2.73 tff(2269,axiom,((~c0_1(a646)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause228')).
% 3.82/2.73 tff(2270,plain,
% 3.82/2.73 ((~hskp25) | (~c0_1(a646))),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2269, 2268])).
% 3.82/2.74 tff(2271,plain,
% 3.82/2.74 ((~hskp25) | (~c0_1(a646))),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2270, 2267])).
% 3.82/2.74 tff(2272,plain,
% 3.82/2.74 (~c0_1(a646)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2271, 2266])).
% 3.82/2.74 tff(2273,plain,
% 3.82/2.74 (((~hskp25) | (~c2_1(a646))) <=> ((~hskp25) | (~c2_1(a646)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2274,plain,
% 3.82/2.74 (((~c2_1(a646)) | (~hskp25)) <=> ((~hskp25) | (~c2_1(a646)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2275,axiom,((~c2_1(a646)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause227')).
% 3.82/2.74 tff(2276,plain,
% 3.82/2.74 ((~hskp25) | (~c2_1(a646))),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2275, 2274])).
% 3.82/2.74 tff(2277,plain,
% 3.82/2.74 ((~hskp25) | (~c2_1(a646))),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2276, 2273])).
% 3.82/2.74 tff(2278,plain,
% 3.82/2.74 (~c2_1(a646)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2277, 2266])).
% 3.82/2.74 tff(2279,plain,
% 3.82/2.74 (((~hskp25) | c3_1(a646)) <=> ((~hskp25) | c3_1(a646))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2280,axiom,((~hskp25) | c3_1(a646)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 3.82/2.74 tff(2281,plain,
% 3.82/2.74 ((~hskp25) | c3_1(a646)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2280, 2279])).
% 3.82/2.74 tff(2282,plain,
% 3.82/2.74 ((~hskp25) | c3_1(a646)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2281, 2279])).
% 3.82/2.74 tff(2283,plain,
% 3.82/2.74 ((~hskp25) | c3_1(a646)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2282, 2279])).
% 3.82/2.74 tff(2284,plain,
% 3.82/2.74 ((~hskp25) | c3_1(a646)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2283, 2279])).
% 3.82/2.74 tff(2285,plain,
% 3.82/2.74 ((~hskp25) | c3_1(a646)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2284, 2279])).
% 3.82/2.74 tff(2286,plain,
% 3.82/2.74 ((~hskp25) | c3_1(a646)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2285, 2279])).
% 3.82/2.74 tff(2287,plain,
% 3.82/2.74 ((~hskp25) | c3_1(a646)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2286, 2279])).
% 3.82/2.74 tff(2288,plain,
% 3.82/2.74 ((~hskp25) | c3_1(a646)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2287, 2279])).
% 3.82/2.74 tff(2289,plain,
% 3.82/2.74 (c3_1(a646)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2288, 2266])).
% 3.82/2.74 tff(2290,plain,
% 3.82/2.74 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a646) | c0_1(a646) | (~ndr1_0) | (~c3_1(a646)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a646) | c0_1(a646) | (~ndr1_0) | (~c3_1(a646)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2291,plain,
% 3.82/2.74 ((hskp29 | hskp3 | (~ndr1_0) | c2_1(a646) | c0_1(a646) | (~c3_1(a646))) <=> (hskp29 | hskp3 | c2_1(a646) | c0_1(a646) | (~ndr1_0) | (~c3_1(a646)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2292,plain,
% 3.82/2.74 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a646) | c0_1(a646) | (~c3_1(a646)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a646) | c0_1(a646) | (~ndr1_0) | (~c3_1(a646))))),
% 3.82/2.74 inference(monotonicity,[status(thm)],[2291])).
% 3.82/2.74 tff(2293,plain,
% 3.82/2.74 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a646) | c0_1(a646) | (~c3_1(a646)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a646) | c0_1(a646) | (~ndr1_0) | (~c3_1(a646)))),
% 3.82/2.74 inference(transitivity,[status(thm)],[2292, 2290])).
% 3.82/2.74 tff(2294,plain,
% 3.82/2.74 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a646) | c0_1(a646) | (~c3_1(a646)))),
% 3.82/2.74 inference(quant_inst,[status(thm)],[])).
% 3.82/2.74 tff(2295,plain,
% 3.82/2.74 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a646) | c0_1(a646) | (~ndr1_0) | (~c3_1(a646))),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2294, 2293])).
% 3.82/2.74 tff(2296,plain,
% 3.82/2.74 ($false),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2295, 96, 2265, 2264, 2289, 2278, 2272, 1024])).
% 3.82/2.74 tff(2297,plain,((~hskp25) | hskp29 | hskp3), inference(lemma,lemma(discharge,[]))).
% 3.82/2.74 tff(2298,plain,
% 3.82/2.74 (~hskp25),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2297, 2265, 2264])).
% 3.82/2.74 tff(2299,plain,
% 3.82/2.74 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c3_1(a669)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c3_1(a669)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2300,plain,
% 3.82/2.74 ((hskp58 | hskp41 | (~ndr1_0) | c2_1(a669) | (~c3_1(a669)) | (~c0_1(a669))) <=> (hskp58 | hskp41 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c3_1(a669)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2301,plain,
% 3.82/2.74 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a669) | (~c3_1(a669)) | (~c0_1(a669)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c3_1(a669))))),
% 3.82/2.74 inference(monotonicity,[status(thm)],[2300])).
% 3.82/2.74 tff(2302,plain,
% 3.82/2.74 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a669) | (~c3_1(a669)) | (~c0_1(a669)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c3_1(a669)))),
% 3.82/2.74 inference(transitivity,[status(thm)],[2301, 2299])).
% 3.82/2.74 tff(2303,plain,
% 3.82/2.74 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a669) | (~c3_1(a669)) | (~c0_1(a669)))),
% 3.82/2.74 inference(quant_inst,[status(thm)],[])).
% 3.82/2.74 tff(2304,plain,
% 3.82/2.74 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c3_1(a669))),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2303, 2302])).
% 3.82/2.74 tff(2305,plain,
% 3.82/2.74 (~c3_1(a669)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2304, 96, 146, 106, 2139, 2137, 116])).
% 3.82/2.74 tff(2306,plain,
% 3.82/2.74 (^[U: $i] : refl((hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 3.82/2.74 inference(bind,[status(th)],[])).
% 3.82/2.74 tff(2307,plain,
% 3.82/2.74 (![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 3.82/2.74 inference(quant_intro,[status(thm)],[2306])).
% 3.82/2.74 tff(2308,plain,
% 3.82/2.74 (![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2309,plain,
% 3.82/2.74 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_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)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) | hskp25) | hskp52) <=> ((hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp52))), rewrite(((hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp52) <=> (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) | hskp25) | hskp52) <=> (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 3.82/2.74 inference(bind,[status(th)],[])).
% 3.82/2.74 tff(2310,plain,
% 3.82/2.74 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) | hskp25) | hskp52) <=> ![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 3.82/2.74 inference(quant_intro,[status(thm)],[2309])).
% 3.82/2.74 tff(2311,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) | hskp25) | hskp52)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause284')).
% 3.82/2.74 tff(2312,plain,
% 3.82/2.74 (![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2311, 2310])).
% 3.82/2.74 tff(2313,plain,
% 3.82/2.74 (![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2312, 2308])).
% 3.82/2.74 tff(2314,plain,(
% 3.82/2.74 ![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 3.82/2.74 inference(skolemize,[status(sab)],[2313])).
% 3.82/2.74 tff(2315,plain,
% 3.82/2.74 (![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2314, 2307])).
% 3.82/2.74 tff(2316,plain,
% 3.82/2.74 (((~![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp52 | hskp25 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | c3_1(a669))) <=> ((~![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp52 | hskp25 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | c3_1(a669))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2317,plain,
% 3.82/2.74 ((hskp52 | hskp25 | (~ndr1_0) | c3_1(a669) | c2_1(a669) | (~c0_1(a669))) <=> (hskp52 | hskp25 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | c3_1(a669))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2318,plain,
% 3.82/2.74 (((~![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp52 | hskp25 | (~ndr1_0) | c3_1(a669) | c2_1(a669) | (~c0_1(a669)))) <=> ((~![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp52 | hskp25 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | c3_1(a669)))),
% 3.82/2.74 inference(monotonicity,[status(thm)],[2317])).
% 3.82/2.74 tff(2319,plain,
% 3.82/2.74 (((~![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp52 | hskp25 | (~ndr1_0) | c3_1(a669) | c2_1(a669) | (~c0_1(a669)))) <=> ((~![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp52 | hskp25 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | c3_1(a669))),
% 3.82/2.74 inference(transitivity,[status(thm)],[2318, 2316])).
% 3.82/2.74 tff(2320,plain,
% 3.82/2.74 ((~![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp52 | hskp25 | (~ndr1_0) | c3_1(a669) | c2_1(a669) | (~c0_1(a669)))),
% 3.82/2.74 inference(quant_inst,[status(thm)],[])).
% 3.82/2.74 tff(2321,plain,
% 3.82/2.74 ((~![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp52 | hskp25 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | c3_1(a669)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2320, 2319])).
% 3.82/2.74 tff(2322,plain,
% 3.82/2.74 (hskp52 | hskp25),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2321, 96, 2139, 2137, 2315, 2305])).
% 3.82/2.74 tff(2323,plain,
% 3.82/2.74 (hskp52),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2322, 2298])).
% 3.82/2.74 tff(2324,plain,
% 3.82/2.74 (((~hskp52) | (~c2_1(a647))) <=> ((~hskp52) | (~c2_1(a647)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2325,plain,
% 3.82/2.74 (((~c2_1(a647)) | (~hskp52)) <=> ((~hskp52) | (~c2_1(a647)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2326,axiom,((~c2_1(a647)) | (~hskp52)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 3.82/2.74 tff(2327,plain,
% 3.82/2.74 ((~hskp52) | (~c2_1(a647))),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2326, 2325])).
% 3.82/2.74 tff(2328,plain,
% 3.82/2.74 ((~hskp52) | (~c2_1(a647))),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2327, 2324])).
% 3.82/2.74 tff(2329,plain,
% 3.82/2.74 (~c2_1(a647)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2328, 2323])).
% 3.82/2.74 tff(2330,plain,
% 3.82/2.74 (((~hskp52) | c0_1(a647)) <=> ((~hskp52) | c0_1(a647))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2331,axiom,((~hskp52) | c0_1(a647)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 3.82/2.74 tff(2332,plain,
% 3.82/2.74 ((~hskp52) | c0_1(a647)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2331, 2330])).
% 3.82/2.74 tff(2333,plain,
% 3.82/2.74 ((~hskp52) | c0_1(a647)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2332, 2330])).
% 3.82/2.74 tff(2334,plain,
% 3.82/2.74 ((~hskp52) | c0_1(a647)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2333, 2330])).
% 3.82/2.74 tff(2335,plain,
% 3.82/2.74 ((~hskp52) | c0_1(a647)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2334, 2330])).
% 3.82/2.74 tff(2336,plain,
% 3.82/2.74 ((~hskp52) | c0_1(a647)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2335, 2330])).
% 3.82/2.74 tff(2337,plain,
% 3.82/2.74 ((~hskp52) | c0_1(a647)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2336, 2330])).
% 3.82/2.74 tff(2338,plain,
% 3.82/2.74 ((~hskp52) | c0_1(a647)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2337, 2330])).
% 3.82/2.74 tff(2339,plain,
% 3.82/2.74 ((~hskp52) | c0_1(a647)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2338, 2330])).
% 3.82/2.74 tff(2340,plain,
% 3.82/2.74 (c0_1(a647)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2339, 2323])).
% 3.82/2.74 tff(2341,plain,
% 3.82/2.74 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a647) | (~ndr1_0) | (~c3_1(a647)) | (~c0_1(a647)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a647) | (~ndr1_0) | (~c3_1(a647)) | (~c0_1(a647)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2342,plain,
% 3.82/2.74 ((hskp58 | hskp41 | (~ndr1_0) | c2_1(a647) | (~c3_1(a647)) | (~c0_1(a647))) <=> (hskp58 | hskp41 | c2_1(a647) | (~ndr1_0) | (~c3_1(a647)) | (~c0_1(a647)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2343,plain,
% 3.82/2.74 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a647) | (~c3_1(a647)) | (~c0_1(a647)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a647) | (~ndr1_0) | (~c3_1(a647)) | (~c0_1(a647))))),
% 3.82/2.74 inference(monotonicity,[status(thm)],[2342])).
% 3.82/2.74 tff(2344,plain,
% 3.82/2.74 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a647) | (~c3_1(a647)) | (~c0_1(a647)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a647) | (~ndr1_0) | (~c3_1(a647)) | (~c0_1(a647)))),
% 3.82/2.74 inference(transitivity,[status(thm)],[2343, 2341])).
% 3.82/2.74 tff(2345,plain,
% 3.82/2.74 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a647) | (~c3_1(a647)) | (~c0_1(a647)))),
% 3.82/2.74 inference(quant_inst,[status(thm)],[])).
% 3.82/2.74 tff(2346,plain,
% 3.82/2.74 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a647) | (~ndr1_0) | (~c3_1(a647)) | (~c0_1(a647))),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2345, 2344])).
% 3.82/2.74 tff(2347,plain,
% 3.82/2.74 (~c3_1(a647)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2346, 96, 146, 106, 2340, 2329, 116])).
% 3.82/2.74 tff(2348,plain,
% 3.82/2.74 (((~hskp52) | (~c1_1(a647))) <=> ((~hskp52) | (~c1_1(a647)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2349,plain,
% 3.82/2.74 (((~c1_1(a647)) | (~hskp52)) <=> ((~hskp52) | (~c1_1(a647)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2350,axiom,((~c1_1(a647)) | (~hskp52)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 3.82/2.74 tff(2351,plain,
% 3.82/2.74 ((~hskp52) | (~c1_1(a647))),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2350, 2349])).
% 3.82/2.74 tff(2352,plain,
% 3.82/2.74 ((~hskp52) | (~c1_1(a647))),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2351, 2348])).
% 3.82/2.74 tff(2353,plain,
% 3.82/2.74 (~c1_1(a647)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2352, 2323])).
% 3.82/2.74 tff(2354,assumption,(~hskp62), introduced(assumption)).
% 3.82/2.74 tff(2355,plain,
% 3.82/2.74 (((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | c2_1(a647) | c1_1(a647) | (~ndr1_0) | c3_1(a647))) <=> ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp63 | hskp62 | c2_1(a647) | c1_1(a647) | (~ndr1_0) | c3_1(a647))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2356,plain,
% 3.82/2.74 ((hskp63 | hskp62 | (~ndr1_0) | c3_1(a647) | c1_1(a647) | c2_1(a647)) <=> (hskp63 | hskp62 | c2_1(a647) | c1_1(a647) | (~ndr1_0) | c3_1(a647))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2357,plain,
% 3.82/2.74 (((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | (~ndr1_0) | c3_1(a647) | c1_1(a647) | c2_1(a647))) <=> ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | c2_1(a647) | c1_1(a647) | (~ndr1_0) | c3_1(a647)))),
% 3.82/2.74 inference(monotonicity,[status(thm)],[2356])).
% 3.82/2.74 tff(2358,plain,
% 3.82/2.74 (((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | (~ndr1_0) | c3_1(a647) | c1_1(a647) | c2_1(a647))) <=> ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp63 | hskp62 | c2_1(a647) | c1_1(a647) | (~ndr1_0) | c3_1(a647))),
% 3.82/2.74 inference(transitivity,[status(thm)],[2357, 2355])).
% 3.82/2.74 tff(2359,plain,
% 3.82/2.74 ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | (~ndr1_0) | c3_1(a647) | c1_1(a647) | c2_1(a647))),
% 3.82/2.74 inference(quant_inst,[status(thm)],[])).
% 3.82/2.74 tff(2360,plain,
% 3.82/2.74 ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp63 | hskp62 | c2_1(a647) | c1_1(a647) | (~ndr1_0) | c3_1(a647)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2359, 2358])).
% 3.82/2.74 tff(2361,plain,
% 3.82/2.74 (hskp63),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2360, 96, 2354, 2329, 2353, 2158, 2347])).
% 3.82/2.74 tff(2362,plain,
% 3.82/2.74 (~c2_1(a672)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2195, 2361])).
% 3.82/2.74 tff(2363,plain,
% 3.82/2.74 (~c0_1(a672)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2171, 2361])).
% 3.82/2.74 tff(2364,plain,
% 3.82/2.74 (c3_1(a672)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2182, 2361])).
% 3.82/2.74 tff(2365,plain,
% 3.82/2.74 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c0_1(a672) | c2_1(a672) | (~ndr1_0) | (~c3_1(a672)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c0_1(a672) | c2_1(a672) | (~ndr1_0) | (~c3_1(a672)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2366,plain,
% 3.82/2.74 ((hskp29 | hskp3 | (~ndr1_0) | c2_1(a672) | c0_1(a672) | (~c3_1(a672))) <=> (hskp29 | hskp3 | c0_1(a672) | c2_1(a672) | (~ndr1_0) | (~c3_1(a672)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2367,plain,
% 3.82/2.74 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a672) | c0_1(a672) | (~c3_1(a672)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c0_1(a672) | c2_1(a672) | (~ndr1_0) | (~c3_1(a672))))),
% 3.82/2.74 inference(monotonicity,[status(thm)],[2366])).
% 3.82/2.74 tff(2368,plain,
% 3.82/2.74 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a672) | c0_1(a672) | (~c3_1(a672)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c0_1(a672) | c2_1(a672) | (~ndr1_0) | (~c3_1(a672)))),
% 3.82/2.74 inference(transitivity,[status(thm)],[2367, 2365])).
% 3.82/2.74 tff(2369,plain,
% 3.82/2.74 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a672) | c0_1(a672) | (~c3_1(a672)))),
% 3.82/2.74 inference(quant_inst,[status(thm)],[])).
% 3.82/2.74 tff(2370,plain,
% 3.82/2.74 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c0_1(a672) | c2_1(a672) | (~ndr1_0) | (~c3_1(a672))),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2369, 2368])).
% 3.82/2.74 tff(2371,plain,
% 3.82/2.74 ($false),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2370, 96, 2265, 2264, 2364, 2363, 2362, 1024])).
% 3.82/2.74 tff(2372,plain,(hskp29 | hskp3 | hskp62 | hskp58 | hskp41 | (~c0_1(a669)) | c2_1(a669)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.74 tff(2373,plain,
% 3.82/2.74 (hskp29),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2372, 2263, 2048, 105, 106, 2003, 2002])).
% 3.82/2.74 tff(2374,plain,
% 3.82/2.74 (~c0_1(a660)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[1466, 2373])).
% 3.82/2.74 tff(2375,plain,
% 3.82/2.74 (~c3_1(a660)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[1472, 2373])).
% 3.82/2.74 tff(2376,plain,
% 3.82/2.74 (~c1_1(a660)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[1478, 2373])).
% 3.82/2.74 tff(2377,plain,
% 3.82/2.74 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2378,plain,
% 3.82/2.74 (((~ndr1_0) | c3_1(a660) | c2_1(a660) | c0_1(a660) | c1_1(a660) | c3_1(a660) | c0_1(a660)) <=> (c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2379,plain,
% 3.82/2.74 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a660) | c2_1(a660) | c0_1(a660) | c1_1(a660) | c3_1(a660) | c0_1(a660))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660)))),
% 3.82/2.74 inference(monotonicity,[status(thm)],[2378])).
% 3.82/2.74 tff(2380,plain,
% 3.82/2.74 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a660) | c2_1(a660) | c0_1(a660) | c1_1(a660) | c3_1(a660) | c0_1(a660))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660))),
% 3.82/2.74 inference(transitivity,[status(thm)],[2379, 2377])).
% 3.82/2.74 tff(2381,plain,
% 3.82/2.74 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a660) | c2_1(a660) | c0_1(a660) | c1_1(a660) | c3_1(a660) | c0_1(a660))),
% 3.82/2.74 inference(quant_inst,[status(thm)],[])).
% 3.82/2.74 tff(2382,plain,
% 3.82/2.74 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660)),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2381, 2380])).
% 3.82/2.74 tff(2383,plain,
% 3.82/2.74 (c2_1(a660)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2382, 96, 2376, 2375, 2374, 185])).
% 3.82/2.74 tff(2384,plain,
% 3.82/2.74 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a673) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a660)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a673) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a660)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2385,plain,
% 3.82/2.74 (((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673))) <=> (c0_1(a673) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a660)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2386,plain,
% 3.82/2.74 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a673) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a660))))),
% 3.82/2.74 inference(monotonicity,[status(thm)],[2385])).
% 3.82/2.74 tff(2387,plain,
% 3.82/2.74 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a673) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a660)))),
% 3.82/2.74 inference(transitivity,[status(thm)],[2386, 2384])).
% 3.82/2.74 tff(2388,plain,
% 3.82/2.74 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673)))),
% 3.82/2.74 inference(quant_inst,[status(thm)],[])).
% 3.82/2.74 tff(2389,plain,
% 3.82/2.74 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a673) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a660))),
% 3.82/2.74 inference(modus_ponens,[status(thm)],[2388, 2387])).
% 3.82/2.74 tff(2390,plain,
% 3.82/2.74 ($false),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2389, 96, 1825, 1814, 2375, 2374, 23, 1982, 2383])).
% 3.82/2.74 tff(2391,plain,(hskp53 | hskp41 | hskp17 | c3_1(a603) | hskp15), inference(lemma,lemma(discharge,[]))).
% 3.82/2.74 tff(2392,plain,
% 3.82/2.74 (c3_1(a603)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[2391, 1874, 12, 106, 1877])).
% 3.82/2.74 tff(2393,plain,
% 3.82/2.74 (~hskp3),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[1458, 2392])).
% 3.82/2.74 tff(2394,plain,
% 3.82/2.74 (hskp29),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[1939, 13, 2393])).
% 3.82/2.74 tff(2395,plain,
% 3.82/2.74 (~c0_1(a660)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[1466, 2394])).
% 3.82/2.74 tff(2396,plain,
% 3.82/2.74 (~c3_1(a660)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[1472, 2394])).
% 3.82/2.74 tff(2397,plain,
% 3.82/2.74 (~c1_1(a660)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[1478, 2394])).
% 3.82/2.74 tff(2398,plain,
% 3.82/2.74 (hskp61),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[1896, 13, 1788, 106, 1825, 1875])).
% 3.82/2.74 tff(2399,plain,
% 3.82/2.74 (~c0_1(a670)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[387, 2398])).
% 3.82/2.74 tff(2400,plain,
% 3.82/2.74 (~c1_1(a670)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[393, 2398])).
% 3.82/2.74 tff(2401,plain,
% 3.82/2.74 (c2_1(a670)),
% 3.82/2.74 inference(unit_resolution,[status(thm)],[421, 2398])).
% 3.82/2.74 tff(2402,plain,
% 3.82/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a670) | c0_1(a670) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a670) | c0_1(a670) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2403,plain,
% 3.82/2.74 (((~ndr1_0) | c1_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)) | c1_1(a660) | c0_1(a660) | c3_1(a660)) <=> (c1_1(a670) | c0_1(a670) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670)))),
% 3.82/2.74 inference(rewrite,[status(thm)],[])).
% 3.82/2.74 tff(2404,plain,
% 3.82/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)) | c1_1(a660) | c0_1(a660) | c3_1(a660))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a670) | c0_1(a670) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670))))),
% 3.82/2.74 inference(monotonicity,[status(thm)],[2403])).
% 3.82/2.74 tff(2405,plain,
% 3.82/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)) | c1_1(a660) | c0_1(a660) | c3_1(a660))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a670) | c0_1(a670) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670)))),
% 3.82/2.74 inference(transitivity,[status(thm)],[2404, 2402])).
% 3.82/2.74 tff(2406,plain,
% 3.82/2.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)) | c1_1(a660) | c0_1(a660) | c3_1(a660))),
% 3.82/2.74 inference(quant_inst,[status(thm)],[])).
% 3.82/2.74 tff(2407,plain,
% 3.82/2.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a670) | c0_1(a670) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670))),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2406, 2405])).
