TSTP Solution File: SYN505-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN505-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 23:56:01 EDT 2022
% Result : Unsatisfiable 1.79s 1.40s
% Output : Proof 1.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN505-1 : TPTP v8.1.0. Released v2.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 04:50:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 1.79/1.40 % SZS status Unsatisfiable
% 1.79/1.40 % SZS output start Proof
% 1.79/1.40 tff(c3_1_type, type, (
% 1.79/1.40 c3_1: $i > $o)).
% 1.79/1.40 tff(a494_type, type, (
% 1.79/1.40 a494: $i)).
% 1.79/1.40 tff(hskp18_type, type, (
% 1.79/1.40 hskp18: $o)).
% 1.79/1.40 tff(c2_1_type, type, (
% 1.79/1.40 c2_1: $i > $o)).
% 1.79/1.40 tff(a481_type, type, (
% 1.79/1.40 a481: $i)).
% 1.79/1.40 tff(c0_1_type, type, (
% 1.79/1.40 c0_1: $i > $o)).
% 1.79/1.40 tff(c1_1_type, type, (
% 1.79/1.40 c1_1: $i > $o)).
% 1.79/1.40 tff(ndr1_0_type, type, (
% 1.79/1.40 ndr1_0: $o)).
% 1.79/1.40 tff(hskp12_type, type, (
% 1.79/1.40 hskp12: $o)).
% 1.79/1.40 tff(a529_type, type, (
% 1.79/1.40 a529: $i)).
% 1.79/1.40 tff(a507_type, type, (
% 1.79/1.40 a507: $i)).
% 1.79/1.40 tff(hskp7_type, type, (
% 1.79/1.40 hskp7: $o)).
% 1.79/1.40 tff(hskp16_type, type, (
% 1.79/1.40 hskp16: $o)).
% 1.79/1.40 tff(hskp21_type, type, (
% 1.79/1.40 hskp21: $o)).
% 1.79/1.40 tff(a467_type, type, (
% 1.79/1.40 a467: $i)).
% 1.79/1.40 tff(a487_type, type, (
% 1.79/1.40 a487: $i)).
% 1.79/1.40 tff(hskp29_type, type, (
% 1.79/1.40 hskp29: $o)).
% 1.79/1.40 tff(hskp30_type, type, (
% 1.79/1.40 hskp30: $o)).
% 1.79/1.40 tff(a471_type, type, (
% 1.79/1.40 a471: $i)).
% 1.79/1.40 tff(hskp5_type, type, (
% 1.79/1.40 hskp5: $o)).
% 1.79/1.40 tff(hskp10_type, type, (
% 1.79/1.40 hskp10: $o)).
% 1.79/1.40 tff(hskp31_type, type, (
% 1.79/1.40 hskp31: $o)).
% 1.79/1.40 tff(hskp19_type, type, (
% 1.79/1.40 hskp19: $o)).
% 1.79/1.40 tff(a493_type, type, (
% 1.79/1.40 a493: $i)).
% 1.79/1.40 tff(a488_type, type, (
% 1.79/1.40 a488: $i)).
% 1.79/1.40 tff(a500_type, type, (
% 1.79/1.40 a500: $i)).
% 1.79/1.40 tff(hskp2_type, type, (
% 1.79/1.40 hskp2: $o)).
% 1.79/1.40 tff(a464_type, type, (
% 1.79/1.40 a464: $i)).
% 1.79/1.40 tff(hskp3_type, type, (
% 1.79/1.40 hskp3: $o)).
% 1.79/1.40 tff(a465_type, type, (
% 1.79/1.40 a465: $i)).
% 1.79/1.40 tff(a478_type, type, (
% 1.79/1.40 a478: $i)).
% 1.79/1.40 tff(a466_type, type, (
% 1.79/1.40 a466: $i)).
% 1.79/1.40 tff(hskp4_type, type, (
% 1.79/1.40 hskp4: $o)).
% 1.79/1.40 tff(a474_type, type, (
% 1.79/1.40 a474: $i)).
% 1.79/1.40 tff(a482_type, type, (
% 1.79/1.40 a482: $i)).
% 1.79/1.40 tff(hskp17_type, type, (
% 1.79/1.40 hskp17: $o)).
% 1.79/1.40 tff(hskp13_type, type, (
% 1.79/1.40 hskp13: $o)).
% 1.79/1.40 tff(hskp26_type, type, (
% 1.79/1.40 hskp26: $o)).
% 1.79/1.40 tff(a559_type, type, (
% 1.79/1.40 a559: $i)).
% 1.79/1.40 tff(a463_type, type, (
% 1.79/1.40 a463: $i)).
% 1.79/1.40 tff(hskp1_type, type, (
% 1.79/1.40 hskp1: $o)).
% 1.79/1.40 tff(hskp6_type, type, (
% 1.79/1.40 hskp6: $o)).
% 1.79/1.40 tff(a470_type, type, (
% 1.79/1.40 a470: $i)).
% 1.79/1.40 tff(a483_type, type, (
% 1.79/1.40 a483: $i)).