% 3.82/2.75 tff(2408,plain,
% 3.82/2.75 (~c3_1(a670)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2407, 96, 2401, 2400, 2399, 2397, 2396, 2395, 1221])).
% 3.82/2.75 tff(2409,plain,
% 3.82/2.75 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c1_1(a670) | c0_1(a670) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660) | c3_1(a670))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c1_1(a670) | c0_1(a670) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660) | c3_1(a670))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2410,plain,
% 3.82/2.75 (((~ndr1_0) | c3_1(a660) | c2_1(a660) | c0_1(a660) | c1_1(a670) | c3_1(a670) | c0_1(a670)) <=> (c1_1(a670) | c0_1(a670) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660) | c3_1(a670))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2411,plain,
% 3.82/2.75 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a660) | c2_1(a660) | c0_1(a660) | c1_1(a670) | c3_1(a670) | c0_1(a670))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c1_1(a670) | c0_1(a670) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660) | c3_1(a670)))),
% 3.82/2.75 inference(monotonicity,[status(thm)],[2410])).
% 3.82/2.75 tff(2412,plain,
% 3.82/2.75 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a660) | c2_1(a660) | c0_1(a660) | c1_1(a670) | c3_1(a670) | c0_1(a670))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c1_1(a670) | c0_1(a670) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660) | c3_1(a670))),
% 3.82/2.75 inference(transitivity,[status(thm)],[2411, 2409])).
% 3.82/2.75 tff(2413,plain,
% 3.82/2.75 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a660) | c2_1(a660) | c0_1(a660) | c1_1(a670) | c3_1(a670) | c0_1(a670))),
% 3.82/2.75 inference(quant_inst,[status(thm)],[])).
% 3.82/2.75 tff(2414,plain,
% 3.82/2.75 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c1_1(a670) | c0_1(a670) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660) | c3_1(a670)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2413, 2412])).
% 3.82/2.75 tff(2415,plain,
% 3.82/2.75 (c2_1(a660)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2414, 96, 2400, 2399, 2396, 2395, 185, 2408])).
% 3.82/2.75 tff(2416,plain,
% 3.82/2.75 (~hskp54),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1967, 2415, 1874, 2395, 2396, 12])).
% 3.82/2.75 tff(2417,plain,
% 3.82/2.75 (hskp54 | hskp37 | c3_1(a670)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[466, 96, 2401, 2399, 411])).
% 3.82/2.75 tff(2418,plain,
% 3.82/2.75 (hskp37),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2417, 2416, 2408])).
% 3.82/2.75 tff(2419,plain,
% 3.82/2.75 (~c2_1(a607)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[428, 2418])).
% 3.82/2.75 tff(2420,plain,
% 3.82/2.75 (c0_1(a607)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[439, 2418])).
% 3.82/2.75 tff(2421,plain,
% 3.82/2.75 (c1_1(a607)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[450, 2418])).
% 3.82/2.75 tff(2422,plain,
% 3.82/2.75 ($false),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1979, 96, 106, 1788, 1825, 2421, 2420, 2419, 329, 13])).
% 3.82/2.75 tff(2423,plain,(c2_1(a673) | hskp41 | hskp17), inference(lemma,lemma(discharge,[]))).
% 3.82/2.75 tff(2424,plain,
% 3.82/2.75 (c2_1(a673)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2423, 106, 12])).
% 3.82/2.75 tff(2425,plain,
% 3.82/2.75 (~hskp61),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1999, 2424, 1814, 1825])).
% 3.82/2.75 tff(2426,plain,
% 3.82/2.75 (hskp60),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[381, 2425, 1876])).
% 3.82/2.75 tff(2427,plain,
% 3.82/2.75 (~c2_1(a669)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[335, 2426])).
% 3.82/2.75 tff(2428,plain,
% 3.82/2.75 (~hskp14),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[239, 1874, 12, 106])).
% 3.82/2.75 tff(2429,plain,
% 3.82/2.75 (~hskp62),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2047, 2428, 1877, 1875, 106])).
% 3.82/2.75 tff(2430,plain,
% 3.82/2.75 (c0_1(a669)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[358, 2426])).
% 3.82/2.75 tff(2431,plain,
% 3.82/2.75 (hskp29),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2372, 2430, 2429, 1875, 106, 2393, 2427])).
% 3.82/2.75 tff(2432,plain,
% 3.82/2.75 (~c0_1(a660)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1466, 2431])).
% 3.82/2.75 tff(2433,plain,
% 3.82/2.75 (~c3_1(a660)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1472, 2431])).
% 3.82/2.75 tff(2434,plain,
% 3.82/2.75 (~c1_1(a660)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1478, 2431])).
% 3.82/2.75 tff(2435,plain,
% 3.82/2.75 (c2_1(a660)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2382, 96, 2434, 2433, 2432, 185])).
% 3.82/2.75 tff(2436,plain,
% 3.82/2.75 ($false),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2389, 96, 1825, 1814, 2433, 2432, 23, 2424, 2435])).
% 3.82/2.75 tff(2437,plain,(hskp41 | hskp17), inference(lemma,lemma(discharge,[]))).
% 3.82/2.75 tff(2438,plain,
% 3.82/2.75 (hskp41),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2437, 12])).
% 3.82/2.75 tff(2439,plain,
% 3.82/2.75 (c2_1(a617)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[556, 2438])).
% 3.82/2.75 tff(2440,plain,
% 3.82/2.75 (~c1_1(a617)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[517, 2438])).
% 3.82/2.75 tff(2441,plain,
% 3.82/2.75 (c3_1(a617)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[528, 2438])).
% 3.82/2.75 tff(2442,plain,
% 3.82/2.75 (c0_1(a617)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1487, 1461, 2441, 2440, 2439])).
% 3.82/2.75 tff(2443,plain,
% 3.82/2.75 (c2_1(a660)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2382, 96, 1479, 1473, 1467, 185])).
% 3.82/2.75 tff(2444,plain,
% 3.82/2.75 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c3_1(a660) | c0_1(a660) | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | (~c2_1(a660)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c3_1(a660) | c0_1(a660) | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | (~c2_1(a660)))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2445,plain,
% 3.82/2.75 (((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c1_1(a635) | c3_1(a635) | c2_1(a635)) <=> (c3_1(a660) | c0_1(a660) | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | (~c2_1(a660)))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2446,plain,
% 3.82/2.75 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c1_1(a635) | c3_1(a635) | c2_1(a635))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c3_1(a660) | c0_1(a660) | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | (~c2_1(a660))))),
% 3.82/2.75 inference(monotonicity,[status(thm)],[2445])).
% 3.82/2.75 tff(2447,plain,
% 3.82/2.75 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c1_1(a635) | c3_1(a635) | c2_1(a635))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c3_1(a660) | c0_1(a660) | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | (~c2_1(a660)))),
% 3.82/2.75 inference(transitivity,[status(thm)],[2446, 2444])).
% 3.82/2.75 tff(2448,plain,
% 3.82/2.75 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c1_1(a635) | c3_1(a635) | c2_1(a635))),
% 3.82/2.75 inference(quant_inst,[status(thm)],[])).
% 3.82/2.75 tff(2449,plain,
% 3.82/2.75 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c3_1(a660) | c0_1(a660) | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | (~c2_1(a660))),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2448, 2447])).
% 3.82/2.75 tff(2450,plain,
% 3.82/2.75 ($false),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2449, 96, 1958, 1957, 683, 677, 671, 662, 1956])).
% 3.82/2.75 tff(2451,plain,((~hskp20) | c3_1(a660) | c0_1(a660) | (~c2_1(a660))), inference(lemma,lemma(discharge,[]))).
% 3.82/2.75 tff(2452,plain,
% 3.82/2.75 (~hskp20),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2451, 1473, 1467, 2443])).
% 3.82/2.75 tff(2453,plain,
% 3.82/2.75 ($false),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1306, 231, 218, 698, 710, 709, 207, 711, 712])).
% 3.82/2.75 tff(2454,plain,((~hskp14) | (~c0_1(a617)) | c1_1(a617) | hskp20 | (~c3_1(a617)) | (~c2_1(a617))), inference(lemma,lemma(discharge,[]))).
% 3.82/2.75 tff(2455,plain,
% 3.82/2.75 (~hskp14),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2454, 2442, 2440, 2452, 2441, 2439])).
% 3.82/2.75 tff(2456,plain,
% 3.82/2.75 (hskp15 | hskp14 | (~c0_1(a617))),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[612, 96, 2439, 2440, 250])).
% 3.82/2.75 tff(2457,plain,
% 3.82/2.75 (hskp15),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2456, 2455, 2442])).
% 3.82/2.75 tff(2458,plain,
% 3.82/2.75 (hskp53),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[199, 2457, 12])).
% 3.82/2.75 tff(2459,plain,
% 3.82/2.75 (c3_1(a648)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[878, 2458])).
% 3.82/2.75 tff(2460,plain,
% 3.82/2.75 (c0_1(a648)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[867, 2458])).
% 3.82/2.75 tff(2461,plain,
% 3.82/2.75 (~c2_1(a648)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[856, 2458])).
% 3.82/2.75 tff(2462,assumption,(~hskp38), introduced(assumption)).
% 3.82/2.75 tff(2463,plain,
% 3.82/2.75 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | c0_1(a673) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp38 | c0_1(a673) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2464,plain,
% 3.82/2.75 ((hskp38 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a625) | c0_1(a625) | c2_1(a625)) <=> (hskp38 | c0_1(a673) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2465,plain,
% 3.82/2.75 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a625) | c0_1(a625) | c2_1(a625))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | c0_1(a673) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673))))),
% 3.82/2.75 inference(monotonicity,[status(thm)],[2464])).
% 3.82/2.75 tff(2466,plain,
% 3.82/2.75 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a625) | c0_1(a625) | c2_1(a625))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp38 | c0_1(a673) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)))),
% 3.82/2.75 inference(transitivity,[status(thm)],[2465, 2463])).
% 3.82/2.75 tff(2467,plain,
% 3.82/2.75 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a625) | c0_1(a625) | c2_1(a625))),
% 3.82/2.75 inference(quant_inst,[status(thm)],[])).
% 3.82/2.75 tff(2468,plain,
% 3.82/2.75 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp38 | c0_1(a673) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673))),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2467, 2466])).
% 3.82/2.75 tff(2469,plain,
% 3.82/2.75 ($false),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2468, 96, 2462, 1881, 1880, 1984, 1650, 1640, 1639, 11])).
% 3.82/2.75 tff(2470,plain,(c1_1(a625) | hskp38 | (~c3_1(a673)) | (~c1_1(a673)) | c0_1(a673) | c2_1(a625) | c0_1(a625)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.75 tff(2471,plain,
% 3.82/2.75 ($false),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2470, 162, 168, 1881, 1880, 1984, 2462, 1650])).
% 3.82/2.75 tff(2472,plain,((~hskp15) | (~c3_1(a673)) | (~c1_1(a673)) | c0_1(a673) | hskp38 | c2_1(a625)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.75 tff(2473,plain,
% 3.82/2.75 ($false),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2472, 191, 156, 1880, 1984, 2462, 1881])).
% 3.82/2.75 tff(2474,plain,((~hskp15) | (~c1_1(a673)) | c0_1(a673) | hskp38 | (~c3_1(a673))), inference(lemma,lemma(discharge,[]))).
% 3.82/2.75 tff(2475,plain,
% 3.82/2.75 (hskp38),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2474, 156, 1984, 1880, 1881])).
% 3.82/2.75 tff(2476,assumption,(hskp38), introduced(assumption)).
% 3.82/2.75 tff(2477,plain,
% 3.82/2.75 (((~hskp38) | c0_1(a608)) <=> ((~hskp38) | c0_1(a608))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2478,axiom,((~hskp38) | c0_1(a608)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 3.82/2.75 tff(2479,plain,
% 3.82/2.75 ((~hskp38) | c0_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2478, 2477])).
% 3.82/2.75 tff(2480,plain,
% 3.82/2.75 ((~hskp38) | c0_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2479, 2477])).
% 3.82/2.75 tff(2481,plain,
% 3.82/2.75 ((~hskp38) | c0_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2480, 2477])).
% 3.82/2.75 tff(2482,plain,
% 3.82/2.75 ((~hskp38) | c0_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2481, 2477])).
% 3.82/2.75 tff(2483,plain,
% 3.82/2.75 ((~hskp38) | c0_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2482, 2477])).
% 3.82/2.75 tff(2484,plain,
% 3.82/2.75 ((~hskp38) | c0_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2483, 2477])).
% 3.82/2.75 tff(2485,plain,
% 3.82/2.75 ((~hskp38) | c0_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2484, 2477])).
% 3.82/2.75 tff(2486,plain,
% 3.82/2.75 ((~hskp38) | c0_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2485, 2477])).
% 3.82/2.75 tff(2487,plain,
% 3.82/2.75 (c0_1(a608)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2486, 2476])).
% 3.82/2.75 tff(2488,plain,
% 3.82/2.75 (((~hskp38) | c3_1(a608)) <=> ((~hskp38) | c3_1(a608))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2489,axiom,((~hskp38) | c3_1(a608)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 3.82/2.75 tff(2490,plain,
% 3.82/2.75 ((~hskp38) | c3_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2489, 2488])).
% 3.82/2.75 tff(2491,plain,
% 3.82/2.75 ((~hskp38) | c3_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2490, 2488])).
% 3.82/2.75 tff(2492,plain,
% 3.82/2.75 ((~hskp38) | c3_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2491, 2488])).
% 3.82/2.75 tff(2493,plain,
% 3.82/2.75 ((~hskp38) | c3_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2492, 2488])).
% 3.82/2.75 tff(2494,plain,
% 3.82/2.75 ((~hskp38) | c3_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2493, 2488])).
% 3.82/2.75 tff(2495,plain,
% 3.82/2.75 ((~hskp38) | c3_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2494, 2488])).
% 3.82/2.75 tff(2496,plain,
% 3.82/2.75 ((~hskp38) | c3_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2495, 2488])).
% 3.82/2.75 tff(2497,plain,
% 3.82/2.75 ((~hskp38) | c3_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2496, 2488])).
% 3.82/2.75 tff(2498,plain,
% 3.82/2.75 (c3_1(a608)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2497, 2476])).
% 3.82/2.75 tff(2499,plain,
% 3.82/2.75 (((~hskp38) | c1_1(a608)) <=> ((~hskp38) | c1_1(a608))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2500,axiom,((~hskp38) | c1_1(a608)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 3.82/2.75 tff(2501,plain,
% 3.82/2.75 ((~hskp38) | c1_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2500, 2499])).
% 3.82/2.75 tff(2502,plain,
% 3.82/2.75 ((~hskp38) | c1_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2501, 2499])).
% 3.82/2.75 tff(2503,plain,
% 3.82/2.75 ((~hskp38) | c1_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2502, 2499])).
% 3.82/2.75 tff(2504,plain,
% 3.82/2.75 ((~hskp38) | c1_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2503, 2499])).
% 3.82/2.75 tff(2505,plain,
% 3.82/2.75 ((~hskp38) | c1_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2504, 2499])).
% 3.82/2.75 tff(2506,plain,
% 3.82/2.75 ((~hskp38) | c1_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2505, 2499])).
% 3.82/2.75 tff(2507,plain,
% 3.82/2.75 ((~hskp38) | c1_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2506, 2499])).
% 3.82/2.75 tff(2508,plain,
% 3.82/2.75 ((~hskp38) | c1_1(a608)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2507, 2499])).
% 3.82/2.75 tff(2509,plain,
% 3.82/2.75 (c1_1(a608)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2508, 2476])).
% 3.82/2.75 tff(2510,assumption,(~hskp6), introduced(assumption)).
% 3.82/2.75 tff(2511,plain,
% 3.82/2.75 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2512,plain,
% 3.82/2.75 ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)))),
% 3.82/2.75 inference(quant_inst,[status(thm)],[])).
% 3.82/2.75 tff(2513,plain,
% 3.82/2.75 ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608))),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2512, 2511])).
% 3.82/2.75 tff(2514,plain,
% 3.82/2.75 ($false),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2513, 96, 2510, 2509, 2498, 2487, 742])).
% 3.82/2.75 tff(2515,plain,((~hskp38) | hskp6), inference(lemma,lemma(discharge,[]))).
% 3.82/2.75 tff(2516,plain,
% 3.82/2.75 (hskp6),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2515, 2475])).
% 3.82/2.75 tff(2517,plain,
% 3.82/2.75 (c2_1(a609)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[767, 2516])).
% 3.82/2.75 tff(2518,assumption,(hskp16), introduced(assumption)).
% 3.82/2.75 tff(2519,plain,
% 3.82/2.75 (~c0_1(a609)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[754, 2516])).
% 3.82/2.75 tff(2520,plain,
% 3.82/2.75 (~c1_1(a609)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1509, 2516])).
% 3.82/2.75 tff(2521,assumption,(~c1_1(a609)), introduced(assumption)).
% 3.82/2.75 tff(2522,plain,
% 3.82/2.75 (~c3_1(a627)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1170, 2518])).
% 3.82/2.75 tff(2523,plain,
% 3.82/2.75 (c2_1(a627)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1181, 2518])).
% 3.82/2.75 tff(2524,plain,
% 3.82/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c2_1(a627)) | c1_1(a627))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c2_1(a627)) | c1_1(a627))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2525,plain,
% 3.82/2.75 (((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a609) | c0_1(a609) | (~c2_1(a609)) | c2_1(a625) | c1_1(a625) | c0_1(a625)) <=> (c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c2_1(a627)) | c1_1(a627))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2526,plain,
% 3.82/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a609) | c0_1(a609) | (~c2_1(a609)) | c2_1(a625) | c1_1(a625) | c0_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c2_1(a627)) | c1_1(a627)))),
% 3.82/2.75 inference(monotonicity,[status(thm)],[2525])).
% 3.82/2.75 tff(2527,plain,
% 3.82/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a609) | c0_1(a609) | (~c2_1(a609)) | c2_1(a625) | c1_1(a625) | c0_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c2_1(a627)) | c1_1(a627))),
% 3.82/2.75 inference(transitivity,[status(thm)],[2526, 2524])).
% 3.82/2.75 tff(2528,plain,
% 3.82/2.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a609) | c0_1(a609) | (~c2_1(a609)) | c2_1(a625) | c1_1(a625) | c0_1(a625))),
% 3.82/2.75 inference(quant_inst,[status(thm)],[])).
% 3.82/2.75 tff(2529,plain,
% 3.82/2.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c2_1(a627)) | c1_1(a627)),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2528, 2527])).
% 3.82/2.75 tff(2530,plain,
% 3.82/2.75 (c1_1(a627)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2529, 96, 2523, 1523, 2522, 1650, 1640, 1639, 1522, 2521, 1390])).
% 3.82/2.75 tff(2531,plain,
% 3.82/2.75 (c0_1(a627)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1199, 2518])).
% 3.82/2.75 tff(2532,plain,
% 3.82/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | (c3_1(a627) | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a627) | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2533,plain,
% 3.82/2.75 (((~ndr1_0) | (~c3_1(a617)) | (~c0_1(a617)) | (~c2_1(a617)) | c3_1(a627) | (~c2_1(a627)) | (~c0_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a627))) <=> (c3_1(a627) | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2534,plain,
% 3.82/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a617)) | (~c0_1(a617)) | (~c2_1(a617)) | c3_1(a627) | (~c2_1(a627)) | (~c0_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a627)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | (c3_1(a627) | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617))))),
% 3.82/2.75 inference(monotonicity,[status(thm)],[2533])).
% 3.82/2.75 tff(2535,plain,
% 3.82/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a617)) | (~c0_1(a617)) | (~c2_1(a617)) | c3_1(a627) | (~c2_1(a627)) | (~c0_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a627)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a627) | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 3.82/2.75 inference(transitivity,[status(thm)],[2534, 2532])).
% 3.82/2.75 tff(2536,plain,
% 3.82/2.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a617)) | (~c0_1(a617)) | (~c2_1(a617)) | c3_1(a627) | (~c2_1(a627)) | (~c0_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a627)))),
% 3.82/2.75 inference(quant_inst,[status(thm)],[])).
% 3.82/2.75 tff(2537,plain,
% 3.82/2.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a627) | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617))),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2536, 2535])).
% 3.82/2.75 tff(2538,plain,
% 3.82/2.75 ((~c1_1(a627)) | (~c0_1(a617))),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2537, 96, 1051, 1050, 2523, 2531, 2522, 2129])).
% 3.82/2.75 tff(2539,plain,
% 3.82/2.75 (~c0_1(a617)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2538, 2530])).
% 3.82/2.75 tff(2540,plain,
% 3.82/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a648) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2541,plain,
% 3.82/2.75 (((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648))) <=> (c2_1(a648) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2542,plain,
% 3.82/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a648) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648))))),
% 3.82/2.75 inference(monotonicity,[status(thm)],[2541])).
% 3.82/2.75 tff(2543,plain,
% 3.82/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.82/2.75 inference(transitivity,[status(thm)],[2542, 2540])).
% 3.82/2.75 tff(2544,plain,
% 3.82/2.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))),
% 3.82/2.75 inference(quant_inst,[status(thm)],[])).
% 3.82/2.75 tff(2545,plain,
% 3.82/2.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648))),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2544, 2543])).
% 3.82/2.75 tff(2546,plain,
% 3.82/2.75 ((~c3_1(a609)) | (~c1_1(a627))),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2545, 96, 882, 881, 2523, 1523, 880, 2522, 1522, 1040])).
% 3.82/2.75 tff(2547,plain,
% 3.82/2.75 (~c3_1(a609)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2546, 2530])).
% 3.82/2.75 tff(2548,plain,
% 3.82/2.75 (c3_1(a609) | c0_1(a617)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1517, 96, 1051, 1050, 1048, 1522, 2521, 1221])).
% 3.82/2.75 tff(2549,plain,
% 3.82/2.75 ($false),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2548, 2547, 2539])).
% 3.82/2.75 tff(2550,plain,((~hskp16) | c0_1(a609) | c1_1(a609) | (~c3_1(a648)) | (~c0_1(a648)) | (~c2_1(a609)) | c2_1(a648) | c2_1(a625) | c1_1(a625) | c0_1(a625)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.75 tff(2551,plain,
% 3.82/2.75 ($false),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2550, 2520, 2519, 2518, 882, 881, 2517, 880, 191, 168, 162])).
% 3.82/2.75 tff(2552,plain,((~hskp15) | (~hskp16) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | c0_1(a673) | (~c1_1(a673)) | (~c3_1(a673))), inference(lemma,lemma(discharge,[]))).
% 3.82/2.75 tff(2553,plain,
% 3.82/2.75 ($false),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2552, 2461, 2460, 1825, 1814, 2457, 2459, 1867, 1788])).
% 3.82/2.75 tff(2554,plain,((~hskp29) | hskp17 | c2_1(a673)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.75 tff(2555,plain,
% 3.82/2.75 (~hskp29),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2554, 13, 12])).
% 3.82/2.75 tff(2556,plain,
% 3.82/2.75 (hskp3),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1939, 2555, 13])).
% 3.82/2.75 tff(2557,plain,
% 3.82/2.75 (~c3_1(a603)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1458, 2556])).
% 3.82/2.75 tff(2558,assumption,(~hskp16), introduced(assumption)).
% 3.82/2.75 tff(2559,plain,
% 3.82/2.75 (c0_1(a603)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1682, 2556])).
% 3.82/2.75 tff(2560,plain,
% 3.82/2.75 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | c0_1(a673) | c3_1(a603) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a673) | c3_1(a603) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2561,plain,
% 3.82/2.75 ((hskp16 | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a603)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673))) <=> (hskp16 | c0_1(a673) | c3_1(a603) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2562,plain,
% 3.82/2.75 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a603)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | c0_1(a673) | c3_1(a603) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a603)) | (~c0_1(a603))))),
% 3.82/2.75 inference(monotonicity,[status(thm)],[2561])).
% 3.82/2.75 tff(2563,plain,
% 3.82/2.75 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a603)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a673) | c3_1(a603) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.82/2.75 inference(transitivity,[status(thm)],[2562, 2560])).
% 3.82/2.75 tff(2564,plain,
% 3.82/2.75 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a603)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673)))),
% 3.82/2.75 inference(quant_inst,[status(thm)],[])).
% 3.82/2.75 tff(2565,plain,
% 3.82/2.75 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a673) | c3_1(a603) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a603)) | (~c0_1(a603))),
% 3.82/2.75 inference(modus_ponens,[status(thm)],[2564, 2563])).
% 3.82/2.75 tff(2566,plain,
% 3.82/2.75 (hskp16 | (~c2_1(a603))),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2565, 96, 1788, 2559, 1814, 2557, 1798, 13])).
% 3.82/2.75 tff(2567,plain,
% 3.82/2.75 (~c2_1(a603)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2566, 2558])).
% 3.82/2.75 tff(2568,plain,
% 3.82/2.75 (hskp20 | c2_1(a603)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1253, 96, 2439, 2441, 2559, 2440, 2557, 723])).
% 3.82/2.75 tff(2569,plain,
% 3.82/2.75 (hskp20),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[2568, 2567])).
% 3.82/2.75 tff(2570,plain,
% 3.82/2.75 (~c1_1(a635)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[682, 2569])).
% 3.82/2.75 tff(2571,plain,
% 3.82/2.75 (~c2_1(a635)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[676, 2569])).
% 3.82/2.75 tff(2572,plain,
% 3.82/2.75 (~c3_1(a635)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[670, 2569])).
% 3.82/2.75 tff(2573,plain,
% 3.82/2.75 (hskp9),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1164, 2558, 12])).
% 3.82/2.75 tff(2574,plain,
% 3.82/2.75 (~c3_1(a613)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1118, 2573])).
% 3.82/2.75 tff(2575,plain,
% 3.82/2.75 (c2_1(a613)),
% 3.82/2.75 inference(unit_resolution,[status(thm)],[1130, 2573])).
% 3.82/2.75 tff(2576,plain,
% 3.82/2.75 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | c0_1(a673) | c3_1(a613) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a613)) | (~c0_1(a613)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a673) | c3_1(a613) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a613)) | (~c0_1(a613)))),
% 3.82/2.75 inference(rewrite,[status(thm)],[])).
% 3.82/2.75 tff(2577,plain,
% 3.82/2.75 ((hskp16 | (~ndr1_0) | c3_1(a613) | (~c0_1(a613)) | (~c2_1(a613)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673))) <=> (hskp16 | c0_1(a673) | c3_1(a613) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a613)) | (~c0_1(a613)))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2578,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a613) | (~c0_1(a613)) | (~c2_1(a613)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | c0_1(a673) | c3_1(a613) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a613)) | (~c0_1(a613))))),
% 3.82/2.76 inference(monotonicity,[status(thm)],[2577])).
% 3.82/2.76 tff(2579,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a613) | (~c0_1(a613)) | (~c2_1(a613)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a673) | c3_1(a613) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a613)) | (~c0_1(a613)))),
% 3.82/2.76 inference(transitivity,[status(thm)],[2578, 2576])).
% 3.82/2.76 tff(2580,plain,
% 3.82/2.76 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a613) | (~c0_1(a613)) | (~c2_1(a613)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673)))),
% 3.82/2.76 inference(quant_inst,[status(thm)],[])).
% 3.82/2.76 tff(2581,plain,
% 3.82/2.76 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a673) | c3_1(a613) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a613)) | (~c0_1(a613))),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2580, 2579])).
% 3.82/2.76 tff(2582,plain,
% 3.82/2.76 (~c0_1(a613)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2581, 96, 2558, 1881, 2575, 1984, 2574, 1798, 13])).
% 3.82/2.76 tff(2583,assumption,(~c3_1(a635)), introduced(assumption)).
% 3.82/2.76 tff(2584,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c1_1(a635) | c2_1(a635) | c3_1(a635) | c3_1(a613) | (~ndr1_0) | (~c2_1(a613)) | c0_1(a613))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c1_1(a635) | c2_1(a635) | c3_1(a635) | c3_1(a613) | (~ndr1_0) | (~c2_1(a613)) | c0_1(a613))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2585,plain,
% 3.82/2.76 (((~ndr1_0) | c3_1(a613) | c0_1(a613) | (~c2_1(a613)) | c1_1(a635) | c3_1(a635) | c2_1(a635)) <=> (c1_1(a635) | c2_1(a635) | c3_1(a635) | c3_1(a613) | (~ndr1_0) | (~c2_1(a613)) | c0_1(a613))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2586,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a613) | c0_1(a613) | (~c2_1(a613)) | c1_1(a635) | c3_1(a635) | c2_1(a635))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c1_1(a635) | c2_1(a635) | c3_1(a635) | c3_1(a613) | (~ndr1_0) | (~c2_1(a613)) | c0_1(a613)))),
% 3.82/2.76 inference(monotonicity,[status(thm)],[2585])).
% 3.82/2.76 tff(2587,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a613) | c0_1(a613) | (~c2_1(a613)) | c1_1(a635) | c3_1(a635) | c2_1(a635))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c1_1(a635) | c2_1(a635) | c3_1(a635) | c3_1(a613) | (~ndr1_0) | (~c2_1(a613)) | c0_1(a613))),
% 3.82/2.76 inference(transitivity,[status(thm)],[2586, 2584])).
% 3.82/2.76 tff(2588,plain,
% 3.82/2.76 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a613) | c0_1(a613) | (~c2_1(a613)) | c1_1(a635) | c3_1(a635) | c2_1(a635))),
% 3.82/2.76 inference(quant_inst,[status(thm)],[])).
% 3.82/2.76 tff(2589,plain,
% 3.82/2.76 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c1_1(a635) | c2_1(a635) | c3_1(a635) | c3_1(a613) | (~ndr1_0) | (~c2_1(a613)) | c0_1(a613)),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2588, 2587])).
% 3.82/2.76 tff(2590,plain,
% 3.82/2.76 ($false),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2589, 96, 2575, 1046, 1049, 2583, 2574, 662, 2582])).
% 3.82/2.76 tff(2591,plain,(hskp16 | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~c3_1(a673)) | c0_1(a673) | c2_1(a673) | hskp17), inference(lemma,lemma(discharge,[]))).
% 3.82/2.76 tff(2592,plain,
% 3.82/2.76 ($false),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2591, 2572, 2571, 12, 1788, 13, 1814, 2558, 2570])).
% 3.82/2.76 tff(2593,plain,(hskp16 | hskp17 | c2_1(a673)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.76 tff(2594,plain,
% 3.82/2.76 (hskp16),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2593, 13, 12])).
% 3.82/2.76 tff(2595,plain,
% 3.82/2.76 (hskp53),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[199, 156, 12])).
% 3.82/2.76 tff(2596,plain,
% 3.82/2.76 (c0_1(a648)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[867, 2595])).
% 3.82/2.76 tff(2597,plain,
% 3.82/2.76 (c3_1(a648)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[878, 2595])).
% 3.82/2.76 tff(2598,plain,
% 3.82/2.76 (~c2_1(a648)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[856, 2595])).
% 3.82/2.76 tff(2599,plain,
% 3.82/2.76 ($false),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2552, 2598, 2597, 1825, 1814, 2518, 156, 2596, 1788])).
% 3.82/2.76 tff(2600,plain,((~hskp15) | (~hskp16) | hskp17), inference(lemma,lemma(discharge,[]))).
% 3.82/2.76 tff(2601,plain,
% 3.82/2.76 (~hskp15),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2600, 2594, 12])).
% 3.82/2.76 tff(2602,plain,
% 3.82/2.76 (hskp53),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[615, 281, 12, 2438, 280])).
% 3.82/2.76 tff(2603,plain,
% 3.82/2.76 (~c2_1(a648)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[856, 2602])).
% 3.82/2.76 tff(2604,plain,
% 3.82/2.76 (c3_1(a648)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[878, 2602])).
% 3.82/2.76 tff(2605,plain,
% 3.82/2.76 (c0_1(a648)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[867, 2602])).
% 3.82/2.76 tff(2606,plain,
% 3.82/2.76 ($false),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[1284, 2605, 2604, 281, 1030, 2603, 12, 280])).
% 3.82/2.76 tff(2607,plain,(hskp15 | c3_1(a603) | hskp17 | hskp14), inference(lemma,lemma(discharge,[]))).
% 3.82/2.76 tff(2608,plain,
% 3.82/2.76 (hskp14),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2607, 2601, 12, 2557])).
% 3.82/2.76 tff(2609,plain,
% 3.82/2.76 (hskp5),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[628, 35, 12, 2438])).
% 3.82/2.76 tff(2610,plain,
% 3.82/2.76 (~c3_1(a606)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[634, 2609])).
% 3.82/2.76 tff(2611,plain,
% 3.82/2.76 (hskp53 | c0_1(a617)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[535, 96, 12, 2441, 2440, 34])).
% 3.82/2.76 tff(2612,plain,
% 3.82/2.76 (c0_1(a617)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2611, 35])).
% 3.82/2.76 tff(2613,plain,
% 3.82/2.76 (hskp20),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2454, 2612, 2440, 201, 2441, 2439])).
% 3.82/2.76 tff(2614,plain,
% 3.82/2.76 (c2_1(a606)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[651, 2609])).
% 3.82/2.76 tff(2615,plain,
% 3.82/2.76 (~c0_1(a606)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[640, 2609])).
% 3.82/2.76 tff(2616,plain,
% 3.82/2.76 ($false),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[692, 2615, 2614, 2613, 2610])).
% 3.82/2.76 tff(2617,plain,(hskp53 | (~hskp14) | hskp17), inference(lemma,lemma(discharge,[]))).
% 3.82/2.76 tff(2618,plain,
% 3.82/2.76 (hskp53),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2617, 2608, 12])).
% 3.82/2.76 tff(2619,plain,
% 3.82/2.76 (c3_1(a648)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[878, 2618])).
% 3.82/2.76 tff(2620,plain,
% 3.82/2.76 (c0_1(a648)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[867, 2618])).
% 3.82/2.76 tff(2621,plain,
% 3.82/2.76 (~c2_1(a648)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[856, 2618])).
% 3.82/2.76 tff(2622,plain,
% 3.82/2.76 ($false),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[1452, 2621, 2620, 2601, 2557, 12, 2619])).
% 3.82/2.76 tff(2623,plain,(c2_1(a673) | hskp17), inference(lemma,lemma(discharge,[]))).
% 3.82/2.76 tff(2624,plain,
% 3.82/2.76 (c2_1(a673)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2623, 12])).
% 3.82/2.76 tff(2625,plain,
% 3.82/2.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a673) | c1_1(a617) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a673) | c1_1(a617) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2626,plain,
% 3.82/2.76 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c0_1(a673) | (~c1_1(a673)) | (~c2_1(a673))) <=> (c0_1(a673) | c1_1(a617) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2627,plain,
% 3.82/2.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c0_1(a673) | (~c1_1(a673)) | (~c2_1(a673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a673) | c1_1(a617) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))))),
% 3.82/2.76 inference(monotonicity,[status(thm)],[2626])).
% 3.82/2.76 tff(2628,plain,
% 3.82/2.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c0_1(a673) | (~c1_1(a673)) | (~c2_1(a673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a673) | c1_1(a617) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.82/2.76 inference(transitivity,[status(thm)],[2627, 2625])).
% 3.82/2.76 tff(2629,plain,
% 3.82/2.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c0_1(a673) | (~c1_1(a673)) | (~c2_1(a673)))),
% 3.82/2.76 inference(quant_inst,[status(thm)],[])).
% 3.82/2.76 tff(2630,plain,
% 3.82/2.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a673) | c1_1(a617) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2629, 2628])).
% 3.82/2.76 tff(2631,plain,
% 3.82/2.76 ((~c2_1(a673)) | c0_1(a617)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2630, 96, 1825, 2439, 2441, 1814, 2440, 1566])).
% 3.82/2.76 tff(2632,plain,
% 3.82/2.76 (c0_1(a617)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2631, 2624])).
% 3.82/2.76 tff(2633,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (c1_1(a617) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a617)) | (~c0_1(a617)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | c1_1(a617) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a617)) | (~c0_1(a617)))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2634,plain,
% 3.82/2.76 (((~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617))) <=> (c1_1(a617) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a617)) | (~c0_1(a617)))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2635,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (c1_1(a617) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a617)) | (~c0_1(a617))))),
% 3.82/2.76 inference(monotonicity,[status(thm)],[2634])).
% 3.82/2.76 tff(2636,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | c1_1(a617) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a617)) | (~c0_1(a617)))),
% 3.82/2.76 inference(transitivity,[status(thm)],[2635, 2633])).
% 3.82/2.76 tff(2637,plain,
% 3.82/2.76 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)))),
% 3.82/2.76 inference(quant_inst,[status(thm)],[])).
% 3.82/2.76 tff(2638,plain,
% 3.82/2.76 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | c1_1(a617) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a617)) | (~c0_1(a617))),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2637, 2636])).
% 3.82/2.76 tff(2639,plain,
% 3.82/2.76 ((~c2_1(a673)) | (~c0_1(a617))),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2638, 96, 1788, 1825, 2439, 2440, 546])).
% 3.82/2.76 tff(2640,plain,
% 3.82/2.76 ($false),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2639, 2632, 2624])).
% 3.82/2.76 tff(2641,plain,(hskp17), inference(lemma,lemma(discharge,[]))).
% 3.82/2.76 tff(2642,plain,
% 3.82/2.76 (((~hskp17) | (~c1_1(a628))) <=> ((~hskp17) | (~c1_1(a628)))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2643,plain,
% 3.82/2.76 (((~c1_1(a628)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a628)))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2644,axiom,((~c1_1(a628)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause243')).
% 3.82/2.76 tff(2645,plain,
% 3.82/2.76 ((~hskp17) | (~c1_1(a628))),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2644, 2643])).
% 3.82/2.76 tff(2646,plain,
% 3.82/2.76 ((~hskp17) | (~c1_1(a628))),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2645, 2642])).
% 3.82/2.76 tff(2647,plain,
% 3.82/2.76 (~c1_1(a628)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2646, 2641])).
% 3.82/2.76 tff(2648,plain,
% 3.82/2.76 (((~hskp17) | (~c2_1(a628))) <=> ((~hskp17) | (~c2_1(a628)))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2649,plain,
% 3.82/2.76 (((~c2_1(a628)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a628)))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2650,axiom,((~c2_1(a628)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause242')).
% 3.82/2.76 tff(2651,plain,
% 3.82/2.76 ((~hskp17) | (~c2_1(a628))),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2650, 2649])).
% 3.82/2.76 tff(2652,plain,
% 3.82/2.76 ((~hskp17) | (~c2_1(a628))),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2651, 2648])).
% 3.82/2.76 tff(2653,plain,
% 3.82/2.76 (~c2_1(a628)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2652, 2641])).
% 3.82/2.76 tff(2654,assumption,(hskp5), introduced(assumption)).
% 3.82/2.76 tff(2655,plain,
% 3.82/2.76 (~c3_1(a606)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[634, 2654])).
% 3.82/2.76 tff(2656,plain,
% 3.82/2.76 (~c0_1(a606)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[640, 2654])).
% 3.82/2.76 tff(2657,plain,
% 3.82/2.76 (c2_1(a606)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[651, 2654])).
% 3.82/2.76 tff(2658,plain,
% 3.82/2.76 (~c1_1(a606)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[1767, 96, 2657, 2656, 2655, 23])).
% 3.82/2.76 tff(2659,plain,
% 3.82/2.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a628) | c1_1(a628) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c2_1(a606)) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a628) | c1_1(a628) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c2_1(a606)) | c0_1(a628))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2660,plain,
% 3.82/2.76 (((~ndr1_0) | c3_1(a606) | c1_1(a606) | (~c2_1(a606)) | c1_1(a606) | c0_1(a606) | (~c2_1(a606)) | c2_1(a628) | c1_1(a628) | c0_1(a628)) <=> (c2_1(a628) | c1_1(a628) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c2_1(a606)) | c0_1(a628))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2661,plain,
% 3.82/2.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a606) | c1_1(a606) | (~c2_1(a606)) | c1_1(a606) | c0_1(a606) | (~c2_1(a606)) | c2_1(a628) | c1_1(a628) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a628) | c1_1(a628) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c2_1(a606)) | c0_1(a628)))),
% 3.82/2.76 inference(monotonicity,[status(thm)],[2660])).
% 3.82/2.76 tff(2662,plain,
% 3.82/2.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a606) | c1_1(a606) | (~c2_1(a606)) | c1_1(a606) | c0_1(a606) | (~c2_1(a606)) | c2_1(a628) | c1_1(a628) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a628) | c1_1(a628) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c2_1(a606)) | c0_1(a628))),
% 3.82/2.76 inference(transitivity,[status(thm)],[2661, 2659])).
% 3.82/2.76 tff(2663,plain,
% 3.82/2.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a606) | c1_1(a606) | (~c2_1(a606)) | c1_1(a606) | c0_1(a606) | (~c2_1(a606)) | c2_1(a628) | c1_1(a628) | c0_1(a628))),
% 3.82/2.76 inference(quant_inst,[status(thm)],[])).
% 3.82/2.76 tff(2664,plain,
% 3.82/2.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a628) | c1_1(a628) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c2_1(a606)) | c0_1(a628)),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2663, 2662])).
% 3.82/2.76 tff(2665,plain,
% 3.82/2.76 ($false),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2664, 96, 2657, 2653, 2647, 2656, 2655, 1390, 1, 2658])).
% 3.82/2.76 tff(2666,plain,((~hskp5) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.76 tff(2667,plain,
% 3.82/2.76 (~hskp5),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2666, 1])).
% 3.82/2.76 tff(2668,plain,
% 3.82/2.76 (((~hskp17) | c3_1(a628)) <=> ((~hskp17) | c3_1(a628))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2669,axiom,((~hskp17) | c3_1(a628)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 3.82/2.76 tff(2670,plain,
% 3.82/2.76 ((~hskp17) | c3_1(a628)),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2669, 2668])).
% 3.82/2.76 tff(2671,plain,
% 3.82/2.76 ((~hskp17) | c3_1(a628)),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2670, 2668])).
% 3.82/2.76 tff(2672,plain,
% 3.82/2.76 ((~hskp17) | c3_1(a628)),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2671, 2668])).
% 3.82/2.76 tff(2673,plain,
% 3.82/2.76 ((~hskp17) | c3_1(a628)),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2672, 2668])).
% 3.82/2.76 tff(2674,plain,
% 3.82/2.76 ((~hskp17) | c3_1(a628)),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2673, 2668])).
% 3.82/2.76 tff(2675,plain,
% 3.82/2.76 ((~hskp17) | c3_1(a628)),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2674, 2668])).
% 3.82/2.76 tff(2676,plain,
% 3.82/2.76 ((~hskp17) | c3_1(a628)),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2675, 2668])).
% 3.82/2.76 tff(2677,plain,
% 3.82/2.76 ((~hskp17) | c3_1(a628)),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2676, 2668])).
% 3.82/2.76 tff(2678,plain,
% 3.82/2.76 (c3_1(a628)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2677, 2641])).
% 3.82/2.76 tff(2679,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a669) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a669)) | (~c1_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a669) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a669)) | (~c1_1(a669)))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2680,plain,
% 3.82/2.76 ((hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669))) <=> (hskp5 | c2_1(a669) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a669)) | (~c1_1(a669)))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2681,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a669) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a669)) | (~c1_1(a669))))),
% 3.82/2.76 inference(monotonicity,[status(thm)],[2680])).
% 3.82/2.76 tff(2682,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a669) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a669)) | (~c1_1(a669)))),
% 3.82/2.76 inference(transitivity,[status(thm)],[2681, 2679])).
% 3.82/2.76 tff(2683,plain,
% 3.82/2.76 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))),
% 3.82/2.76 inference(quant_inst,[status(thm)],[])).
% 3.82/2.76 tff(2684,plain,
% 3.82/2.76 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a669) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a669)) | (~c1_1(a669))),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2683, 2682])).
% 3.82/2.76 tff(2685,plain,
% 3.82/2.76 ($false),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2684, 96, 583, 359, 348, 2678, 336, 2653, 2647, 567])).
% 3.82/2.76 tff(2686,plain,((~hskp60) | hskp5), inference(lemma,lemma(discharge,[]))).
% 3.82/2.76 tff(2687,plain,
% 3.82/2.76 (~hskp60),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2686, 2667])).
% 3.82/2.76 tff(2688,assumption,(~c1_1(a658)), introduced(assumption)).
% 3.82/2.76 tff(2689,assumption,(~c2_1(a658)), introduced(assumption)).
% 3.82/2.76 tff(2690,plain,
% 3.82/2.76 (~hskp56),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[1400, 2689])).
% 3.82/2.76 tff(2691,assumption,(hskp42), introduced(assumption)).
% 3.82/2.76 tff(2692,plain,
% 3.82/2.76 (~c3_1(a618)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[1002, 2691])).
% 3.82/2.76 tff(2693,assumption,(~hskp56), introduced(assumption)).
% 3.82/2.76 tff(2694,plain,
% 3.82/2.76 (c1_1(a618)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[957, 2691])).
% 3.82/2.76 tff(2695,plain,
% 3.82/2.76 (~c2_1(a618)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[923, 2691])).
% 3.82/2.76 tff(2696,assumption,(hskp17), introduced(assumption)).
% 3.82/2.76 tff(2697,plain,
% 3.82/2.76 (~c1_1(a628)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2646, 2696])).
% 3.82/2.76 tff(2698,plain,
% 3.82/2.76 (~c2_1(a628)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2652, 2696])).
% 3.82/2.76 tff(2699,assumption,(~c3_1(a618)), introduced(assumption)).
% 3.82/2.76 tff(2700,assumption,(~c2_1(a618)), introduced(assumption)).
% 3.82/2.76 tff(2701,plain,
% 3.82/2.76 (c3_1(a628)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2677, 2696])).
% 3.82/2.76 tff(2702,assumption,(c1_1(a618)), introduced(assumption)).
% 3.82/2.76 tff(2703,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c3_1(a628)))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2704,plain,
% 3.82/2.76 ((hskp56 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c1_1(a628) | c2_1(a628) | (~c3_1(a628))) <=> (hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c3_1(a628)))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2705,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c3_1(a628))))),
% 3.82/2.76 inference(monotonicity,[status(thm)],[2704])).
% 3.82/2.76 tff(2706,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c3_1(a628)))),
% 3.82/2.76 inference(transitivity,[status(thm)],[2705, 2703])).
% 3.82/2.76 tff(2707,plain,
% 3.82/2.76 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)))),
% 3.82/2.76 inference(quant_inst,[status(thm)],[])).
% 3.82/2.76 tff(2708,plain,
% 3.82/2.76 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c3_1(a628))),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2707, 2706])).
% 3.82/2.76 tff(2709,plain,
% 3.82/2.76 ($false),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2708, 96, 2693, 2702, 2701, 2700, 2699, 2698, 2697, 1348])).
% 3.82/2.76 tff(2710,plain,((~hskp17) | hskp56 | (~c1_1(a618)) | c2_1(a618) | c3_1(a618)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.76 tff(2711,plain,
% 3.82/2.76 (hskp56 | (~c1_1(a618)) | c2_1(a618) | c3_1(a618)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2710, 2641])).
% 3.82/2.76 tff(2712,plain,
% 3.82/2.76 ($false),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2711, 2695, 2694, 2693, 2692])).
% 3.82/2.76 tff(2713,plain,((~hskp42) | hskp56), inference(lemma,lemma(discharge,[]))).
% 3.82/2.76 tff(2714,plain,
% 3.82/2.76 (~hskp42),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2713, 2690])).
% 3.82/2.76 tff(2715,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c2_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c0_1(a658)) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c2_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c0_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2716,plain,
% 3.82/2.76 ((hskp42 | (~ndr1_0) | c1_1(a658) | c2_1(a658) | (~c0_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628))) <=> (hskp42 | c2_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c0_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2717,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a658) | c2_1(a658) | (~c0_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c2_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c0_1(a658)) | c0_1(a628) | (~c3_1(a628))))),
% 3.82/2.76 inference(monotonicity,[status(thm)],[2716])).
% 3.82/2.76 tff(2718,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a658) | c2_1(a658) | (~c0_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c2_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c0_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.76 inference(transitivity,[status(thm)],[2717, 2715])).