% 1.79/1.40 tff(hskp14_type, type, (
% 1.79/1.40 hskp14: $o)).
% 1.79/1.40 tff(a472_type, type, (
% 1.79/1.40 a472: $i)).
% 1.79/1.40 tff(hskp8_type, type, (
% 1.79/1.40 hskp8: $o)).
% 1.79/1.40 tff(a521_type, type, (
% 1.79/1.40 a521: $i)).
% 1.79/1.40 tff(hskp23_type, type, (
% 1.79/1.40 hskp23: $o)).
% 1.79/1.40 tff(1,plain,
% 1.79/1.40 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)))),
% 1.79/1.40 inference(bind,[status(th)],[])).
% 1.79/1.40 tff(2,plain,
% 1.79/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.79/1.40 inference(quant_intro,[status(thm)],[1])).
% 1.79/1.40 tff(3,plain,
% 1.79/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(4,plain,
% 1.79/1.40 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | 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)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))))),
% 1.79/1.40 inference(bind,[status(th)],[])).
% 1.79/1.40 tff(5,plain,
% 1.79/1.40 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.79/1.40 inference(quant_intro,[status(thm)],[4])).
% 1.79/1.40 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 1.79/1.40 tff(7,plain,
% 1.79/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.79/1.40 tff(8,plain,
% 1.79/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.79/1.40 tff(9,plain,(
% 1.79/1.40 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.79/1.40 inference(skolemize,[status(sab)],[8])).
% 1.79/1.40 tff(10,plain,
% 1.79/1.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.79/1.40 tff(11,plain,
% 1.79/1.40 (^[U: $i] : refl((hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.79/1.40 inference(bind,[status(th)],[])).
% 1.79/1.40 tff(12,plain,
% 1.79/1.40 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.79/1.40 inference(quant_intro,[status(thm)],[11])).
% 1.79/1.40 tff(13,plain,
% 1.79/1.40 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(14,plain,
% 1.79/1.40 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp7) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp7))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp7) | hskp16) <=> ((hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp16))), rewrite(((hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp16) <=> (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp7) | hskp16) <=> (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.79/1.40 inference(bind,[status(th)],[])).
% 1.79/1.40 tff(15,plain,
% 1.79/1.40 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp7) | hskp16) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.79/1.40 inference(quant_intro,[status(thm)],[14])).
% 1.79/1.40 tff(16,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp7) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 1.79/1.40 tff(17,plain,
% 1.79/1.40 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.79/1.40 tff(18,plain,
% 1.79/1.40 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.79/1.40 tff(19,plain,(
% 1.79/1.40 ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.79/1.40 inference(skolemize,[status(sab)],[18])).
% 1.79/1.40 tff(20,plain,
% 1.79/1.40 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[19, 12])).
% 1.79/1.40 tff(21,assumption,(~hskp12), introduced(assumption)).
% 1.79/1.40 tff(22,assumption,(hskp16), introduced(assumption)).
% 1.79/1.40 tff(23,plain,
% 1.79/1.40 (((~hskp16) | (~c1_1(a487))) <=> ((~hskp16) | (~c1_1(a487)))),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(24,plain,
% 1.79/1.40 (((~c1_1(a487)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a487)))),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(25,axiom,((~c1_1(a487)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 1.79/1.40 tff(26,plain,
% 1.79/1.40 ((~hskp16) | (~c1_1(a487))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 1.79/1.40 tff(27,plain,
% 1.79/1.40 ((~hskp16) | (~c1_1(a487))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[26, 23])).
% 1.79/1.40 tff(28,plain,
% 1.79/1.40 (~c1_1(a487)),
% 1.79/1.40 inference(unit_resolution,[status(thm)],[27, 22])).
% 1.79/1.40 tff(29,assumption,(~c2_1(a471)), introduced(assumption)).
% 1.79/1.40 tff(30,assumption,(~c0_1(a471)), introduced(assumption)).
% 1.79/1.40 tff(31,assumption,(~hskp5), introduced(assumption)).
% 1.79/1.40 tff(32,plain,
% 1.79/1.40 (^[U: $i] : refl((hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.79/1.40 inference(bind,[status(th)],[])).
% 1.79/1.40 tff(33,plain,
% 1.79/1.40 (![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.79/1.40 inference(quant_intro,[status(thm)],[32])).
% 1.79/1.40 tff(34,plain,
% 1.79/1.40 (![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(35,plain,
% 1.79/1.40 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp12) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp12))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp12) <=> (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp12) <=> (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.79/1.40 inference(bind,[status(th)],[])).
% 1.79/1.40 tff(36,plain,
% 1.79/1.40 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp12) <=> ![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.79/1.40 inference(quant_intro,[status(thm)],[35])).
% 1.79/1.40 tff(37,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 1.79/1.40 tff(38,plain,
% 1.79/1.40 (![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.79/1.40 tff(39,plain,
% 1.79/1.40 (![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[38, 34])).
% 1.79/1.40 tff(40,plain,(
% 1.79/1.40 ![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.79/1.40 inference(skolemize,[status(sab)],[39])).
% 1.79/1.40 tff(41,plain,
% 1.79/1.40 (![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[40, 33])).