% 3.82/2.76 tff(2719,plain,
% 3.82/2.76 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a658) | c2_1(a658) | (~c0_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.76 inference(quant_inst,[status(thm)],[])).
% 3.82/2.76 tff(2720,plain,
% 3.82/2.76 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c2_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c0_1(a658)) | c0_1(a628) | (~c3_1(a628))),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2719, 2718])).
% 3.82/2.76 tff(2721,plain,
% 3.82/2.76 (hskp42 | c2_1(a658) | (~c0_1(a658))),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2720, 96, 2678, 2688, 2647, 900, 1])).
% 3.82/2.76 tff(2722,plain,
% 3.82/2.76 (~c0_1(a658)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2721, 2714, 2689])).
% 3.82/2.76 tff(2723,plain,
% 3.82/2.76 (~hskp42),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2713, 2693])).
% 3.82/2.76 tff(2724,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a628)))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2725,plain,
% 3.82/2.76 ((hskp56 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c1_1(a628) | c2_1(a628) | (~c3_1(a628))) <=> (hskp56 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a628)))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2726,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a628))))),
% 3.82/2.76 inference(monotonicity,[status(thm)],[2725])).
% 3.82/2.76 tff(2727,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a628)))),
% 3.82/2.76 inference(transitivity,[status(thm)],[2726, 2724])).
% 3.82/2.76 tff(2728,plain,
% 3.82/2.76 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)))),
% 3.82/2.76 inference(quant_inst,[status(thm)],[])).
% 3.82/2.76 tff(2729,plain,
% 3.82/2.76 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a628))),
% 3.82/2.76 inference(modus_ponens,[status(thm)],[2728, 2727])).
% 3.82/2.76 tff(2730,plain,
% 3.82/2.76 (hskp56 | (~c1_1(a603)) | c2_1(a603)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2729, 96, 2678, 2653, 2647, 1030, 1348])).
% 3.82/2.76 tff(2731,plain,
% 3.82/2.76 (~c1_1(a603)),
% 3.82/2.76 inference(unit_resolution,[status(thm)],[2730, 2693, 1903])).
% 3.82/2.76 tff(2732,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c0_1(a603) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c0_1(a603) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2733,plain,
% 3.82/2.76 (((~ndr1_0) | c3_1(a603) | c2_1(a603) | c0_1(a603) | c1_1(a603) | c3_1(a603) | c0_1(a603)) <=> (c0_1(a603) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 3.82/2.76 inference(rewrite,[status(thm)],[])).
% 3.82/2.76 tff(2734,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a603) | c2_1(a603) | c0_1(a603) | c1_1(a603) | c3_1(a603) | c0_1(a603))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c0_1(a603) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603)))),
% 3.82/2.76 inference(monotonicity,[status(thm)],[2733])).
% 3.82/2.76 tff(2735,plain,
% 3.82/2.76 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a603) | c2_1(a603) | c0_1(a603) | c1_1(a603) | c3_1(a603) | c0_1(a603))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c0_1(a603) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 3.82/2.77 inference(transitivity,[status(thm)],[2734, 2732])).
% 3.82/2.77 tff(2736,plain,
% 3.82/2.77 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a603) | c2_1(a603) | c0_1(a603) | c1_1(a603) | c3_1(a603) | c0_1(a603))),
% 3.82/2.77 inference(quant_inst,[status(thm)],[])).
% 3.82/2.77 tff(2737,plain,
% 3.82/2.77 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c0_1(a603) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603)),
% 3.82/2.77 inference(modus_ponens,[status(thm)],[2736, 2735])).
% 3.82/2.77 tff(2738,plain,
% 3.82/2.77 (c0_1(a603)),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[2737, 96, 2731, 1030, 185, 1903])).
% 3.82/2.77 tff(2739,plain,
% 3.82/2.77 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a628) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a628) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2740,plain,
% 3.82/2.77 ((hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628))) <=> (hskp42 | c1_1(a628) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2741,plain,
% 3.82/2.77 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a628) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a628) | (~c3_1(a628))))),
% 3.82/2.77 inference(monotonicity,[status(thm)],[2740])).
% 3.82/2.77 tff(2742,plain,
% 3.82/2.77 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a628) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.77 inference(transitivity,[status(thm)],[2741, 2739])).
% 3.82/2.77 tff(2743,plain,
% 3.82/2.77 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.77 inference(quant_inst,[status(thm)],[])).
% 3.82/2.77 tff(2744,plain,
% 3.82/2.77 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a628) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a628) | (~c3_1(a628))),
% 3.82/2.77 inference(modus_ponens,[status(thm)],[2743, 2742])).
% 3.82/2.77 tff(2745,plain,
% 3.82/2.77 ((~c0_1(a603)) | c0_1(a628)),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[2744, 96, 2723, 2678, 2647, 2731, 900, 1903])).
% 3.82/2.77 tff(2746,plain,
% 3.82/2.77 (c0_1(a628)),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[2745, 2738])).
% 3.82/2.77 tff(2747,plain,
% 3.82/2.77 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a628)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a628)))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2748,plain,
% 3.82/2.77 ((hskp58 | hskp41 | (~ndr1_0) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628))) <=> (hskp58 | hskp41 | c2_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a628)))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2749,plain,
% 3.82/2.77 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a628))))),
% 3.82/2.77 inference(monotonicity,[status(thm)],[2748])).
% 3.82/2.77 tff(2750,plain,
% 3.82/2.77 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a628)))),
% 3.82/2.77 inference(transitivity,[status(thm)],[2749, 2747])).
% 3.82/2.77 tff(2751,plain,
% 3.82/2.77 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)))),
% 3.82/2.77 inference(quant_inst,[status(thm)],[])).
% 3.82/2.77 tff(2752,plain,
% 3.82/2.77 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a628))),
% 3.82/2.77 inference(modus_ponens,[status(thm)],[2751, 2750])).
% 3.82/2.77 tff(2753,plain,
% 3.82/2.77 (hskp58 | hskp41 | (~c0_1(a628))),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[2752, 96, 2678, 2653, 116])).
% 3.82/2.77 tff(2754,plain,
% 3.82/2.77 (hskp58),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[2753, 2746, 106])).
% 3.82/2.77 tff(2755,plain,
% 3.82/2.77 (~c1_1(a663)),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[41, 2754])).
% 3.82/2.77 tff(2756,plain,
% 3.82/2.77 (~c0_1(a663)),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[47, 2754])).
% 3.82/2.77 tff(2757,plain,
% 3.82/2.77 (c3_1(a663)),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[58, 2754])).
% 3.82/2.77 tff(2758,plain,
% 3.82/2.77 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a663)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a663)))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2759,plain,
% 3.82/2.77 ((hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a663) | c0_1(a663) | (~c3_1(a663))) <=> (hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a663)))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2760,plain,
% 3.82/2.77 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a663))))),
% 3.82/2.77 inference(monotonicity,[status(thm)],[2759])).
% 3.82/2.77 tff(2761,plain,
% 3.82/2.77 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a663)))),
% 3.82/2.77 inference(transitivity,[status(thm)],[2760, 2758])).
% 3.82/2.77 tff(2762,plain,
% 3.82/2.77 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)))),
% 3.82/2.77 inference(quant_inst,[status(thm)],[])).
% 3.82/2.77 tff(2763,plain,
% 3.82/2.77 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a663))),
% 3.82/2.77 inference(modus_ponens,[status(thm)],[2762, 2761])).
% 3.82/2.77 tff(2764,plain,
% 3.82/2.77 ($false),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[2763, 96, 2723, 2757, 2756, 2755, 2653, 2647, 900, 2746])).
% 3.82/2.77 tff(2765,plain,(hskp56 | hskp41 | c2_1(a603) | c3_1(a603)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.77 tff(2766,plain,
% 3.82/2.77 (hskp41),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[2765, 1903, 2693, 1030])).
% 3.82/2.77 tff(2767,plain,
% 3.82/2.77 (~c1_1(a617)),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[517, 2766])).
% 3.82/2.77 tff(2768,assumption,(~c0_1(a658)), introduced(assumption)).
% 3.82/2.77 tff(2769,plain,
% 3.82/2.77 (c2_1(a617)),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[556, 2766])).
% 3.82/2.77 tff(2770,plain,
% 3.82/2.77 (c3_1(a617)),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[528, 2766])).
% 3.82/2.77 tff(2771,assumption,(c1_1(a603)), introduced(assumption)).
% 3.82/2.77 tff(2772,plain,
% 3.82/2.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a628)))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2773,plain,
% 3.82/2.77 ((hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a603) | (~c1_1(a603)) | (~c0_1(a603))) <=> (hskp5 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a628)))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2774,plain,
% 3.82/2.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a603) | (~c1_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a628))))),
% 3.82/2.77 inference(monotonicity,[status(thm)],[2773])).
% 3.82/2.77 tff(2775,plain,
% 3.82/2.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a603) | (~c1_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a628)))),
% 3.82/2.77 inference(transitivity,[status(thm)],[2774, 2772])).
% 3.82/2.77 tff(2776,plain,
% 3.82/2.77 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a603) | (~c1_1(a603)) | (~c0_1(a603)))),
% 3.82/2.77 inference(quant_inst,[status(thm)],[])).
% 3.82/2.77 tff(2777,plain,
% 3.82/2.77 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a628))),
% 3.82/2.77 inference(modus_ponens,[status(thm)],[2776, 2775])).
% 3.82/2.77 tff(2778,plain,
% 3.82/2.77 ((~c1_1(a603)) | (~c0_1(a603))),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[2777, 96, 2667, 2678, 2653, 2647, 567, 1903])).
% 3.82/2.77 tff(2779,plain,
% 3.82/2.77 (~c0_1(a603)),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[2778, 2771])).
% 3.82/2.77 tff(2780,plain,
% 3.82/2.77 (~hskp3),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[1664, 2771])).
% 3.82/2.77 tff(2781,plain,
% 3.82/2.77 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2782,plain,
% 3.82/2.77 ((hskp29 | hskp3 | (~ndr1_0) | c2_1(a628) | c0_1(a628) | (~c3_1(a628))) <=> (hskp29 | hskp3 | c2_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2783,plain,
% 3.82/2.77 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a628) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628))))),
% 3.82/2.77 inference(monotonicity,[status(thm)],[2782])).
% 3.82/2.77 tff(2784,plain,
% 3.82/2.77 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a628) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.77 inference(transitivity,[status(thm)],[2783, 2781])).
% 3.82/2.77 tff(2785,plain,
% 3.82/2.77 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a628) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.77 inference(quant_inst,[status(thm)],[])).
% 3.82/2.77 tff(2786,plain,
% 3.82/2.77 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628))),
% 3.82/2.77 inference(modus_ponens,[status(thm)],[2785, 2784])).
% 3.82/2.77 tff(2787,plain,
% 3.82/2.77 (hskp29 | hskp3 | c0_1(a628)),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[2786, 96, 2678, 2653, 1024])).
% 3.82/2.77 tff(2788,plain,
% 3.82/2.77 (hskp29),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[2787, 2780, 1])).
% 3.82/2.77 tff(2789,assumption,(~c0_1(a603)), introduced(assumption)).
% 3.82/2.77 tff(2790,plain,
% 3.82/2.77 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c3_1(a603) | (~ndr1_0) | c2_1(a603))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2791,plain,
% 3.82/2.77 (((~ndr1_0) | c3_1(a603) | c2_1(a603) | c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660)) <=> (c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2792,plain,
% 3.82/2.77 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a603) | c2_1(a603) | c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c3_1(a603) | (~ndr1_0) | c2_1(a603)))),
% 3.82/2.77 inference(monotonicity,[status(thm)],[2791])).
% 3.82/2.77 tff(2793,plain,
% 3.82/2.77 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a603) | c2_1(a603) | c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 3.82/2.77 inference(transitivity,[status(thm)],[2792, 2790])).
% 3.82/2.77 tff(2794,plain,
% 3.82/2.77 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a603) | c2_1(a603) | c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660))),
% 3.82/2.77 inference(quant_inst,[status(thm)],[])).
% 3.82/2.77 tff(2795,plain,
% 3.82/2.77 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c3_1(a603) | (~ndr1_0) | c2_1(a603)),
% 3.82/2.77 inference(modus_ponens,[status(thm)],[2794, 2793])).
% 3.82/2.77 tff(2796,plain,
% 3.82/2.77 ($false),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[2795, 96, 2789, 1479, 1473, 1467, 1030, 185, 1903])).
% 3.82/2.77 tff(2797,plain,((~hskp29) | c0_1(a603) | c3_1(a603) | c2_1(a603)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.77 tff(2798,plain,
% 3.82/2.77 ($false),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[2797, 2788, 2779, 1030, 1903])).
% 3.82/2.77 tff(2799,plain,((~c1_1(a603)) | c3_1(a603) | c2_1(a603) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.77 tff(2800,plain,
% 3.82/2.77 (~c1_1(a603)),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[2799, 1903, 1, 1030])).
% 3.82/2.77 tff(2801,assumption,(~hskp42), introduced(assumption)).
% 3.82/2.77 tff(2802,plain,
% 3.82/2.77 (^[V: $i, U: $i] : refl((hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) <=> (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)))),
% 3.82/2.77 inference(bind,[status(th)],[])).
% 3.82/2.77 tff(2803,plain,
% 3.82/2.77 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.82/2.77 inference(quant_intro,[status(thm)],[2802])).
% 3.82/2.77 tff(2804,plain,
% 3.82/2.77 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2805,plain,
% 3.82/2.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c3_1(V))), (((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c3_1(V)) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c3_1(V)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c0_1(V))), (((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c0_1(V)))), ((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))), ((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)))), (((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))), (((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)))), ((((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))), ((((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)))), (((((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) | c0_1(U)) | c1_1(U)) | hskp42) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) | hskp42))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) | hskp42) <=> (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))), (((((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) | c0_1(U)) | c1_1(U)) | hskp42) <=> (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))))),
% 3.82/2.77 inference(bind,[status(th)],[])).
% 3.82/2.77 tff(2806,plain,
% 3.82/2.77 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) | c0_1(U)) | c1_1(U)) | hskp42) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.82/2.77 inference(quant_intro,[status(thm)],[2805])).
% 3.82/2.77 tff(2807,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) | c0_1(U)) | c1_1(U)) | hskp42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause300')).
% 3.82/2.77 tff(2808,plain,
% 3.82/2.77 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.82/2.77 inference(modus_ponens,[status(thm)],[2807, 2806])).
% 3.82/2.77 tff(2809,plain,
% 3.82/2.77 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.82/2.77 inference(modus_ponens,[status(thm)],[2808, 2804])).
% 3.82/2.77 tff(2810,plain,(
% 3.82/2.77 ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.82/2.77 inference(skolemize,[status(sab)],[2809])).
% 3.82/2.77 tff(2811,plain,
% 3.82/2.77 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 3.82/2.77 inference(modus_ponens,[status(thm)],[2810, 2803])).
% 3.82/2.77 tff(2812,plain,
% 3.82/2.77 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | c3_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | c0_1(a658) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp42 | c3_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | c0_1(a658) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2813,plain,
% 3.82/2.77 ((hskp42 | (~ndr1_0) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a658) | c3_1(a658) | c0_1(a658)) <=> (hskp42 | c3_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | c0_1(a658) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2814,plain,
% 3.82/2.77 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a658) | c3_1(a658) | c0_1(a658))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | c3_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | c0_1(a658) | c0_1(a628) | (~c3_1(a628))))),
% 3.82/2.77 inference(monotonicity,[status(thm)],[2813])).
% 3.82/2.77 tff(2815,plain,
% 3.82/2.77 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a658) | c3_1(a658) | c0_1(a658))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp42 | c3_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | c0_1(a658) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.77 inference(transitivity,[status(thm)],[2814, 2812])).
% 3.82/2.77 tff(2816,plain,
% 3.82/2.77 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a658) | c3_1(a658) | c0_1(a658))),
% 3.82/2.77 inference(quant_inst,[status(thm)],[])).
% 3.82/2.77 tff(2817,plain,
% 3.82/2.77 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp42 | c3_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | c0_1(a658) | c0_1(a628) | (~c3_1(a628))),
% 3.82/2.77 inference(modus_ponens,[status(thm)],[2816, 2815])).
% 3.82/2.77 tff(2818,plain,
% 3.82/2.77 (hskp42 | c3_1(a658) | c0_1(a658)),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[2817, 96, 2678, 2688, 2647, 2811, 1])).
% 3.82/2.77 tff(2819,plain,
% 3.82/2.77 (c3_1(a658)),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[2818, 2801, 2768])).
% 3.82/2.77 tff(2820,plain,
% 3.82/2.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a603) | c1_1(a658) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c1_1(a658) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2821,plain,
% 3.82/2.77 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a603) | c0_1(a603) | c3_1(a603)) <=> (c0_1(a603) | c1_1(a658) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2822,plain,
% 3.82/2.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a603) | c0_1(a603) | c3_1(a603))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a603) | c1_1(a658) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c2_1(a617)) | (~c3_1(a617))))),
% 3.82/2.77 inference(monotonicity,[status(thm)],[2821])).
% 3.82/2.77 tff(2823,plain,
% 3.82/2.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a603) | c0_1(a603) | c3_1(a603))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c1_1(a658) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c2_1(a617)) | (~c3_1(a617)))),
% 3.82/2.77 inference(transitivity,[status(thm)],[2822, 2820])).
% 3.82/2.77 tff(2824,plain,
% 3.82/2.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a603) | c0_1(a603) | c3_1(a603))),
% 3.82/2.77 inference(quant_inst,[status(thm)],[])).
% 3.82/2.77 tff(2825,plain,
% 3.82/2.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c1_1(a658) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c2_1(a617)) | (~c3_1(a617))),
% 3.82/2.77 inference(modus_ponens,[status(thm)],[2824, 2823])).
% 3.82/2.77 tff(2826,plain,
% 3.82/2.77 (c0_1(a603)),
% 3.82/2.77 inference(unit_resolution,[status(thm)],[2825, 96, 2819, 712, 711, 2688, 710, 2800, 1030, 1221, 2768])).
% 3.82/2.77 tff(2827,plain,
% 3.82/2.77 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a658) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a658) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a658) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a658) | (~c3_1(a658)))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2828,plain,
% 3.82/2.77 ((hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658))) <=> (hskp42 | c1_1(a658) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a658) | (~c3_1(a658)))),
% 3.82/2.77 inference(rewrite,[status(thm)],[])).
% 3.82/2.77 tff(2829,plain,
% 3.82/2.77 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a658) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a658) | (~c3_1(a658))))),
% 3.82/2.77 inference(monotonicity,[status(thm)],[2828])).
% 3.82/2.77 tff(2830,plain,
% 3.82/2.77 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a658) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a658) | (~c3_1(a658)))),
% 3.82/2.77 inference(transitivity,[status(thm)],[2829, 2827])).
% 3.82/2.77 tff(2831,plain,
% 3.82/2.77 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)))),
% 3.82/2.78 inference(quant_inst,[status(thm)],[])).
% 3.82/2.78 tff(2832,plain,
% 3.82/2.78 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a658) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a658) | (~c3_1(a658))),
% 3.82/2.78 inference(modus_ponens,[status(thm)],[2831, 2830])).
% 3.82/2.78 tff(2833,plain,
% 3.82/2.78 ($false),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2832, 96, 2801, 2819, 2826, 2688, 2800, 900, 1903, 2768])).
% 3.82/2.78 tff(2834,plain,(c2_1(a603) | hskp42 | c1_1(a658) | c0_1(a658) | (~c2_1(a617)) | (~c3_1(a617)) | c1_1(a617) | c3_1(a603) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.78 tff(2835,plain,
% 3.82/2.78 ($false),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2834, 2770, 2769, 2688, 1030, 2768, 1903, 2767, 2723, 1])).
% 3.82/2.78 tff(2836,plain,(c2_1(a603) | c1_1(a658) | c3_1(a603) | c0_1(a658) | c0_1(a628) | hskp56), inference(lemma,lemma(discharge,[]))).
% 3.82/2.78 tff(2837,plain,
% 3.82/2.78 (c2_1(a603)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2836, 2722, 1030, 2688, 1, 2690])).
% 3.82/2.78 tff(2838,plain,
% 3.82/2.78 (c3_1(a658)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2818, 2714, 2722])).
% 3.82/2.78 tff(2839,assumption,(c3_1(a658)), introduced(assumption)).
% 3.82/2.78 tff(2840,plain,
% 3.82/2.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a658) | c1_1(a658) | c2_1(a599) | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a599)) | (~c1_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a658) | c1_1(a658) | c2_1(a599) | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a599)) | (~c1_1(a599)))),
% 3.82/2.78 inference(rewrite,[status(thm)],[])).
% 3.82/2.78 tff(2841,plain,
% 3.82/2.78 ((hskp5 | (~ndr1_0) | c1_1(a658) | c2_1(a658) | (~c3_1(a658)) | c2_1(a599) | (~c1_1(a599)) | (~c0_1(a599))) <=> (hskp5 | c2_1(a658) | c1_1(a658) | c2_1(a599) | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a599)) | (~c1_1(a599)))),
% 3.82/2.78 inference(rewrite,[status(thm)],[])).
% 3.82/2.78 tff(2842,plain,
% 3.82/2.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a658) | c2_1(a658) | (~c3_1(a658)) | c2_1(a599) | (~c1_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a658) | c1_1(a658) | c2_1(a599) | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a599)) | (~c1_1(a599))))),
% 3.82/2.78 inference(monotonicity,[status(thm)],[2841])).
% 3.82/2.78 tff(2843,plain,
% 3.82/2.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a658) | c2_1(a658) | (~c3_1(a658)) | c2_1(a599) | (~c1_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a658) | c1_1(a658) | c2_1(a599) | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a599)) | (~c1_1(a599)))),
% 3.82/2.78 inference(transitivity,[status(thm)],[2842, 2840])).
% 3.82/2.78 tff(2844,plain,
% 3.82/2.78 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a658) | c2_1(a658) | (~c3_1(a658)) | c2_1(a599) | (~c1_1(a599)) | (~c0_1(a599)))),
% 3.82/2.78 inference(quant_inst,[status(thm)],[])).
% 3.82/2.78 tff(2845,plain,
% 3.82/2.78 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a658) | c1_1(a658) | c2_1(a599) | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a599)) | (~c1_1(a599))),
% 3.82/2.78 inference(modus_ponens,[status(thm)],[2844, 2843])).
% 3.82/2.78 tff(2846,plain,
% 3.82/2.78 (~c1_1(a599)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2845, 96, 583, 2689, 2839, 145, 2688, 123, 567])).
% 3.82/2.78 tff(2847,plain,
% 3.82/2.78 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a658) | c2_1(a599) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c0_1(a599)) | c1_1(a599))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a658) | c2_1(a599) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c0_1(a599)) | c1_1(a599))),
% 3.82/2.78 inference(rewrite,[status(thm)],[])).
% 3.82/2.78 tff(2848,plain,
% 3.82/2.78 ((hskp42 | (~ndr1_0) | c1_1(a599) | c2_1(a599) | (~c0_1(a599)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658))) <=> (hskp42 | c1_1(a658) | c2_1(a599) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c0_1(a599)) | c1_1(a599))),
% 3.82/2.78 inference(rewrite,[status(thm)],[])).
% 3.82/2.78 tff(2849,plain,
% 3.82/2.78 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a599) | c2_1(a599) | (~c0_1(a599)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a658) | c2_1(a599) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c0_1(a599)) | c1_1(a599)))),
% 3.82/2.78 inference(monotonicity,[status(thm)],[2848])).
% 3.82/2.78 tff(2850,plain,
% 3.82/2.78 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a599) | c2_1(a599) | (~c0_1(a599)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a658) | c2_1(a599) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c0_1(a599)) | c1_1(a599))),
% 3.82/2.78 inference(transitivity,[status(thm)],[2849, 2847])).
% 3.82/2.78 tff(2851,plain,
% 3.82/2.78 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a599) | c2_1(a599) | (~c0_1(a599)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)))),
% 3.82/2.78 inference(quant_inst,[status(thm)],[])).
% 3.82/2.78 tff(2852,plain,
% 3.82/2.78 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a658) | c2_1(a599) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c0_1(a599)) | c1_1(a599)),
% 3.82/2.78 inference(modus_ponens,[status(thm)],[2851, 2850])).
% 3.82/2.78 tff(2853,plain,
% 3.82/2.78 ($false),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2852, 96, 2714, 2839, 145, 2688, 123, 900, 2768, 2846])).
% 3.82/2.78 tff(2854,plain,((~hskp33) | (~c3_1(a658)) | c1_1(a658) | c0_1(a658) | hskp5 | c2_1(a658)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.78 tff(2855,plain,
% 3.82/2.78 (~hskp33),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2854, 2838, 2688, 2722, 2667, 2689])).
% 3.82/2.78 tff(2856,plain,
% 3.82/2.78 (hskp61),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[381, 2855, 2687])).
% 3.82/2.78 tff(2857,assumption,(c2_1(a603)), introduced(assumption)).
% 3.82/2.78 tff(2858,plain,
% 3.82/2.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a670) | c0_1(a670) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a628) | (~c2_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a670) | c0_1(a670) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a628) | (~c2_1(a670)))),
% 3.82/2.78 inference(rewrite,[status(thm)],[])).
% 3.82/2.78 tff(2859,plain,
% 3.82/2.78 (((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a628) | c1_1(a628) | c0_1(a628)) <=> (c1_1(a670) | c0_1(a670) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a628) | (~c2_1(a670)))),
% 3.82/2.78 inference(rewrite,[status(thm)],[])).
% 3.82/2.78 tff(2860,plain,
% 3.82/2.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a628) | c1_1(a628) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a670) | c0_1(a670) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a628) | (~c2_1(a670))))),
% 3.82/2.78 inference(monotonicity,[status(thm)],[2859])).
% 3.82/2.78 tff(2861,plain,
% 3.82/2.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a628) | c1_1(a628) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a670) | c0_1(a670) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a628) | (~c2_1(a670)))),
% 3.82/2.78 inference(transitivity,[status(thm)],[2860, 2858])).
% 3.82/2.78 tff(2862,plain,
% 3.82/2.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a628) | c1_1(a628) | c0_1(a628))),
% 3.82/2.78 inference(quant_inst,[status(thm)],[])).
% 3.82/2.78 tff(2863,plain,
% 3.82/2.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a670) | c0_1(a670) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a628) | (~c2_1(a670))),
% 3.82/2.78 inference(modus_ponens,[status(thm)],[2862, 2861])).
% 3.82/2.78 tff(2864,plain,
% 3.82/2.78 ($false),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2863, 96, 1908, 1906, 1905, 2653, 2647, 1233, 1030, 1390, 2857, 1])).
% 3.82/2.78 tff(2865,plain,((~hskp61) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.78 tff(2866,plain,
% 3.82/2.78 (c1_1(a603)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2865, 2856, 2837, 1030, 1])).
% 3.82/2.78 tff(2867,plain,
% 3.82/2.78 (~hskp3),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[1664, 2866])).
% 3.82/2.78 tff(2868,plain,
% 3.82/2.78 (hskp29),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2787, 2867, 1])).
% 3.82/2.78 tff(2869,plain,
% 3.82/2.78 (~c0_1(a660)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[1466, 2868])).
% 3.82/2.78 tff(2870,plain,
% 3.82/2.78 (~c3_1(a660)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[1472, 2868])).
% 3.82/2.78 tff(2871,plain,
% 3.82/2.78 (~c1_1(a660)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[1478, 2868])).
% 3.82/2.78 tff(2872,plain,
% 3.82/2.78 (~c0_1(a670)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[387, 2856])).
% 3.82/2.78 tff(2873,plain,
% 3.82/2.78 (~c1_1(a670)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[393, 2856])).
% 3.82/2.78 tff(2874,plain,
% 3.82/2.78 (c2_1(a670)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[421, 2856])).
% 3.82/2.78 tff(2875,plain,
% 3.82/2.78 (~c3_1(a670)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2407, 96, 2874, 2873, 2872, 2871, 2870, 2869, 1221])).
% 3.82/2.78 tff(2876,plain,
% 3.82/2.78 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a658) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | c3_1(a670))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a658) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | c3_1(a670))),
% 3.82/2.78 inference(rewrite,[status(thm)],[])).
% 3.82/2.78 tff(2877,plain,
% 3.82/2.78 ((hskp42 | (~ndr1_0) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a670) | c3_1(a670) | c0_1(a670)) <=> (hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a658) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | c3_1(a670))),
% 3.82/2.78 inference(rewrite,[status(thm)],[])).
% 3.82/2.78 tff(2878,plain,
% 3.82/2.78 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | (~ndr1_0) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a670) | c3_1(a670) | c0_1(a670))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a658) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | c3_1(a670)))),
% 3.82/2.78 inference(monotonicity,[status(thm)],[2877])).
% 3.82/2.78 tff(2879,plain,
% 3.82/2.78 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | (~ndr1_0) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a670) | c3_1(a670) | c0_1(a670))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a658) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | c3_1(a670))),
% 3.82/2.78 inference(transitivity,[status(thm)],[2878, 2876])).
% 3.82/2.78 tff(2880,plain,
% 3.82/2.78 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | (~ndr1_0) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a670) | c3_1(a670) | c0_1(a670))),
% 3.82/2.78 inference(quant_inst,[status(thm)],[])).
% 3.82/2.78 tff(2881,plain,
% 3.82/2.78 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a658) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | c3_1(a670)),
% 3.82/2.78 inference(modus_ponens,[status(thm)],[2880, 2879])).
% 3.82/2.78 tff(2882,plain,
% 3.82/2.78 ($false),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2881, 96, 2714, 2838, 2873, 2872, 2688, 2811, 2722, 2875])).
% 3.82/2.78 tff(2883,plain,(c2_1(a658) | c1_1(a658) | c0_1(a628) | c3_1(a603)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.78 tff(2884,plain,
% 3.82/2.78 (c3_1(a603)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2883, 2689, 1, 2688])).
% 3.82/2.78 tff(2885,plain,
% 3.82/2.78 (~hskp3),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[1458, 2884])).
% 3.82/2.78 tff(2886,plain,
% 3.82/2.78 (hskp29),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2787, 2885, 1])).
% 3.82/2.78 tff(2887,plain,
% 3.82/2.78 (~c3_1(a660)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[1472, 2886])).
% 3.82/2.78 tff(2888,plain,
% 3.82/2.78 (~c1_1(a660)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[1478, 2886])).
% 3.82/2.78 tff(2889,plain,
% 3.82/2.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a599) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a599)) | (~c1_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a599) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a599)) | (~c1_1(a599)))),
% 3.82/2.78 inference(rewrite,[status(thm)],[])).
% 3.82/2.78 tff(2890,plain,
% 3.82/2.78 ((hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a599) | (~c1_1(a599)) | (~c0_1(a599))) <=> (hskp5 | c2_1(a599) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a599)) | (~c1_1(a599)))),
% 3.82/2.78 inference(rewrite,[status(thm)],[])).
% 3.82/2.78 tff(2891,plain,
% 3.82/2.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a599) | (~c1_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a599) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a599)) | (~c1_1(a599))))),
% 3.82/2.78 inference(monotonicity,[status(thm)],[2890])).
% 3.82/2.78 tff(2892,plain,
% 3.82/2.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a599) | (~c1_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a599) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a599)) | (~c1_1(a599)))),
% 3.82/2.78 inference(transitivity,[status(thm)],[2891, 2889])).
% 3.82/2.78 tff(2893,plain,
% 3.82/2.78 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a599) | (~c1_1(a599)) | (~c0_1(a599)))),
% 3.82/2.78 inference(quant_inst,[status(thm)],[])).
% 3.82/2.78 tff(2894,plain,
% 3.82/2.78 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a599) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a599)) | (~c1_1(a599))),
% 3.82/2.78 inference(modus_ponens,[status(thm)],[2893, 2892])).
% 3.82/2.78 tff(2895,plain,
% 3.82/2.78 (~c1_1(a599)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2894, 96, 2667, 145, 2678, 123, 2653, 2647, 567])).
% 3.82/2.78 tff(2896,plain,
% 3.82/2.78 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c2_1(a599) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | (~c0_1(a599)) | c1_1(a599))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c2_1(a599) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | (~c0_1(a599)) | c1_1(a599))),
% 3.82/2.78 inference(rewrite,[status(thm)],[])).
% 3.82/2.78 tff(2897,plain,
% 3.82/2.78 ((hskp42 | (~ndr1_0) | c1_1(a599) | c2_1(a599) | (~c0_1(a599)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628))) <=> (hskp42 | c2_1(a599) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | (~c0_1(a599)) | c1_1(a599))),
% 3.82/2.78 inference(rewrite,[status(thm)],[])).
% 3.82/2.78 tff(2898,plain,
% 3.82/2.78 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a599) | c2_1(a599) | (~c0_1(a599)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c2_1(a599) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | (~c0_1(a599)) | c1_1(a599)))),
% 3.82/2.78 inference(monotonicity,[status(thm)],[2897])).
% 3.82/2.78 tff(2899,plain,
% 3.82/2.78 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a599) | c2_1(a599) | (~c0_1(a599)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c2_1(a599) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | (~c0_1(a599)) | c1_1(a599))),
% 3.82/2.78 inference(transitivity,[status(thm)],[2898, 2896])).
% 3.82/2.78 tff(2900,plain,
% 3.82/2.78 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a599) | c2_1(a599) | (~c0_1(a599)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.78 inference(quant_inst,[status(thm)],[])).
% 3.82/2.78 tff(2901,plain,
% 3.82/2.78 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c2_1(a599) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | (~c0_1(a599)) | c1_1(a599)),
% 3.82/2.78 inference(modus_ponens,[status(thm)],[2900, 2899])).
% 3.82/2.78 tff(2902,plain,
% 3.82/2.78 ($false),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2901, 96, 2801, 145, 2678, 123, 2647, 900, 1, 2895])).
% 3.82/2.78 tff(2903,plain,((~hskp33) | hskp42 | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.78 tff(2904,plain,
% 3.82/2.78 (~hskp33),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2903, 2714, 1])).
% 3.82/2.78 tff(2905,plain,
% 3.82/2.78 (hskp61),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[381, 2904, 2687])).
% 3.82/2.78 tff(2906,plain,
% 3.82/2.78 (~c0_1(a670)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[387, 2905])).
% 3.82/2.78 tff(2907,plain,
% 3.82/2.78 (~c1_1(a670)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[393, 2905])).
% 3.82/2.78 tff(2908,plain,
% 3.82/2.78 (c2_1(a670)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[421, 2905])).
% 3.82/2.78 tff(2909,plain,
% 3.82/2.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c0_1(a658) | (~c2_1(a660)) | (~c2_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c0_1(a658) | (~c2_1(a660)) | (~c2_1(a670)))),
% 3.82/2.78 inference(rewrite,[status(thm)],[])).
% 3.82/2.78 tff(2910,plain,
% 3.82/2.78 (((~ndr1_0) | c3_1(a660) | c1_1(a660) | (~c2_1(a660)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a658) | c1_1(a658) | c0_1(a658)) <=> (c2_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c0_1(a658) | (~c2_1(a660)) | (~c2_1(a670)))),
% 3.82/2.78 inference(rewrite,[status(thm)],[])).
% 3.82/2.78 tff(2911,plain,
% 3.82/2.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a660) | c1_1(a660) | (~c2_1(a660)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a658) | c1_1(a658) | c0_1(a658))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c0_1(a658) | (~c2_1(a660)) | (~c2_1(a670))))),
% 3.82/2.78 inference(monotonicity,[status(thm)],[2910])).
% 3.82/2.78 tff(2912,plain,
% 3.82/2.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a660) | c1_1(a660) | (~c2_1(a660)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a658) | c1_1(a658) | c0_1(a658))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c0_1(a658) | (~c2_1(a660)) | (~c2_1(a670)))),
% 3.82/2.78 inference(transitivity,[status(thm)],[2911, 2909])).
% 3.82/2.78 tff(2913,plain,
% 3.82/2.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a660) | c1_1(a660) | (~c2_1(a660)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a658) | c1_1(a658) | c0_1(a658))),
% 3.82/2.78 inference(quant_inst,[status(thm)],[])).
% 3.82/2.78 tff(2914,plain,
% 3.82/2.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c0_1(a658) | (~c2_1(a660)) | (~c2_1(a670))),
% 3.82/2.78 inference(modus_ponens,[status(thm)],[2913, 2912])).
% 3.82/2.78 tff(2915,plain,
% 3.82/2.78 (~c2_1(a660)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2914, 96, 2908, 2689, 2907, 2906, 2688, 2888, 2887, 1390, 2722])).
% 3.82/2.78 tff(2916,plain,
% 3.82/2.78 (~c0_1(a660)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[1466, 2886])).
% 3.82/2.78 tff(2917,plain,
% 3.82/2.78 ($false),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2382, 96, 2888, 2887, 2916, 185, 2915])).
% 3.82/2.78 tff(2918,plain,(c2_1(a658) | c1_1(a658) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.78 tff(2919,plain,
% 3.82/2.78 (c2_1(a658)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2918, 2688, 1])).
% 3.82/2.78 tff(2920,assumption,(~c3_1(a658)), introduced(assumption)).
% 3.82/2.78 tff(2921,plain,
% 3.82/2.78 (~hskp56),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[1372, 2920])).
% 3.82/2.78 tff(2922,plain,
% 3.82/2.78 (~hskp42),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2713, 2921])).
% 3.82/2.78 tff(2923,plain,
% 3.82/2.78 (~hskp33),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2903, 2922, 1])).
% 3.82/2.78 tff(2924,plain,
% 3.82/2.78 (hskp61),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[381, 2923, 2687])).
% 3.82/2.78 tff(2925,plain,
% 3.82/2.78 (~c0_1(a670)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[387, 2924])).
% 3.82/2.78 tff(2926,plain,
% 3.82/2.78 (~c1_1(a670)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[393, 2924])).
% 3.82/2.78 tff(2927,assumption,(c2_1(a658)), introduced(assumption)).
% 3.82/2.78 tff(2928,plain,
% 3.82/2.78 (c2_1(a670)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[421, 2924])).
% 3.82/2.78 tff(2929,plain,
% 3.82/2.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | c0_1(a628) | (~c2_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | c0_1(a628) | (~c2_1(a670)))),
% 3.82/2.78 inference(rewrite,[status(thm)],[])).
% 3.82/2.78 tff(2930,plain,
% 3.82/2.78 (((~ndr1_0) | c3_1(a658) | c1_1(a658) | (~c2_1(a658)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a628) | c1_1(a628) | c0_1(a628)) <=> (c3_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | c0_1(a628) | (~c2_1(a670)))),
% 3.82/2.78 inference(rewrite,[status(thm)],[])).
% 3.82/2.78 tff(2931,plain,
% 3.82/2.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a658) | c1_1(a658) | (~c2_1(a658)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a628) | c1_1(a628) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | c0_1(a628) | (~c2_1(a670))))),
% 3.82/2.78 inference(monotonicity,[status(thm)],[2930])).
% 3.82/2.78 tff(2932,plain,
% 3.82/2.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a658) | c1_1(a658) | (~c2_1(a658)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a628) | c1_1(a628) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | c0_1(a628) | (~c2_1(a670)))),
% 3.82/2.78 inference(transitivity,[status(thm)],[2931, 2929])).
% 3.82/2.78 tff(2933,plain,
% 3.82/2.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a658) | c1_1(a658) | (~c2_1(a658)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a628) | c1_1(a628) | c0_1(a628))),
% 3.82/2.78 inference(quant_inst,[status(thm)],[])).
% 3.82/2.78 tff(2934,plain,
% 3.82/2.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | c0_1(a628) | (~c2_1(a670))),
% 3.82/2.78 inference(modus_ponens,[status(thm)],[2933, 2932])).
% 3.82/2.78 tff(2935,plain,
% 3.82/2.78 ($false),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2934, 96, 2928, 2927, 2920, 2926, 2925, 2688, 2653, 2647, 1390, 1])).
% 3.82/2.78 tff(2936,plain,(c3_1(a658) | (~c2_1(a658)) | c1_1(a658) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.78 tff(2937,plain,
% 3.82/2.78 (c3_1(a658)),
% 3.82/2.78 inference(unit_resolution,[status(thm)],[2936, 2919, 2688, 1])).
% 3.82/2.78 tff(2938,plain,
% 3.82/2.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a607) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a607)) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a607) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 3.82/2.78 inference(rewrite,[status(thm)],[])).
% 3.82/2.78 tff(2939,plain,
% 3.82/2.78 ((hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp5 | c2_1(a607) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 3.82/2.78 inference(rewrite,[status(thm)],[])).
% 3.82/2.78 tff(2940,plain,
% 3.82/2.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a607) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a607)) | (~c1_1(a607))))),
% 3.82/2.78 inference(monotonicity,[status(thm)],[2939])).
% 3.82/2.78 tff(2941,plain,
% 3.82/2.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a607) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 3.82/2.79 inference(transitivity,[status(thm)],[2940, 2938])).
% 3.82/2.79 tff(2942,plain,
% 3.82/2.79 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 3.82/2.79 inference(quant_inst,[status(thm)],[])).
% 3.82/2.79 tff(2943,plain,
% 3.82/2.79 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a607) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a607)) | (~c1_1(a607))),
% 3.82/2.79 inference(modus_ponens,[status(thm)],[2942, 2941])).
% 3.82/2.79 tff(2944,plain,
% 3.82/2.79 ($false),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[2943, 96, 583, 451, 440, 2678, 429, 2653, 2647, 567])).
% 3.82/2.79 tff(2945,plain,((~hskp37) | hskp5), inference(lemma,lemma(discharge,[]))).
% 3.82/2.79 tff(2946,plain,
% 3.82/2.79 (~hskp37),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[2945, 2667])).
% 3.82/2.79 tff(2947,plain,
% 3.82/2.79 (((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c0_1(a658)) | (~c2_1(a658)) | (~c3_1(a658)))) <=> ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp37 | hskp5 | (~ndr1_0) | (~c0_1(a658)) | (~c2_1(a658)) | (~c3_1(a658)))),
% 3.82/2.79 inference(rewrite,[status(thm)],[])).
% 3.82/2.79 tff(2948,plain,
% 3.82/2.79 ((hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a658)) | (~c2_1(a658))) <=> (hskp37 | hskp5 | (~ndr1_0) | (~c0_1(a658)) | (~c2_1(a658)) | (~c3_1(a658)))),
% 3.82/2.79 inference(rewrite,[status(thm)],[])).
% 3.82/2.79 tff(2949,plain,
% 3.82/2.79 (((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a658)) | (~c2_1(a658)))) <=> ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c0_1(a658)) | (~c2_1(a658)) | (~c3_1(a658))))),
% 3.82/2.79 inference(monotonicity,[status(thm)],[2948])).
% 3.82/2.79 tff(2950,plain,
% 3.82/2.79 (((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a658)) | (~c2_1(a658)))) <=> ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp37 | hskp5 | (~ndr1_0) | (~c0_1(a658)) | (~c2_1(a658)) | (~c3_1(a658)))),
% 3.82/2.79 inference(transitivity,[status(thm)],[2949, 2947])).
% 3.82/2.79 tff(2951,plain,
% 3.82/2.79 ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a658)) | (~c2_1(a658)))),
% 3.82/2.79 inference(quant_inst,[status(thm)],[])).
% 3.82/2.79 tff(2952,plain,
% 3.82/2.79 ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp37 | hskp5 | (~ndr1_0) | (~c0_1(a658)) | (~c2_1(a658)) | (~c3_1(a658))),
% 3.82/2.79 inference(modus_ponens,[status(thm)],[2951, 2950])).
% 3.82/2.79 tff(2953,plain,
% 3.82/2.79 (~c0_1(a658)),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[2952, 96, 2946, 2667, 2919, 2937, 581])).
% 3.82/2.79 tff(2954,plain,
% 3.82/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.79 inference(rewrite,[status(thm)],[])).
% 3.82/2.79 tff(2955,plain,
% 3.82/2.79 (((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a660) | c0_1(a660) | c3_1(a660)) <=> (c1_1(a658) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.79 inference(rewrite,[status(thm)],[])).
% 3.82/2.79 tff(2956,plain,
% 3.82/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a660) | c0_1(a660) | c3_1(a660))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628))))),
% 3.82/2.79 inference(monotonicity,[status(thm)],[2955])).
% 3.82/2.79 tff(2957,plain,
% 3.82/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a660) | c0_1(a660) | c3_1(a660))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.79 inference(transitivity,[status(thm)],[2956, 2954])).
% 3.82/2.79 tff(2958,plain,
% 3.82/2.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a660) | c0_1(a660) | c3_1(a660))),
% 3.82/2.79 inference(quant_inst,[status(thm)],[])).
% 3.82/2.79 tff(2959,plain,
% 3.82/2.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628))),
% 3.82/2.79 inference(modus_ponens,[status(thm)],[2958, 2957])).
% 3.82/2.79 tff(2960,plain,
% 3.82/2.79 ($false),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[2959, 96, 2927, 2839, 2678, 2688, 1479, 1473, 1467, 2647, 1221, 1])).
% 3.82/2.79 tff(2961,plain,((~hskp29) | (~c2_1(a658)) | (~c3_1(a658)) | c1_1(a658) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.79 tff(2962,plain,
% 3.82/2.79 (~hskp29),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[2961, 2919, 2937, 2688, 1])).
% 3.82/2.79 tff(2963,plain,
% 3.82/2.79 (hskp3),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[2787, 2962, 1])).
% 3.82/2.79 tff(2964,plain,
% 3.82/2.79 (~c3_1(a603)),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[1458, 2963])).
% 3.82/2.79 tff(2965,plain,
% 3.82/2.79 (c0_1(a603)),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[2737, 96, 2800, 1030, 185, 1903])).
% 3.82/2.79 tff(2966,plain,
% 3.82/2.79 (hskp42 | (~c0_1(a603))),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[2744, 96, 2678, 2647, 2800, 900, 1903, 1])).
% 3.82/2.79 tff(2967,plain,
% 3.82/2.79 (hskp42),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[2966, 2965])).
% 3.82/2.79 tff(2968,plain,
% 3.82/2.79 (hskp56),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[2713, 2967])).
% 3.82/2.79 tff(2969,plain,
% 3.82/2.79 (c3_1(a658)),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[1372, 2968])).
% 3.82/2.79 tff(2970,plain,
% 3.82/2.79 (~c3_1(a618)),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[1002, 2967])).
% 3.82/2.79 tff(2971,plain,
% 3.82/2.79 (~c2_1(a618)),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[923, 2967])).
% 3.82/2.79 tff(2972,plain,
% 3.82/2.79 (c2_1(a658)),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[2883, 1030, 1, 2688])).
% 3.82/2.79 tff(2973,plain,
% 3.82/2.79 (c1_1(a618)),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[957, 2967])).
% 3.82/2.79 tff(2974,plain,
% 3.82/2.79 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a628)))),
% 3.82/2.79 inference(rewrite,[status(thm)],[])).
% 3.82/2.79 tff(2975,plain,
% 3.82/2.79 ((hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618))) <=> (hskp5 | c2_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a628)))),
% 3.82/2.79 inference(rewrite,[status(thm)],[])).
% 3.82/2.79 tff(2976,plain,
% 3.82/2.79 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a628))))),
% 3.82/2.79 inference(monotonicity,[status(thm)],[2975])).
% 3.82/2.79 tff(2977,plain,
% 3.82/2.79 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a628)))),
% 3.82/2.79 inference(transitivity,[status(thm)],[2976, 2974])).
% 3.82/2.79 tff(2978,plain,
% 3.82/2.79 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618)))),
% 3.82/2.79 inference(quant_inst,[status(thm)],[])).
% 3.82/2.79 tff(2979,plain,
% 3.82/2.79 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a628))),
% 3.82/2.79 inference(modus_ponens,[status(thm)],[2978, 2977])).
% 3.82/2.79 tff(2980,plain,
% 3.82/2.79 (~c0_1(a618)),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[2979, 96, 2667, 2973, 2678, 2971, 2653, 2647, 567])).
% 3.82/2.79 tff(2981,assumption,(~c0_1(a618)), introduced(assumption)).
% 3.82/2.79 tff(2982,assumption,(c3_1(a670)), introduced(assumption)).
% 3.82/2.79 tff(2983,assumption,(~c0_1(a670)), introduced(assumption)).
% 3.82/2.79 tff(2984,assumption,(c2_1(a670)), introduced(assumption)).
% 3.82/2.79 tff(2985,plain,
% 3.82/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a674) | c0_1(a670) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)) | (~c2_1(a670)) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a674) | c0_1(a670) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)) | (~c2_1(a670)) | (~c3_1(a670)))),
% 3.82/2.79 inference(rewrite,[status(thm)],[])).
% 3.82/2.79 tff(2986,plain,
% 3.82/2.79 (((~ndr1_0) | c0_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a674) | (~c2_1(a674)) | (~c0_1(a674)) | c2_1(a628) | c1_1(a628) | (~c3_1(a628))) <=> (c1_1(a674) | c0_1(a670) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)) | (~c2_1(a670)) | (~c3_1(a670)))),
% 3.82/2.79 inference(rewrite,[status(thm)],[])).
% 3.82/2.79 tff(2987,plain,
% 3.82/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a674) | (~c2_1(a674)) | (~c0_1(a674)) | c2_1(a628) | c1_1(a628) | (~c3_1(a628)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a674) | c0_1(a670) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)) | (~c2_1(a670)) | (~c3_1(a670))))),
% 3.82/2.79 inference(monotonicity,[status(thm)],[2986])).
% 3.82/2.79 tff(2988,plain,
% 3.82/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a674) | (~c2_1(a674)) | (~c0_1(a674)) | c2_1(a628) | c1_1(a628) | (~c3_1(a628)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a674) | c0_1(a670) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)) | (~c2_1(a670)) | (~c3_1(a670)))),
% 3.82/2.79 inference(transitivity,[status(thm)],[2987, 2985])).
% 3.82/2.79 tff(2989,plain,
% 3.82/2.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a674) | (~c2_1(a674)) | (~c0_1(a674)) | c2_1(a628) | c1_1(a628) | (~c3_1(a628)))),
% 3.82/2.79 inference(quant_inst,[status(thm)],[])).
% 3.82/2.79 tff(2990,plain,
% 3.82/2.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a674) | c0_1(a670) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)) | (~c2_1(a670)) | (~c3_1(a670))),
% 3.82/2.79 inference(modus_ponens,[status(thm)],[2989, 2988])).
% 3.82/2.79 tff(2991,plain,
% 3.82/2.79 ($false),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[2990, 96, 279, 268, 2984, 2678, 257, 2983, 2653, 2647, 708, 2982])).
% 3.82/2.79 tff(2992,plain,((~hskp65) | (~c2_1(a670)) | c0_1(a670) | (~c3_1(a670))), inference(lemma,lemma(discharge,[]))).
% 3.82/2.79 tff(2993,plain,
% 3.82/2.79 (~c3_1(a670)),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[2992, 1908, 251, 1905])).
% 3.82/2.79 tff(2994,plain,
% 3.82/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670))),
% 3.82/2.79 inference(rewrite,[status(thm)],[])).
% 3.82/2.79 tff(2995,plain,
% 3.82/2.79 (((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a670) | c0_1(a670) | c3_1(a670)) <=> (c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670))),
% 3.82/2.79 inference(rewrite,[status(thm)],[])).
% 3.82/2.79 tff(2996,plain,
% 3.82/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a670) | c0_1(a670) | c3_1(a670))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670)))),
% 3.82/2.79 inference(monotonicity,[status(thm)],[2995])).
% 3.82/2.79 tff(2997,plain,
% 3.82/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a670) | c0_1(a670) | c3_1(a670))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670))),
% 3.82/2.79 inference(transitivity,[status(thm)],[2996, 2994])).
% 3.82/2.79 tff(2998,plain,
% 3.82/2.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a670) | c0_1(a670) | c3_1(a670))),
% 3.82/2.79 inference(quant_inst,[status(thm)],[])).
% 3.82/2.79 tff(2999,plain,
% 3.82/2.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670)),
% 3.82/2.79 inference(modus_ponens,[status(thm)],[2998, 2997])).
% 3.82/2.79 tff(3000,plain,
% 3.82/2.79 ($false),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[2999, 96, 2927, 2839, 2678, 1906, 1905, 2688, 2647, 1221, 2993, 1])).
% 3.82/2.79 tff(3001,plain,((~hskp61) | (~c2_1(a658)) | (~c3_1(a658)) | c1_1(a658) | c0_1(a628) | (~hskp65)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.79 tff(3002,plain,
% 3.82/2.79 (~hskp61),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[3001, 251, 2839, 2688, 1, 2927])).
% 3.82/2.79 tff(3003,plain,
% 3.82/2.79 (hskp33),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[381, 3002, 2687])).
% 3.82/2.79 tff(3004,plain,
% 3.82/2.79 (~c2_1(a599)),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[122, 3003])).
% 3.82/2.79 tff(3005,plain,
% 3.82/2.79 (c3_1(a599)),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[133, 3003])).
% 3.82/2.79 tff(3006,plain,
% 3.82/2.79 (c0_1(a599)),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[144, 3003])).
% 3.82/2.79 tff(3007,plain,
% 3.82/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a599)) | (~c3_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a599)) | (~c3_1(a599)))),
% 3.82/2.79 inference(rewrite,[status(thm)],[])).
% 3.82/2.79 tff(3008,plain,
% 3.82/2.79 (((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c0_1(a658)) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a618) | c0_1(a618) | c3_1(a618)) <=> (c1_1(a658) | c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a599)) | (~c3_1(a599)))),
% 3.82/2.79 inference(rewrite,[status(thm)],[])).
% 3.82/2.79 tff(3009,plain,
% 3.82/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c0_1(a658)) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a618) | c0_1(a618) | c3_1(a618))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a599)) | (~c3_1(a599))))),
% 3.82/2.79 inference(monotonicity,[status(thm)],[3008])).
% 3.82/2.79 tff(3010,plain,
% 3.82/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c0_1(a658)) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a618) | c0_1(a618) | c3_1(a618))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a599)) | (~c3_1(a599)))),
% 3.82/2.79 inference(transitivity,[status(thm)],[3009, 3007])).
% 3.82/2.79 tff(3011,plain,
% 3.82/2.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c0_1(a658)) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a618) | c0_1(a618) | c3_1(a618))),
% 3.82/2.79 inference(quant_inst,[status(thm)],[])).
% 3.82/2.79 tff(3012,plain,
% 3.82/2.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a599)) | (~c3_1(a599))),
% 3.82/2.79 inference(modus_ponens,[status(thm)],[3011, 3010])).
% 3.82/2.79 tff(3013,plain,
% 3.82/2.79 (~c0_1(a658)),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[3012, 96, 2839, 3006, 3005, 2688, 2700, 2699, 3004, 997, 2981])).
% 3.82/2.79 tff(3014,plain,
% 3.82/2.79 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)) | (~c1_1(a599)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)) | (~c1_1(a599)))),
% 3.82/2.79 inference(rewrite,[status(thm)],[])).
% 3.82/2.79 tff(3015,plain,
% 3.82/2.79 ((hskp6 | (~ndr1_0) | (~c3_1(a599)) | (~c1_1(a599)) | (~c0_1(a599))) <=> (hskp6 | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)) | (~c1_1(a599)))),
% 3.82/2.79 inference(rewrite,[status(thm)],[])).
% 3.82/2.79 tff(3016,plain,
% 3.82/2.79 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a599)) | (~c1_1(a599)) | (~c0_1(a599)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)) | (~c1_1(a599))))),
% 3.82/2.79 inference(monotonicity,[status(thm)],[3015])).
% 3.82/2.79 tff(3017,plain,
% 3.82/2.79 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a599)) | (~c1_1(a599)) | (~c0_1(a599)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)) | (~c1_1(a599)))),
% 3.82/2.79 inference(transitivity,[status(thm)],[3016, 3014])).
% 3.82/2.79 tff(3018,plain,
% 3.82/2.79 ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a599)) | (~c1_1(a599)) | (~c0_1(a599)))),
% 3.82/2.79 inference(quant_inst,[status(thm)],[])).
% 3.82/2.79 tff(3019,plain,
% 3.82/2.79 ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)) | (~c1_1(a599))),
% 3.82/2.79 inference(modus_ponens,[status(thm)],[3018, 3017])).
% 3.82/2.79 tff(3020,plain,
% 3.82/2.79 (~c1_1(a599)),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[3019, 96, 2510, 145, 134, 742])).
% 3.82/2.79 tff(3021,plain,
% 3.82/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a599)) | (~c3_1(a599)) | c1_1(a599))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a599)) | (~c3_1(a599)) | c1_1(a599))),
% 3.82/2.79 inference(rewrite,[status(thm)],[])).
% 3.82/2.79 tff(3022,plain,
% 3.82/2.79 (((~ndr1_0) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a618) | c0_1(a618) | c3_1(a618)) <=> (c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a599)) | (~c3_1(a599)) | c1_1(a599))),
% 3.82/2.79 inference(rewrite,[status(thm)],[])).
% 3.82/2.79 tff(3023,plain,
% 3.82/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a618) | c0_1(a618) | c3_1(a618))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a599)) | (~c3_1(a599)) | c1_1(a599)))),
% 3.82/2.79 inference(monotonicity,[status(thm)],[3022])).
% 3.82/2.79 tff(3024,plain,
% 3.82/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a618) | c0_1(a618) | c3_1(a618))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a599)) | (~c3_1(a599)) | c1_1(a599))),
% 3.82/2.79 inference(transitivity,[status(thm)],[3023, 3021])).
% 3.82/2.79 tff(3025,plain,
% 3.82/2.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a618) | c0_1(a618) | c3_1(a618))),
% 3.82/2.79 inference(quant_inst,[status(thm)],[])).
% 3.82/2.79 tff(3026,plain,
% 3.82/2.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a599)) | (~c3_1(a599)) | c1_1(a599)),
% 3.82/2.79 inference(modus_ponens,[status(thm)],[3025, 3024])).
% 3.82/2.79 tff(3027,plain,
% 3.82/2.79 ($false),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[3026, 96, 145, 134, 2700, 2699, 123, 997, 2981, 3020])).
% 3.82/2.79 tff(3028,plain,((~hskp33) | c2_1(a618) | c3_1(a618) | c0_1(a618) | hskp6), inference(lemma,lemma(discharge,[]))).
% 3.82/2.79 tff(3029,plain,
% 3.82/2.79 (hskp6),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[3028, 3003, 2699, 2981, 2700])).
% 3.82/2.79 tff(3030,plain,
% 3.82/2.79 (~c0_1(a609)),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[754, 3029])).
% 3.82/2.79 tff(3031,plain,
% 3.82/2.79 (c2_1(a609)),
% 3.82/2.79 inference(unit_resolution,[status(thm)],[767, 3029])).
% 3.82/2.79 tff(3032,plain,
% 3.82/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a674) | c2_1(a628) | c1_1(a628) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a674) | c2_1(a628) | c1_1(a628) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)))),
% 3.82/2.79 inference(rewrite,[status(thm)],[])).
% 3.82/2.79 tff(3033,plain,
% 3.82/2.79 (((~ndr1_0) | c0_1(a609) | (~c3_1(a609)) | (~c2_1(a609)) | c1_1(a674) | (~c2_1(a674)) | (~c0_1(a674)) | c2_1(a628) | c1_1(a628) | (~c3_1(a628))) <=> (c1_1(a674) | c2_1(a628) | c1_1(a628) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)))),
% 3.82/2.79 inference(rewrite,[status(thm)],[])).
% 3.82/2.79 tff(3034,plain,
% 3.82/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a609) | (~c3_1(a609)) | (~c2_1(a609)) | c1_1(a674) | (~c2_1(a674)) | (~c0_1(a674)) | c2_1(a628) | c1_1(a628) | (~c3_1(a628)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a674) | c2_1(a628) | c1_1(a628) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628))))),
% 3.82/2.79 inference(monotonicity,[status(thm)],[3033])).
% 3.82/2.79 tff(3035,plain,
% 3.82/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a609) | (~c3_1(a609)) | (~c2_1(a609)) | c1_1(a674) | (~c2_1(a674)) | (~c0_1(a674)) | c2_1(a628) | c1_1(a628) | (~c3_1(a628)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a674) | c2_1(a628) | c1_1(a628) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)))),
% 3.82/2.79 inference(transitivity,[status(thm)],[3034, 3032])).
% 3.82/2.79 tff(3036,plain,
% 3.82/2.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a609) | (~c3_1(a609)) | (~c2_1(a609)) | c1_1(a674) | (~c2_1(a674)) | (~c0_1(a674)) | c2_1(a628) | c1_1(a628) | (~c3_1(a628)))),
% 3.82/2.79 inference(quant_inst,[status(thm)],[])).
% 3.82/2.80 tff(3037,plain,
% 3.82/2.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a674) | c2_1(a628) | c1_1(a628) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628))),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3036, 3035])).
% 3.82/2.80 tff(3038,plain,
% 3.82/2.80 (~c3_1(a609)),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[3037, 96, 279, 268, 2678, 3031, 257, 2653, 2647, 3030, 708])).
% 3.82/2.80 tff(3039,plain,
% 3.82/2.80 (~c1_1(a609)),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[1509, 3029])).
% 3.82/2.80 tff(3040,plain,
% 3.82/2.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3041,plain,
% 3.82/2.80 (((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a609) | c0_1(a609) | c3_1(a609)) <=> (c1_1(a658) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3042,plain,
% 3.82/2.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a609) | c0_1(a609) | c3_1(a609))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a658) | (~c2_1(a658)) | (~c3_1(a658))))),
% 3.82/2.80 inference(monotonicity,[status(thm)],[3041])).
% 3.82/2.80 tff(3043,plain,
% 3.82/2.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a609) | c0_1(a609) | c3_1(a609))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))),
% 3.82/2.80 inference(transitivity,[status(thm)],[3042, 3040])).
% 3.82/2.80 tff(3044,plain,
% 3.82/2.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a609) | c0_1(a609) | c3_1(a609))),
% 3.82/2.80 inference(quant_inst,[status(thm)],[])).
% 3.82/2.80 tff(3045,plain,
% 3.82/2.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a658) | (~c2_1(a658)) | (~c3_1(a658))),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3044, 3043])).
% 3.82/2.80 tff(3046,plain,
% 3.82/2.80 ($false),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[3045, 96, 2927, 2839, 2688, 3030, 3039, 1221, 3038, 3013])).
% 3.82/2.80 tff(3047,plain,((~hskp65) | (~c2_1(a658)) | (~c3_1(a658)) | c1_1(a658) | c2_1(a618) | c3_1(a618) | c0_1(a618) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.80 tff(3048,plain,
% 3.82/2.80 (~hskp65),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[3047, 2980, 2972, 2688, 2971, 2970, 2969, 1])).
% 3.82/2.80 tff(3049,plain,
% 3.82/2.80 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a658) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a658)) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a658) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a658)) | (~c3_1(a658)))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3050,plain,
% 3.82/2.80 ((hskp20 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a658) | (~c2_1(a658)) | (~c3_1(a658))) <=> (hskp20 | c1_1(a658) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a658)) | (~c3_1(a658)))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3051,plain,
% 3.82/2.80 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a658) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a658)) | (~c3_1(a658))))),
% 3.82/2.80 inference(monotonicity,[status(thm)],[3050])).
% 3.82/2.80 tff(3052,plain,
% 3.82/2.80 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a658) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a658)) | (~c3_1(a658)))),
% 3.82/2.80 inference(transitivity,[status(thm)],[3051, 3049])).
% 3.82/2.80 tff(3053,plain,
% 3.82/2.80 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))),
% 3.82/2.80 inference(quant_inst,[status(thm)],[])).
% 3.82/2.80 tff(3054,plain,
% 3.82/2.80 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a658) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a658)) | (~c3_1(a658))),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3053, 3052])).
% 3.82/2.80 tff(3055,plain,
% 3.82/2.80 (hskp20 | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a658)) | (~c3_1(a658))),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[3054, 96, 2688, 1030, 723])).
% 3.82/2.80 tff(3056,plain,
% 3.82/2.80 (hskp20),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[3055, 2969, 2972, 2965, 1903])).
% 3.82/2.80 tff(3057,plain,
% 3.82/2.80 (~c3_1(a635)),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[670, 3056])).
% 3.82/2.80 tff(3058,plain,
% 3.82/2.80 (~c1_1(a635)),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[682, 3056])).
% 3.82/2.80 tff(3059,plain,
% 3.82/2.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c1_1(a635) | c3_1(a635) | c1_1(a628) | (~ndr1_0) | c0_1(a635) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c1_1(a635) | c3_1(a635) | c1_1(a628) | (~ndr1_0) | c0_1(a635) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3060,plain,
% 3.82/2.80 (((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a635) | c0_1(a635) | c3_1(a635)) <=> (c1_1(a658) | c1_1(a635) | c3_1(a635) | c1_1(a628) | (~ndr1_0) | c0_1(a635) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3061,plain,
% 3.82/2.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a635) | c0_1(a635) | c3_1(a635))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c1_1(a635) | c3_1(a635) | c1_1(a628) | (~ndr1_0) | c0_1(a635) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628))))),
% 3.82/2.80 inference(monotonicity,[status(thm)],[3060])).
% 3.82/2.80 tff(3062,plain,
% 3.82/2.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a635) | c0_1(a635) | c3_1(a635))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c1_1(a635) | c3_1(a635) | c1_1(a628) | (~ndr1_0) | c0_1(a635) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.80 inference(transitivity,[status(thm)],[3061, 3059])).
% 3.82/2.80 tff(3063,plain,
% 3.82/2.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a635) | c0_1(a635) | c3_1(a635))),
% 3.82/2.80 inference(quant_inst,[status(thm)],[])).
% 3.82/2.80 tff(3064,plain,
% 3.82/2.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c1_1(a635) | c3_1(a635) | c1_1(a628) | (~ndr1_0) | c0_1(a635) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628))),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3063, 3062])).
% 3.82/2.80 tff(3065,plain,
% 3.82/2.80 (c0_1(a635)),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[3064, 96, 2972, 2969, 2678, 2688, 3058, 3057, 2647, 1221, 1])).
% 3.82/2.80 tff(3066,plain,
% 3.82/2.80 (~c2_1(a635)),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[676, 3056])).
% 3.82/2.80 tff(3067,plain,
% 3.82/2.80 (hskp6),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[2515, 2476])).
% 3.82/2.80 tff(3068,plain,
% 3.82/2.80 (~c1_1(a609)),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[1509, 3067])).
% 3.82/2.80 tff(3069,plain,
% 3.82/2.80 (~c0_1(a609)),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[754, 3067])).
% 3.82/2.80 tff(3070,plain,
% 3.82/2.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c1_1(a628) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c1_1(a628) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3071,plain,
% 3.82/2.80 (((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a609) | c0_1(a609) | c3_1(a609)) <=> (c1_1(a658) | c1_1(a628) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3072,plain,
% 3.82/2.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a609) | c0_1(a609) | c3_1(a609))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c1_1(a628) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628))))),
% 3.82/2.80 inference(monotonicity,[status(thm)],[3071])).
% 3.82/2.80 tff(3073,plain,
% 3.82/2.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a609) | c0_1(a609) | c3_1(a609))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c1_1(a628) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 3.82/2.80 inference(transitivity,[status(thm)],[3072, 3070])).
% 3.82/2.80 tff(3074,plain,
% 3.82/2.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a609) | c0_1(a609) | c3_1(a609))),
% 3.82/2.80 inference(quant_inst,[status(thm)],[])).
% 3.82/2.80 tff(3075,plain,
% 3.82/2.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c1_1(a628) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628))),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3074, 3073])).
% 3.82/2.80 tff(3076,plain,
% 3.82/2.80 (c3_1(a609)),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[3075, 96, 2927, 2839, 2678, 2688, 2647, 3069, 3068, 1221, 1])).
% 3.82/2.80 tff(3077,plain,
% 3.82/2.80 (c2_1(a609)),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[767, 3067])).
% 3.82/2.80 tff(3078,plain,
% 3.82/2.80 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | c2_1(a618) | c3_1(a618) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a618)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp45 | c2_1(a618) | c3_1(a618) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a618)))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3079,plain,
% 3.82/2.80 ((hskp45 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609))) <=> (hskp45 | c2_1(a618) | c3_1(a618) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a618)))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3080,plain,
% 3.82/2.80 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | c2_1(a618) | c3_1(a618) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a618))))),
% 3.82/2.80 inference(monotonicity,[status(thm)],[3079])).
% 3.82/2.80 tff(3081,plain,
% 3.82/2.80 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp45 | c2_1(a618) | c3_1(a618) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a618)))),
% 3.82/2.80 inference(transitivity,[status(thm)],[3080, 3078])).
% 3.82/2.80 tff(3082,plain,
% 3.82/2.80 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)))),
% 3.82/2.80 inference(quant_inst,[status(thm)],[])).
% 3.82/2.80 tff(3083,plain,
% 3.82/2.80 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp45 | c2_1(a618) | c3_1(a618) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a618))),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3082, 3081])).
% 3.82/2.80 tff(3084,plain,
% 3.82/2.80 (hskp45),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[3083, 96, 2702, 3077, 2700, 2699, 3069, 1063, 3076])).
% 3.82/2.80 tff(3085,plain,
% 3.82/2.80 (c3_1(a623)),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[1100, 3084])).
% 3.82/2.80 tff(3086,plain,
% 3.82/2.80 (^[V: $i, U: $i] : refl((hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 3.82/2.80 inference(bind,[status(th)],[])).
% 3.82/2.80 tff(3087,plain,
% 3.82/2.80 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.82/2.80 inference(quant_intro,[status(thm)],[3086])).
% 3.82/2.80 tff(3088,plain,
% 3.82/2.80 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3089,plain,
% 3.82/2.80 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp36) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp36))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp36) <=> (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp36) <=> (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 3.82/2.80 inference(bind,[status(th)],[])).
% 3.82/2.80 tff(3090,plain,
% 3.82/2.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp36) <=> ![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.82/2.80 inference(quant_intro,[status(thm)],[3089])).
% 3.82/2.80 tff(3091,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp36)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause315')).
% 3.82/2.80 tff(3092,plain,
% 3.82/2.80 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3091, 3090])).
% 3.82/2.80 tff(3093,plain,
% 3.82/2.80 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3092, 3088])).
% 3.82/2.80 tff(3094,plain,(
% 3.82/2.80 ![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.82/2.80 inference(skolemize,[status(sab)],[3093])).
% 3.82/2.80 tff(3095,plain,
% 3.82/2.80 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3094, 3087])).
% 3.82/2.80 tff(3096,plain,
% 3.82/2.80 (((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp36 | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | (~c0_1(a635)))) <=> ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp36 | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | (~c0_1(a635)))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3097,plain,
% 3.82/2.80 ((hskp36 | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | c1_1(a635) | c2_1(a635) | (~c0_1(a635))) <=> (hskp36 | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | (~c0_1(a635)))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3098,plain,
% 3.82/2.80 (((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp36 | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | c1_1(a635) | c2_1(a635) | (~c0_1(a635)))) <=> ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp36 | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | (~c0_1(a635))))),
% 3.82/2.80 inference(monotonicity,[status(thm)],[3097])).
% 3.82/2.80 tff(3099,plain,
% 3.82/2.80 (((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp36 | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | c1_1(a635) | c2_1(a635) | (~c0_1(a635)))) <=> ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp36 | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | (~c0_1(a635)))),
% 3.82/2.80 inference(transitivity,[status(thm)],[3098, 3096])).
% 3.82/2.80 tff(3100,plain,
% 3.82/2.80 ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp36 | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | c1_1(a635) | c2_1(a635) | (~c0_1(a635)))),
% 3.82/2.80 inference(quant_inst,[status(thm)],[])).
% 3.82/2.80 tff(3101,plain,
% 3.82/2.80 ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp36 | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | (~c0_1(a635))),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3100, 3099])).
% 3.82/2.80 tff(3102,plain,
% 3.82/2.80 (hskp36),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[3101, 96, 2509, 2498, 2487, 1046, 1049, 3095, 1045])).
% 3.82/2.80 tff(3103,plain,
% 3.82/2.80 (((~hskp36) | (~c3_1(a605))) <=> ((~hskp36) | (~c3_1(a605)))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3104,plain,
% 3.82/2.80 (((~c3_1(a605)) | (~hskp36)) <=> ((~hskp36) | (~c3_1(a605)))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3105,axiom,((~c3_1(a605)) | (~hskp36)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause206')).
% 3.82/2.80 tff(3106,plain,
% 3.82/2.80 ((~hskp36) | (~c3_1(a605))),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3105, 3104])).
% 3.82/2.80 tff(3107,plain,
% 3.82/2.80 ((~hskp36) | (~c3_1(a605))),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3106, 3103])).
% 3.82/2.80 tff(3108,plain,
% 3.82/2.80 (~c3_1(a605)),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[3107, 3102])).
% 3.82/2.80 tff(3109,plain,
% 3.82/2.80 (~c0_1(a623)),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[1089, 3084])).
% 3.82/2.80 tff(3110,plain,
% 3.82/2.80 (((~hskp36) | c1_1(a605)) <=> ((~hskp36) | c1_1(a605))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3111,axiom,((~hskp36) | c1_1(a605)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 3.82/2.80 tff(3112,plain,
% 3.82/2.80 ((~hskp36) | c1_1(a605)),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3111, 3110])).
% 3.82/2.80 tff(3113,plain,
% 3.82/2.80 ((~hskp36) | c1_1(a605)),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3112, 3110])).
% 3.82/2.80 tff(3114,plain,
% 3.82/2.80 ((~hskp36) | c1_1(a605)),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3113, 3110])).
% 3.82/2.80 tff(3115,plain,
% 3.82/2.80 ((~hskp36) | c1_1(a605)),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3114, 3110])).
% 3.82/2.80 tff(3116,plain,
% 3.82/2.80 ((~hskp36) | c1_1(a605)),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3115, 3110])).
% 3.82/2.80 tff(3117,plain,
% 3.82/2.80 ((~hskp36) | c1_1(a605)),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3116, 3110])).
% 3.82/2.80 tff(3118,plain,
% 3.82/2.80 ((~hskp36) | c1_1(a605)),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3117, 3110])).
% 3.82/2.80 tff(3119,plain,
% 3.82/2.80 ((~hskp36) | c1_1(a605)),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3118, 3110])).
% 3.82/2.80 tff(3120,plain,
% 3.82/2.80 (c1_1(a605)),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[3119, 3102])).
% 3.82/2.80 tff(3121,plain,
% 3.82/2.80 (c2_1(a623)),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[1111, 3084])).
% 3.82/2.80 tff(3122,plain,
% 3.82/2.80 (((~hskp36) | c0_1(a605)) <=> ((~hskp36) | c0_1(a605))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3123,axiom,((~hskp36) | c0_1(a605)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 3.82/2.80 tff(3124,plain,
% 3.82/2.80 ((~hskp36) | c0_1(a605)),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3123, 3122])).
% 3.82/2.80 tff(3125,plain,
% 3.82/2.80 ((~hskp36) | c0_1(a605)),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3124, 3122])).
% 3.82/2.80 tff(3126,plain,
% 3.82/2.80 ((~hskp36) | c0_1(a605)),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3125, 3122])).
% 3.82/2.80 tff(3127,plain,
% 3.82/2.80 ((~hskp36) | c0_1(a605)),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3126, 3122])).
% 3.82/2.80 tff(3128,plain,
% 3.82/2.80 ((~hskp36) | c0_1(a605)),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3127, 3122])).
% 3.82/2.80 tff(3129,plain,
% 3.82/2.80 ((~hskp36) | c0_1(a605)),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3128, 3122])).
% 3.82/2.80 tff(3130,plain,
% 3.82/2.80 ((~hskp36) | c0_1(a605)),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3129, 3122])).
% 3.82/2.80 tff(3131,plain,
% 3.82/2.80 ((~hskp36) | c0_1(a605)),
% 3.82/2.80 inference(modus_ponens,[status(thm)],[3130, 3122])).
% 3.82/2.80 tff(3132,plain,
% 3.82/2.80 (c0_1(a605)),
% 3.82/2.80 inference(unit_resolution,[status(thm)],[3131, 3102])).
% 3.82/2.80 tff(3133,assumption,(~c2_1(a605)), introduced(assumption)).
% 3.82/2.80 tff(3134,assumption,(~c1_1(a628)), introduced(assumption)).
% 3.82/2.80 tff(3135,assumption,(~c2_1(a628)), introduced(assumption)).
% 3.82/2.80 tff(3136,assumption,(c3_1(a628)), introduced(assumption)).
% 3.82/2.80 tff(3137,assumption,(c0_1(a605)), introduced(assumption)).
% 3.82/2.80 tff(3138,assumption,(c1_1(a605)), introduced(assumption)).
% 3.82/2.80 tff(3139,plain,
% 3.82/2.80 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a605) | (~c0_1(a605)) | (~c1_1(a605)) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a605) | (~c0_1(a605)) | (~c1_1(a605)) | (~c3_1(a628)))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3140,plain,
% 3.82/2.80 ((hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a605) | (~c1_1(a605)) | (~c0_1(a605))) <=> (hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a605) | (~c0_1(a605)) | (~c1_1(a605)) | (~c3_1(a628)))),
% 3.82/2.80 inference(rewrite,[status(thm)],[])).
% 3.82/2.80 tff(3141,plain,
% 3.82/2.80 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a605) | (~c1_1(a605)) | (~c0_1(a605)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a605) | (~c0_1(a605)) | (~c1_1(a605)) | (~c3_1(a628))))),
% 3.82/2.80 inference(monotonicity,[status(thm)],[3140])).
% 3.82/2.80 tff(3142,plain,
% 3.82/2.80 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a605) | (~c1_1(a605)) | (~c0_1(a605)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a605) | (~c0_1(a605)) | (~c1_1(a605)) | (~c3_1(a628)))),
% 3.82/2.81 inference(transitivity,[status(thm)],[3141, 3139])).
% 3.82/2.81 tff(3143,plain,
% 3.82/2.81 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a605) | (~c1_1(a605)) | (~c0_1(a605)))),
% 3.82/2.81 inference(quant_inst,[status(thm)],[])).
% 3.82/2.81 tff(3144,plain,
% 3.82/2.81 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a605) | (~c0_1(a605)) | (~c1_1(a605)) | (~c3_1(a628))),
% 3.82/2.81 inference(modus_ponens,[status(thm)],[3143, 3142])).
% 3.82/2.81 tff(3145,plain,
% 3.82/2.81 ($false),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3144, 96, 583, 3138, 3137, 3136, 3135, 3134, 567, 3133])).
% 3.82/2.81 tff(3146,plain,(c2_1(a605) | hskp5 | (~c1_1(a605)) | (~c0_1(a605)) | (~c3_1(a628)) | c2_1(a628) | c1_1(a628)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.81 tff(3147,plain,
% 3.82/2.81 (c2_1(a605) | hskp5 | (~c1_1(a605)) | (~c0_1(a605))),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3146, 2647, 2678, 2653])).
% 3.82/2.81 tff(3148,plain,
% 3.82/2.81 (c2_1(a605)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3147, 3120, 2667, 3132])).
% 3.82/2.81 tff(3149,assumption,(c2_1(a605)), introduced(assumption)).
% 3.82/2.81 tff(3150,assumption,(~c3_1(a605)), introduced(assumption)).
% 3.82/2.81 tff(3151,assumption,(c0_1(a608)), introduced(assumption)).
% 3.82/2.81 tff(3152,assumption,(c3_1(a608)), introduced(assumption)).
% 3.82/2.81 tff(3153,plain,
% 3.82/2.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | (c3_1(a605) | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | (~c2_1(a605)) | (~c0_1(a605)) | (~c1_1(a605)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a605) | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | (~c2_1(a605)) | (~c0_1(a605)) | (~c1_1(a605)))),
% 3.82/2.81 inference(rewrite,[status(thm)],[])).
% 3.82/2.81 tff(3154,plain,
% 3.82/2.81 (((~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | c3_1(a605) | (~c2_1(a605)) | (~c0_1(a605)) | (~c0_1(a605)) | (~c1_1(a605)) | (~c2_1(a605))) <=> (c3_1(a605) | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | (~c2_1(a605)) | (~c0_1(a605)) | (~c1_1(a605)))),
% 3.82/2.81 inference(rewrite,[status(thm)],[])).
% 3.82/2.81 tff(3155,plain,
% 3.82/2.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | c3_1(a605) | (~c2_1(a605)) | (~c0_1(a605)) | (~c0_1(a605)) | (~c1_1(a605)) | (~c2_1(a605)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | (c3_1(a605) | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | (~c2_1(a605)) | (~c0_1(a605)) | (~c1_1(a605))))),
% 3.82/2.81 inference(monotonicity,[status(thm)],[3154])).
% 3.82/2.81 tff(3156,plain,
% 3.82/2.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | c3_1(a605) | (~c2_1(a605)) | (~c0_1(a605)) | (~c0_1(a605)) | (~c1_1(a605)) | (~c2_1(a605)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a605) | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | (~c2_1(a605)) | (~c0_1(a605)) | (~c1_1(a605)))),
% 3.82/2.81 inference(transitivity,[status(thm)],[3155, 3153])).
% 3.82/2.81 tff(3157,plain,
% 3.82/2.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | c3_1(a605) | (~c2_1(a605)) | (~c0_1(a605)) | (~c0_1(a605)) | (~c1_1(a605)) | (~c2_1(a605)))),
% 3.82/2.81 inference(quant_inst,[status(thm)],[])).
% 3.82/2.81 tff(3158,plain,
% 3.82/2.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a605) | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | (~c2_1(a605)) | (~c0_1(a605)) | (~c1_1(a605))),
% 3.82/2.81 inference(modus_ponens,[status(thm)],[3157, 3156])).
% 3.82/2.81 tff(3159,plain,
% 3.82/2.81 ((~c2_1(a608)) | (~c2_1(a605))),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3158, 96, 3152, 3151, 3138, 3137, 3150, 2129])).
% 3.82/2.81 tff(3160,plain,
% 3.82/2.81 (~c2_1(a608)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3159, 3149])).
% 3.82/2.81 tff(3161,plain,
% 3.82/2.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c0_1(a623) | c3_1(a605) | (~ndr1_0) | c2_1(a608) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a605)) | (~c1_1(a605)) | (~c2_1(a623)) | (~c3_1(a623)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c0_1(a623) | c3_1(a605) | (~ndr1_0) | c2_1(a608) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a605)) | (~c1_1(a605)) | (~c2_1(a623)) | (~c3_1(a623)))),
% 3.82/2.81 inference(rewrite,[status(thm)],[])).
% 3.82/2.81 tff(3162,plain,
% 3.82/2.81 (((~ndr1_0) | c3_1(a605) | (~c1_1(a605)) | (~c2_1(a605)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a608) | (~c0_1(a608)) | (~c3_1(a608))) <=> (c0_1(a623) | c3_1(a605) | (~ndr1_0) | c2_1(a608) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a605)) | (~c1_1(a605)) | (~c2_1(a623)) | (~c3_1(a623)))),
% 3.82/2.81 inference(rewrite,[status(thm)],[])).
% 3.82/2.81 tff(3163,plain,
% 3.82/2.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a605) | (~c1_1(a605)) | (~c2_1(a605)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a608) | (~c0_1(a608)) | (~c3_1(a608)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c0_1(a623) | c3_1(a605) | (~ndr1_0) | c2_1(a608) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a605)) | (~c1_1(a605)) | (~c2_1(a623)) | (~c3_1(a623))))),
% 3.82/2.81 inference(monotonicity,[status(thm)],[3162])).
% 3.82/2.81 tff(3164,plain,
% 3.82/2.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a605) | (~c1_1(a605)) | (~c2_1(a605)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a608) | (~c0_1(a608)) | (~c3_1(a608)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c0_1(a623) | c3_1(a605) | (~ndr1_0) | c2_1(a608) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a605)) | (~c1_1(a605)) | (~c2_1(a623)) | (~c3_1(a623)))),
% 3.82/2.81 inference(transitivity,[status(thm)],[3163, 3161])).
% 3.82/2.81 tff(3165,plain,
% 3.82/2.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a605) | (~c1_1(a605)) | (~c2_1(a605)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a608) | (~c0_1(a608)) | (~c3_1(a608)))),
% 3.82/2.81 inference(quant_inst,[status(thm)],[])).
% 3.82/2.81 tff(3166,plain,
% 3.82/2.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c0_1(a623) | c3_1(a605) | (~ndr1_0) | c2_1(a608) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a605)) | (~c1_1(a605)) | (~c2_1(a623)) | (~c3_1(a623))),
% 3.82/2.81 inference(modus_ponens,[status(thm)],[3165, 3164])).
% 3.82/2.81 tff(3167,plain,
% 3.82/2.81 ($false),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3166, 96, 1144, 1143, 3152, 3151, 3138, 1120, 3150, 1040, 3160, 3149])).
% 3.82/2.81 tff(3168,plain,((~c2_1(a605)) | (~c3_1(a623)) | (~c2_1(a623)) | (~c3_1(a608)) | (~c0_1(a608)) | (~c1_1(a605)) | c0_1(a623) | c3_1(a605) | (~c0_1(a605))), inference(lemma,lemma(discharge,[]))).
% 3.82/2.81 tff(3169,plain,
% 3.82/2.81 ($false),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3168, 3148, 3132, 3121, 2498, 2487, 3120, 3109, 3108, 3085])).
% 3.82/2.81 tff(3170,plain,((~hskp38) | (~c1_1(a618)) | c2_1(a618) | c3_1(a618) | c1_1(a635) | c2_1(a635) | (~c0_1(a635)) | (~c2_1(a658)) | (~c3_1(a658)) | c1_1(a658) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.81 tff(3171,plain,
% 3.82/2.81 (~hskp38),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3170, 2973, 2971, 2970, 3058, 3066, 3065, 2972, 2969, 2688, 1])).
% 3.82/2.81 tff(3172,assumption,(hskp66), introduced(assumption)).
% 3.82/2.81 tff(3173,plain,
% 3.82/2.81 (~c2_1(a675)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[296, 3172])).
% 3.82/2.81 tff(3174,plain,
% 3.82/2.81 (c1_1(a675)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[318, 3172])).
% 3.82/2.81 tff(3175,plain,
% 3.82/2.81 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a675) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | (~c0_1(a675)) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a675) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | (~c0_1(a675)) | (~c3_1(a628)))),
% 3.82/2.81 inference(rewrite,[status(thm)],[])).
% 3.82/2.81 tff(3176,plain,
% 3.82/2.81 ((hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a675) | (~c1_1(a675)) | (~c0_1(a675))) <=> (hskp5 | c2_1(a675) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | (~c0_1(a675)) | (~c3_1(a628)))),
% 3.82/2.81 inference(rewrite,[status(thm)],[])).
% 3.82/2.81 tff(3177,plain,
% 3.82/2.81 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a675) | (~c1_1(a675)) | (~c0_1(a675)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a675) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | (~c0_1(a675)) | (~c3_1(a628))))),
% 3.82/2.81 inference(monotonicity,[status(thm)],[3176])).
% 3.82/2.81 tff(3178,plain,
% 3.82/2.81 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a675) | (~c1_1(a675)) | (~c0_1(a675)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a675) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | (~c0_1(a675)) | (~c3_1(a628)))),
% 3.82/2.81 inference(transitivity,[status(thm)],[3177, 3175])).
% 3.82/2.81 tff(3179,plain,
% 3.82/2.81 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a675) | (~c1_1(a675)) | (~c0_1(a675)))),
% 3.82/2.81 inference(quant_inst,[status(thm)],[])).
% 3.82/2.81 tff(3180,plain,
% 3.82/2.81 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a675) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | (~c0_1(a675)) | (~c3_1(a628))),
% 3.82/2.81 inference(modus_ponens,[status(thm)],[3179, 3178])).
% 3.82/2.81 tff(3181,plain,
% 3.82/2.81 (~c0_1(a675)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3180, 96, 2667, 3174, 2678, 3173, 2653, 2647, 567])).
% 3.82/2.81 tff(3182,plain,
% 3.82/2.81 (c3_1(a675)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[307, 3172])).
% 3.82/2.81 tff(3183,plain,
% 3.82/2.81 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | c0_1(a675) | (~c3_1(a675)) | c0_1(a628))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp38 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | c0_1(a675) | (~c3_1(a675)) | c0_1(a628))),
% 3.82/2.81 inference(rewrite,[status(thm)],[])).
% 3.82/2.81 tff(3184,plain,
% 3.82/2.81 ((hskp38 | (~ndr1_0) | c0_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c1_1(a628) | c0_1(a628) | c2_1(a628)) <=> (hskp38 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | c0_1(a675) | (~c3_1(a675)) | c0_1(a628))),
% 3.82/2.81 inference(rewrite,[status(thm)],[])).
% 3.82/2.81 tff(3185,plain,
% 3.82/2.81 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c0_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c1_1(a628) | c0_1(a628) | c2_1(a628))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | c0_1(a675) | (~c3_1(a675)) | c0_1(a628)))),
% 3.82/2.81 inference(monotonicity,[status(thm)],[3184])).
% 3.82/2.81 tff(3186,plain,
% 3.82/2.81 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c0_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c1_1(a628) | c0_1(a628) | c2_1(a628))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp38 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | c0_1(a675) | (~c3_1(a675)) | c0_1(a628))),
% 3.82/2.81 inference(transitivity,[status(thm)],[3185, 3183])).
% 3.82/2.81 tff(3187,plain,
% 3.82/2.81 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c0_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c1_1(a628) | c0_1(a628) | c2_1(a628))),
% 3.82/2.81 inference(quant_inst,[status(thm)],[])).
% 3.82/2.81 tff(3188,plain,
% 3.82/2.81 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp38 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | c0_1(a675) | (~c3_1(a675)) | c0_1(a628)),
% 3.82/2.81 inference(modus_ponens,[status(thm)],[3187, 3186])).
% 3.82/2.81 tff(3189,plain,
% 3.82/2.81 ($false),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3188, 96, 2462, 3174, 3182, 2653, 2647, 11, 3181, 1])).
% 3.82/2.81 tff(3190,plain,((~hskp66) | hskp38 | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.81 tff(3191,plain,
% 3.82/2.81 (~hskp66),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3190, 3171, 1])).
% 3.82/2.81 tff(3192,plain,
% 3.82/2.81 (hskp64),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[94, 3191, 3048])).
% 3.82/2.81 tff(3193,plain,
% 3.82/2.81 (~c0_1(a673)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[1813, 3192])).
% 3.82/2.81 tff(3194,plain,
% 3.82/2.81 (c3_1(a673)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[1787, 3192])).
% 3.82/2.81 tff(3195,plain,
% 3.82/2.81 (c1_1(a673)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[1824, 3192])).
% 3.82/2.81 tff(3196,plain,
% 3.82/2.81 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | c0_1(a673) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | c0_1(a628))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp38 | c0_1(a673) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | c0_1(a628))),
% 3.82/2.81 inference(rewrite,[status(thm)],[])).
% 3.82/2.81 tff(3197,plain,
% 3.82/2.81 ((hskp38 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a628) | c0_1(a628) | c2_1(a628)) <=> (hskp38 | c0_1(a673) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | c0_1(a628))),
% 3.82/2.81 inference(rewrite,[status(thm)],[])).
% 3.82/2.81 tff(3198,plain,
% 3.82/2.81 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a628) | c0_1(a628) | c2_1(a628))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | c0_1(a673) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | c0_1(a628)))),
% 3.82/2.81 inference(monotonicity,[status(thm)],[3197])).
% 3.82/2.81 tff(3199,plain,
% 3.82/2.81 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a628) | c0_1(a628) | c2_1(a628))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp38 | c0_1(a673) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | c0_1(a628))),
% 3.82/2.81 inference(transitivity,[status(thm)],[3198, 3196])).
% 3.82/2.81 tff(3200,plain,
% 3.82/2.81 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a628) | c0_1(a628) | c2_1(a628))),
% 3.82/2.81 inference(quant_inst,[status(thm)],[])).
% 3.82/2.81 tff(3201,plain,
% 3.82/2.81 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp38 | c0_1(a673) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | c0_1(a628)),
% 3.82/2.81 inference(modus_ponens,[status(thm)],[3200, 3199])).
% 3.82/2.81 tff(3202,plain,
% 3.82/2.81 (hskp38 | (~c3_1(a673)) | (~c1_1(a673)) | c0_1(a628)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3201, 96, 1984, 2653, 2647, 11])).
% 3.82/2.81 tff(3203,plain,
% 3.82/2.81 (hskp38),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3202, 1, 1880, 1881])).
% 3.82/2.81 tff(3204,plain,
% 3.82/2.81 (hskp6),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[2515, 3203])).
% 3.82/2.81 tff(3205,plain,
% 3.82/2.81 (~c1_1(a609)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[1509, 3204])).
% 3.82/2.81 tff(3206,plain,
% 3.82/2.81 (~c0_1(a609)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[754, 3204])).
% 3.82/2.81 tff(3207,plain,
% 3.82/2.81 (c3_1(a609)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3075, 96, 2927, 2839, 2678, 2688, 2647, 3206, 3205, 1221, 1])).
% 3.82/2.81 tff(3208,plain,
% 3.82/2.81 (hskp42 | (~c0_1(a603)) | c0_1(a628)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[2744, 96, 2678, 2647, 1233, 900, 1903])).
% 3.82/2.81 tff(3209,plain,
% 3.82/2.81 (hskp42),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3208, 1, 1918])).
% 3.82/2.81 tff(3210,plain,
% 3.82/2.81 (~c3_1(a618)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[1002, 3209])).
% 3.82/2.81 tff(3211,plain,
% 3.82/2.81 (~c2_1(a618)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[923, 3209])).
% 3.82/2.81 tff(3212,plain,
% 3.82/2.81 (c2_1(a609)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[767, 3204])).
% 3.82/2.81 tff(3213,plain,
% 3.82/2.81 (c1_1(a618)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[957, 3209])).
% 3.82/2.81 tff(3214,plain,
% 3.82/2.81 (hskp45),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3083, 96, 3213, 3212, 3211, 3210, 3206, 1063, 3207])).
% 3.82/2.81 tff(3215,plain,
% 3.82/2.81 (c3_1(a623)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[1100, 3214])).
% 3.82/2.81 tff(3216,plain,
% 3.82/2.81 (c0_1(a608)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[2486, 3203])).
% 3.82/2.81 tff(3217,plain,
% 3.82/2.81 (c3_1(a608)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[2497, 3203])).
% 3.82/2.81 tff(3218,plain,
% 3.82/2.81 (c1_1(a608)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[2508, 3203])).
% 3.82/2.81 tff(3219,plain,
% 3.82/2.81 (hskp36),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3101, 96, 3218, 3217, 3216, 1046, 1049, 3095, 1045])).
% 3.82/2.81 tff(3220,plain,
% 3.82/2.81 (~c3_1(a605)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3107, 3219])).
% 3.82/2.81 tff(3221,plain,
% 3.82/2.81 (~c0_1(a623)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[1089, 3214])).
% 3.82/2.81 tff(3222,plain,
% 3.82/2.81 (c1_1(a605)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3119, 3219])).
% 3.82/2.81 tff(3223,plain,
% 3.82/2.81 (c2_1(a623)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[1111, 3214])).
% 3.82/2.81 tff(3224,plain,
% 3.82/2.81 (c0_1(a605)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3131, 3219])).
% 3.82/2.81 tff(3225,plain,
% 3.82/2.81 (c2_1(a605)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3147, 3222, 2667, 3224])).
% 3.82/2.81 tff(3226,plain,
% 3.82/2.81 ($false),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3168, 3225, 3224, 3223, 3217, 3216, 3222, 3221, 3220, 3215])).
% 3.82/2.81 tff(3227,plain,(c0_1(a628) | c1_1(a635) | c2_1(a635) | (~c0_1(a635)) | (~c2_1(a658)) | (~c3_1(a658)) | c1_1(a658) | (~c0_1(a603)) | c1_1(a603) | c2_1(a603) | (~c1_1(a673)) | (~c3_1(a673)) | c0_1(a673)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.81 tff(3228,plain,
% 3.82/2.81 ($false),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3227, 3195, 3194, 3058, 1, 2972, 2969, 2688, 2965, 2800, 1903, 3065, 3066, 3193])).
% 3.82/2.81 tff(3229,plain,(c2_1(a603) | c0_1(a628) | c1_1(a658) | c3_1(a603)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.81 tff(3230,plain,
% 3.82/2.81 (c2_1(a603)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3229, 2964, 2688, 1])).
% 3.82/2.81 tff(3231,plain,
% 3.82/2.81 (~c1_1(a603)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[1664, 2963])).
% 3.82/2.81 tff(3232,plain,
% 3.82/2.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a658) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a658) | (~c2_1(a658)) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a658) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a658) | (~c2_1(a658)) | c0_1(a628))),
% 3.82/2.81 inference(rewrite,[status(thm)],[])).
% 3.82/2.81 tff(3233,plain,
% 3.82/2.81 (((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a628) | c1_1(a628) | c0_1(a628)) <=> (c1_1(a658) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a658) | (~c2_1(a658)) | c0_1(a628))),
% 3.82/2.81 inference(rewrite,[status(thm)],[])).
% 3.82/2.81 tff(3234,plain,
% 3.82/2.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a628) | c1_1(a628) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a658) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a658) | (~c2_1(a658)) | c0_1(a628)))),
% 3.82/2.81 inference(monotonicity,[status(thm)],[3233])).
% 3.82/2.81 tff(3235,plain,
% 3.82/2.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a628) | c1_1(a628) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a658) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a658) | (~c2_1(a658)) | c0_1(a628))),
% 3.82/2.81 inference(transitivity,[status(thm)],[3234, 3232])).
% 3.82/2.81 tff(3236,plain,
% 3.82/2.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a628) | c1_1(a628) | c0_1(a628))),
% 3.82/2.81 inference(quant_inst,[status(thm)],[])).
% 3.82/2.81 tff(3237,plain,
% 3.82/2.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a658) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a658) | (~c2_1(a658)) | c0_1(a628)),
% 3.82/2.81 inference(modus_ponens,[status(thm)],[3236, 3235])).
% 3.82/2.81 tff(3238,plain,
% 3.82/2.81 ($false),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3237, 96, 2919, 2688, 2653, 2647, 3231, 2964, 1390, 3230, 2953, 1])).
% 3.82/2.81 tff(3239,plain,(c1_1(a658) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.81 tff(3240,plain,
% 3.82/2.81 (c1_1(a658)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3239, 1])).
% 3.82/2.81 tff(3241,plain,
% 3.82/2.81 (~hskp56),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[1361, 3240])).
% 3.82/2.81 tff(3242,plain,
% 3.82/2.81 (~hskp42),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[2713, 3241])).
% 3.82/2.81 tff(3243,plain,
% 3.82/2.81 (~hskp33),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[2903, 3242, 1])).
% 3.82/2.81 tff(3244,plain,
% 3.82/2.81 (hskp61),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[381, 3243, 2687])).
% 3.82/2.81 tff(3245,plain,
% 3.82/2.81 (~c0_1(a670)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[387, 3244])).
% 3.82/2.81 tff(3246,plain,
% 3.82/2.81 (c2_1(a670)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[421, 3244])).
% 3.82/2.81 tff(3247,plain,
% 3.82/2.81 (~c1_1(a670)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[393, 3244])).
% 3.82/2.81 tff(3248,plain,
% 3.82/2.81 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670))),
% 3.82/2.81 inference(rewrite,[status(thm)],[])).
% 3.82/2.81 tff(3249,plain,
% 3.82/2.81 ((hskp42 | (~ndr1_0) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a670) | c3_1(a670) | c0_1(a670)) <=> (hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670))),
% 3.82/2.81 inference(rewrite,[status(thm)],[])).
% 3.82/2.81 tff(3250,plain,
% 3.82/2.81 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a670) | c3_1(a670) | c0_1(a670))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670)))),
% 3.82/2.81 inference(monotonicity,[status(thm)],[3249])).
% 3.82/2.81 tff(3251,plain,
% 3.82/2.81 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a670) | c3_1(a670) | c0_1(a670))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670))),
% 3.82/2.81 inference(transitivity,[status(thm)],[3250, 3248])).
% 3.82/2.81 tff(3252,plain,
% 3.82/2.81 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a670) | c3_1(a670) | c0_1(a670))),
% 3.82/2.81 inference(quant_inst,[status(thm)],[])).
% 3.82/2.81 tff(3253,plain,
% 3.82/2.81 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670)),
% 3.82/2.81 inference(modus_ponens,[status(thm)],[3252, 3251])).
% 3.82/2.81 tff(3254,plain,
% 3.82/2.81 (c3_1(a670)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3253, 96, 3242, 2678, 3247, 3245, 2647, 2811, 1])).
% 3.82/2.81 tff(3255,plain,
% 3.82/2.81 (~hskp65),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[2992, 3254, 3246, 3245])).
% 3.82/2.81 tff(3256,plain,
% 3.82/2.81 (~hskp37),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[2945, 583])).
% 3.82/2.81 tff(3257,plain,
% 3.82/2.81 (((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)))) <=> ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)))),
% 3.82/2.81 inference(rewrite,[status(thm)],[])).
% 3.82/2.81 tff(3258,plain,
% 3.82/2.81 ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)))),
% 3.82/2.81 inference(quant_inst,[status(thm)],[])).
% 3.82/2.81 tff(3259,plain,
% 3.82/2.81 ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608))),
% 3.82/2.81 inference(modus_ponens,[status(thm)],[3258, 3257])).
% 3.82/2.81 tff(3260,plain,
% 3.82/2.81 (~c2_1(a608)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3259, 96, 3256, 583, 2498, 2487, 581])).
% 3.82/2.81 tff(3261,plain,
% 3.82/2.81 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608)) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608)) | (~c3_1(a628)))),
% 3.82/2.81 inference(rewrite,[status(thm)],[])).
% 3.82/2.81 tff(3262,plain,
% 3.82/2.81 ((hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608))) <=> (hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608)) | (~c3_1(a628)))),
% 3.82/2.81 inference(rewrite,[status(thm)],[])).
% 3.82/2.81 tff(3263,plain,
% 3.82/2.81 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608)) | (~c3_1(a628))))),
% 3.82/2.81 inference(monotonicity,[status(thm)],[3262])).
% 3.82/2.81 tff(3264,plain,
% 3.82/2.81 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608)) | (~c3_1(a628)))),
% 3.82/2.81 inference(transitivity,[status(thm)],[3263, 3261])).
% 3.82/2.81 tff(3265,plain,
% 3.82/2.81 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608)))),
% 3.82/2.81 inference(quant_inst,[status(thm)],[])).
% 3.82/2.81 tff(3266,plain,
% 3.82/2.81 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608)) | (~c3_1(a628))),
% 3.82/2.81 inference(modus_ponens,[status(thm)],[3265, 3264])).
% 3.82/2.81 tff(3267,plain,
% 3.82/2.81 ($false),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3266, 96, 583, 2509, 2487, 2678, 2653, 2647, 567, 3260])).
% 3.82/2.81 tff(3268,plain,((~hskp38) | hskp5), inference(lemma,lemma(discharge,[]))).
% 3.82/2.81 tff(3269,plain,
% 3.82/2.81 (~hskp38),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3268, 2667])).
% 3.82/2.81 tff(3270,plain,
% 3.82/2.81 (~hskp66),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3190, 3269, 1])).
% 3.82/2.81 tff(3271,plain,
% 3.82/2.81 (hskp64),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[94, 3270, 3255])).
% 3.82/2.81 tff(3272,plain,
% 3.82/2.81 (~c0_1(a673)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[1813, 3271])).
% 3.82/2.81 tff(3273,plain,
% 3.82/2.81 (c1_1(a673)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[1824, 3271])).
% 3.82/2.81 tff(3274,plain,
% 3.82/2.81 (c3_1(a673)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[1787, 3271])).
% 3.82/2.81 tff(3275,plain,
% 3.82/2.81 ($false),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3201, 96, 3269, 3274, 3273, 3272, 2653, 2647, 11, 1])).
% 3.82/2.81 tff(3276,plain,(c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 3.82/2.81 tff(3277,assumption,(c0_1(a628)), introduced(assumption)).
% 3.82/2.81 tff(3278,plain,
% 3.82/2.81 (hskp58),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[2753, 3277, 106])).
% 3.82/2.81 tff(3279,plain,
% 3.82/2.81 (~c1_1(a663)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[41, 3278])).
% 3.82/2.81 tff(3280,plain,
% 3.82/2.81 (~c0_1(a663)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[47, 3278])).
% 3.82/2.81 tff(3281,plain,
% 3.82/2.81 (c3_1(a663)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[58, 3278])).
% 3.82/2.81 tff(3282,plain,
% 3.82/2.81 ($false),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[2763, 96, 2801, 3281, 3280, 3279, 2653, 2647, 900, 3277])).
% 3.82/2.81 tff(3283,plain,((~c0_1(a628)) | hskp42 | hskp41), inference(lemma,lemma(discharge,[]))).
% 3.82/2.81 tff(3284,plain,
% 3.82/2.81 (hskp41),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[3283, 2801, 3276])).
% 3.82/2.81 tff(3285,plain,
% 3.82/2.81 (~c1_1(a617)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[517, 3284])).
% 3.82/2.81 tff(3286,plain,
% 3.82/2.81 (c3_1(a617)),
% 3.82/2.81 inference(unit_resolution,[status(thm)],[528, 3284])).
% 3.82/2.81 tff(3287,plain,
% 3.82/2.81 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a617) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a617) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | c0_1(a617) | (~c3_1(a617)))),
% 3.82/2.82 inference(rewrite,[status(thm)],[])).
% 3.82/2.82 tff(3288,plain,
% 3.82/2.82 ((hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617))) <=> (hskp42 | c1_1(a617) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | c0_1(a617) | (~c3_1(a617)))),
% 3.82/2.82 inference(rewrite,[status(thm)],[])).
% 3.82/2.82 tff(3289,plain,
% 3.82/2.82 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a617) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | c0_1(a617) | (~c3_1(a617))))),
% 3.82/2.82 inference(monotonicity,[status(thm)],[3288])).
% 3.82/2.82 tff(3290,plain,
% 3.82/2.82 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a617) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | c0_1(a617) | (~c3_1(a617)))),
% 3.82/2.82 inference(transitivity,[status(thm)],[3289, 3287])).
% 3.82/2.82 tff(3291,plain,
% 3.82/2.82 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))),
% 3.82/2.82 inference(quant_inst,[status(thm)],[])).
% 3.82/2.82 tff(3292,plain,
% 3.82/2.82 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a617) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | c0_1(a617) | (~c3_1(a617))),
% 3.82/2.82 inference(modus_ponens,[status(thm)],[3291, 3290])).
% 3.82/2.82 tff(3293,plain,
% 3.82/2.82 (c0_1(a617)),
% 3.82/2.82 inference(unit_resolution,[status(thm)],[3292, 96, 2801, 3286, 3285, 2653, 2647, 900, 3276])).
% 3.82/2.82 tff(3294,plain,
% 3.82/2.82 (c2_1(a617)),
% 3.82/2.82 inference(unit_resolution,[status(thm)],[556, 3284])).
% 3.82/2.82 tff(3295,plain,
% 3.82/2.82 ($false),
% 3.82/2.82 inference(unit_resolution,[status(thm)],[1290, 3256, 583, 698])).
% 3.82/2.82 tff(3296,plain,(hskp5 | (~c0_1(a617)) | (~c2_1(a617)) | (~c3_1(a617))), inference(lemma,lemma(discharge,[]))).
% 3.82/2.82 tff(3297,plain,
% 3.82/2.82 (hskp5),
% 3.82/2.82 inference(unit_resolution,[status(thm)],[3296, 3293, 3294, 3286])).
% 3.82/2.82 tff(3298,plain,
% 3.82/2.82 (~c3_1(a606)),
% 3.82/2.82 inference(unit_resolution,[status(thm)],[634, 3297])).
% 3.82/2.82 tff(3299,plain,
% 3.82/2.82 (c2_1(a606)),
% 3.82/2.82 inference(unit_resolution,[status(thm)],[651, 3297])).
% 3.82/2.82 tff(3300,plain,
% 3.82/2.82 (~c0_1(a606)),
% 3.82/2.82 inference(unit_resolution,[status(thm)],[640, 3297])).
% 3.82/2.82 tff(3301,plain,
% 3.82/2.82 (~hskp20),
% 3.82/2.82 inference(unit_resolution,[status(thm)],[692, 3300, 3299, 3298])).
% 3.82/2.82 tff(3302,plain,
% 3.82/2.82 (~hskp14),
% 3.82/2.82 inference(unit_resolution,[status(thm)],[2454, 3301, 3293, 3285, 3286, 3294])).
% 3.82/2.82 tff(3303,plain,
% 3.82/2.82 (hskp15 | hskp14 | (~c0_1(a617))),
% 3.82/2.82 inference(unit_resolution,[status(thm)],[612, 96, 3294, 3285, 250])).
% 3.82/2.82 tff(3304,plain,
% 3.82/2.82 (hskp15),
% 3.82/2.82 inference(unit_resolution,[status(thm)],[3303, 3302, 3293])).
% 3.82/2.82 tff(3305,plain,
% 3.82/2.82 (~c0_1(a625)),
% 3.82/2.82 inference(unit_resolution,[status(thm)],[161, 3304])).
% 3.82/2.82 tff(3306,plain,
% 3.82/2.82 (~c2_1(a625)),
% 3.82/2.82 inference(unit_resolution,[status(thm)],[190, 3304])).
% 3.82/2.82 tff(3307,plain,
% 3.82/2.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c2_1(a628) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c0_1(a628)) | (~c3_1(a628)) | (~c3_1(a617)) | (~c0_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c2_1(a628) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c0_1(a628)) | (~c3_1(a628)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 3.82/2.82 inference(rewrite,[status(thm)],[])).
% 3.82/2.82 tff(3308,plain,
% 3.82/2.82 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a625) | c0_1(a625) | c3_1(a625)) <=> (c1_1(a617) | c2_1(a628) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c0_1(a628)) | (~c3_1(a628)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 3.82/2.82 inference(rewrite,[status(thm)],[])).
% 3.82/2.82 tff(3309,plain,
% 3.82/2.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a625) | c0_1(a625) | c3_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c2_1(a628) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c0_1(a628)) | (~c3_1(a628)) | (~c3_1(a617)) | (~c0_1(a617))))),
% 3.82/2.82 inference(monotonicity,[status(thm)],[3308])).
% 3.82/2.82 tff(3310,plain,
% 3.82/2.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a625) | c0_1(a625) | c3_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c2_1(a628) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c0_1(a628)) | (~c3_1(a628)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 3.82/2.82 inference(transitivity,[status(thm)],[3309, 3307])).
% 3.82/2.82 tff(3311,plain,
% 3.82/2.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a625) | c0_1(a625) | c3_1(a625))),
% 3.82/2.82 inference(quant_inst,[status(thm)],[])).
% 3.82/2.82 tff(3312,plain,
% 3.82/2.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c2_1(a628) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c0_1(a628)) | (~c3_1(a628)) | (~c3_1(a617)) | (~c0_1(a617))),
% 3.82/2.82 inference(modus_ponens,[status(thm)],[3311, 3310])).
% 3.82/2.82 tff(3313,plain,
% 3.82/2.82 (c3_1(a625)),
% 3.82/2.82 inference(unit_resolution,[status(thm)],[3312, 96, 3286, 2678, 3285, 2653, 3306, 3305, 997, 3293, 3276])).
% 3.82/2.82 tff(3314,plain,
% 3.82/2.82 (~c1_1(a625)),
% 3.82/2.82 inference(unit_resolution,[status(thm)],[167, 3304])).
% 3.82/2.82 tff(3315,plain,
% 3.82/2.82 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c2_1(a628) | c1_1(a628) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c2_1(a628) | c1_1(a628) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a628)))),
% 3.82/2.82 inference(rewrite,[status(thm)],[])).
% 3.82/2.82 tff(3316,plain,
% 3.82/2.82 ((hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625))) <=> (hskp42 | c2_1(a628) | c1_1(a628) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a628)))),
% 3.82/2.82 inference(rewrite,[status(thm)],[])).
% 3.82/2.82 tff(3317,plain,
% 3.82/2.82 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c2_1(a628) | c1_1(a628) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a628))))),
% 3.82/2.82 inference(monotonicity,[status(thm)],[3316])).
% 3.82/2.82 tff(3318,plain,
% 3.82/2.82 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c2_1(a628) | c1_1(a628) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a628)))),
% 3.82/2.82 inference(transitivity,[status(thm)],[3317, 3315])).
% 3.82/2.82 tff(3319,plain,
% 3.82/2.82 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))),
% 3.82/2.82 inference(quant_inst,[status(thm)],[])).
% 3.82/2.82 tff(3320,plain,
% 3.82/2.82 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c2_1(a628) | c1_1(a628) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a628))),
% 3.82/2.82 inference(modus_ponens,[status(thm)],[3319, 3318])).
% 3.82/2.82 tff(3321,plain,
% 3.82/2.82 ($false),
% 3.82/2.82 inference(unit_resolution,[status(thm)],[3320, 96, 2801, 2653, 2647, 3314, 3305, 900, 3313, 3276])).
% 3.82/2.82 tff(3322,plain,(hskp42), inference(lemma,lemma(discharge,[]))).
% 3.82/2.82 tff(3323,plain,
% 3.82/2.82 (~c3_1(a618)),
% 3.82/2.82 inference(unit_resolution,[status(thm)],[1002, 3322])).
% 3.82/2.82 tff(3324,plain,
% 3.82/2.82 (~c2_1(a618)),
% 3.82/2.82 inference(unit_resolution,[status(thm)],[923, 3322])).
% 3.82/2.82 tff(3325,plain,
% 3.82/2.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c0_1(a618) | (~c0_1(a628)) | (~c3_1(a628)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c0_1(a618) | (~c0_1(a628)) | (~c3_1(a628)))),
% 3.82/2.82 inference(rewrite,[status(thm)],[])).
% 3.82/2.82 tff(3326,plain,
% 3.82/2.82 (((~ndr1_0) | c1_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a618) | c0_1(a618) | c3_1(a618)) <=> (c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c0_1(a618) | (~c0_1(a628)) | (~c3_1(a628)))),
% 3.82/2.82 inference(rewrite,[status(thm)],[])).
% 3.82/2.82 tff(3327,plain,
% 3.82/2.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a618) | c0_1(a618) | c3_1(a618))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c0_1(a618) | (~c0_1(a628)) | (~c3_1(a628))))),
% 3.82/2.82 inference(monotonicity,[status(thm)],[3326])).
% 3.82/2.82 tff(3328,plain,
% 3.82/2.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a618) | c0_1(a618) | c3_1(a618))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c0_1(a618) | (~c0_1(a628)) | (~c3_1(a628)))),
% 3.82/2.82 inference(transitivity,[status(thm)],[3327, 3325])).
% 3.82/2.82 tff(3329,plain,
% 3.82/2.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a618) | c0_1(a618) | c3_1(a618))),
% 3.82/2.82 inference(quant_inst,[status(thm)],[])).
% 3.82/2.82 tff(3330,plain,
% 3.82/2.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c0_1(a618) | (~c0_1(a628)) | (~c3_1(a628))),
% 3.82/2.82 inference(modus_ponens,[status(thm)],[3329, 3328])).
% 3.82/2.82 tff(3331,plain,
% 3.92/2.83 (c0_1(a618)),
% 3.92/2.83 inference(unit_resolution,[status(thm)],[3330, 96, 2678, 3324, 3323, 2653, 2647, 997, 3276])).
% 3.92/2.83 tff(3332,plain,
% 3.92/2.83 (c1_1(a618)),
% 3.92/2.83 inference(unit_resolution,[status(thm)],[957, 3322])).
% 3.92/2.83 tff(3333,plain,
% 3.92/2.83 (hskp5),
% 3.92/2.83 inference(unit_resolution,[status(thm)],[2979, 96, 3332, 2678, 3324, 2653, 2647, 567, 3331])).
% 3.92/2.83 tff(3334,plain,
% 3.92/2.83 (~c3_1(a606)),
% 3.92/2.83 inference(unit_resolution,[status(thm)],[634, 3333])).
% 3.92/2.83 tff(3335,plain,
% 3.92/2.83 (c2_1(a606)),
% 3.92/2.83 inference(unit_resolution,[status(thm)],[651, 3333])).
% 3.92/2.83 tff(3336,plain,
% 3.92/2.83 (hskp56),
% 3.92/2.83 inference(unit_resolution,[status(thm)],[2713, 3322])).
% 3.92/2.83 tff(3337,plain,
% 3.92/2.83 (~c1_1(a658)),
% 3.92/2.83 inference(unit_resolution,[status(thm)],[1361, 3336])).
% 3.92/2.83 tff(3338,plain,
% 3.92/2.83 (c3_1(a658)),
% 3.92/2.83 inference(unit_resolution,[status(thm)],[1372, 3336])).
% 3.92/2.83 tff(3339,plain,
% 3.92/2.83 (c2_1(a658)),
% 3.92/2.83 inference(unit_resolution,[status(thm)],[1400, 3336])).
% 3.92/2.83 tff(3340,plain,
% 3.92/2.83 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a658) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c0_1(a618)) | (~c2_1(a658)) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a658) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c0_1(a618)) | (~c2_1(a658)) | (~c3_1(a658)))),
% 3.92/2.83 inference(rewrite,[status(thm)],[])).
% 3.92/2.83 tff(3341,plain,
% 3.92/2.83 ((hskp20 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c0_1(a618)) | c1_1(a658) | (~c2_1(a658)) | (~c3_1(a658))) <=> (hskp20 | c1_1(a658) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c0_1(a618)) | (~c2_1(a658)) | (~c3_1(a658)))),
% 3.92/2.83 inference(rewrite,[status(thm)],[])).
% 3.92/2.83 tff(3342,plain,
% 3.92/2.83 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c0_1(a618)) | c1_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a658) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c0_1(a618)) | (~c2_1(a658)) | (~c3_1(a658))))),
% 3.92/2.83 inference(monotonicity,[status(thm)],[3341])).
% 3.92/2.83 tff(3343,plain,
% 3.92/2.83 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c0_1(a618)) | c1_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a658) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c0_1(a618)) | (~c2_1(a658)) | (~c3_1(a658)))),
% 3.92/2.83 inference(transitivity,[status(thm)],[3342, 3340])).
% 3.92/2.83 tff(3344,plain,
% 3.92/2.83 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c0_1(a618)) | c1_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))),
% 3.92/2.83 inference(quant_inst,[status(thm)],[])).
% 3.92/2.83 tff(3345,plain,
% 3.92/2.83 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a658) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c0_1(a618)) | (~c2_1(a658)) | (~c3_1(a658))),
% 3.92/2.83 inference(modus_ponens,[status(thm)],[3344, 3343])).
% 3.92/2.83 tff(3346,plain,
% 3.92/2.83 (hskp20 | (~c0_1(a618))),
% 3.92/2.83 inference(unit_resolution,[status(thm)],[3345, 96, 3339, 3338, 3337, 3324, 3323, 723])).
% 3.92/2.83 tff(3347,plain,
% 3.92/2.83 (hskp20),
% 3.92/2.83 inference(unit_resolution,[status(thm)],[3346, 3331])).
% 3.92/2.83 tff(3348,plain,
% 3.92/2.83 (~c0_1(a606)),
% 3.92/2.83 inference(unit_resolution,[status(thm)],[640, 3333])).
% 3.92/2.83 tff(3349,plain,
% 3.92/2.83 ($false),
% 3.92/2.83 inference(unit_resolution,[status(thm)],[692, 3348, 3347, 3335, 3334])).
% 3.92/2.83 % SZS output end Proof
%------------------------------------------------------------------------------