% 1.79/1.40 tff(42,assumption,(~ndr1_0), introduced(assumption)).
% 1.79/1.40 tff(43,plain,
% 1.79/1.40 ((ndr1_0 | (~hskp10)) <=> (ndr1_0 | (~hskp10))),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(44,plain,
% 1.79/1.40 (((~hskp10) | ndr1_0) <=> (ndr1_0 | (~hskp10))),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(45,axiom,((~hskp10) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause22')).
% 1.79/1.40 tff(46,plain,
% 1.79/1.40 (ndr1_0 | (~hskp10)),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 1.79/1.40 tff(47,plain,
% 1.79/1.40 (ndr1_0 | (~hskp10)),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[46, 43])).
% 1.79/1.40 tff(48,plain,
% 1.79/1.40 (~hskp10),
% 1.79/1.40 inference(unit_resolution,[status(thm)],[47, 42])).
% 1.79/1.40 tff(49,plain,
% 1.79/1.40 (((~hskp31) | ndr1_0) <=> ((~hskp31) | ndr1_0)),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(50,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 1.79/1.40 tff(51,plain,
% 1.79/1.40 ((~hskp31) | ndr1_0),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.79/1.40 tff(52,plain,
% 1.79/1.40 ((~hskp31) | ndr1_0),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[51, 49])).
% 1.79/1.40 tff(53,plain,
% 1.79/1.40 ((~hskp31) | ndr1_0),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[52, 49])).
% 1.79/1.40 tff(54,plain,
% 1.79/1.40 ((~hskp31) | ndr1_0),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[53, 49])).
% 1.79/1.40 tff(55,plain,
% 1.79/1.40 ((~hskp31) | ndr1_0),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[54, 49])).
% 1.79/1.40 tff(56,plain,
% 1.79/1.40 ((~hskp31) | ndr1_0),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[55, 49])).
% 1.79/1.40 tff(57,plain,
% 1.79/1.40 ((~hskp31) | ndr1_0),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[56, 49])).
% 1.79/1.40 tff(58,plain,
% 1.79/1.40 ((~hskp31) | ndr1_0),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[57, 49])).
% 1.79/1.40 tff(59,plain,
% 1.79/1.40 (~hskp31),
% 1.79/1.40 inference(unit_resolution,[status(thm)],[58, 42])).
% 1.79/1.40 tff(60,plain,
% 1.79/1.40 ((ndr1_0 | (~hskp19)) <=> (ndr1_0 | (~hskp19))),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(61,plain,
% 1.79/1.40 (((~hskp19) | ndr1_0) <=> (ndr1_0 | (~hskp19))),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(62,axiom,((~hskp19) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause13')).
% 1.79/1.40 tff(63,plain,
% 1.79/1.40 (ndr1_0 | (~hskp19)),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 1.79/1.40 tff(64,plain,
% 1.79/1.40 (ndr1_0 | (~hskp19)),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[63, 60])).
% 1.79/1.40 tff(65,plain,
% 1.79/1.40 (~hskp19),
% 1.79/1.40 inference(unit_resolution,[status(thm)],[64, 42])).
% 1.79/1.40 tff(66,plain,
% 1.79/1.40 ((hskp31 | hskp19 | hskp10) <=> (hskp31 | hskp19 | hskp10)),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(67,plain,
% 1.79/1.40 (((hskp31 | hskp19) | hskp10) <=> (hskp31 | hskp19 | hskp10)),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(68,plain,
% 1.79/1.40 ((hskp31 | hskp19) <=> (hskp31 | hskp19)),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(69,plain,
% 1.79/1.40 (((hskp31 | hskp19) | hskp10) <=> ((hskp31 | hskp19) | hskp10)),
% 1.79/1.40 inference(monotonicity,[status(thm)],[68])).
% 1.79/1.40 tff(70,plain,
% 1.79/1.40 (((hskp31 | hskp19) | hskp10) <=> (hskp31 | hskp19 | hskp10)),
% 1.79/1.40 inference(transitivity,[status(thm)],[69, 67])).
% 1.79/1.40 tff(71,axiom,((hskp31 | hskp19) | hskp10), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 1.79/1.40 tff(72,plain,
% 1.79/1.40 (hskp31 | hskp19 | hskp10),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.79/1.40 tff(73,plain,
% 1.79/1.40 (hskp31 | hskp19 | hskp10),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[72, 66])).
% 1.79/1.40 tff(74,plain,
% 1.79/1.40 (hskp31 | hskp19 | hskp10),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[73, 66])).
% 1.79/1.40 tff(75,plain,
% 1.79/1.40 (hskp31 | hskp19 | hskp10),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[74, 66])).
% 1.79/1.40 tff(76,plain,
% 1.79/1.40 (hskp31 | hskp19 | hskp10),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[75, 66])).
% 1.79/1.40 tff(77,plain,
% 1.79/1.40 (hskp31 | hskp19 | hskp10),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[76, 66])).
% 1.79/1.40 tff(78,plain,
% 1.79/1.40 (hskp31 | hskp19 | hskp10),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[77, 66])).
% 1.79/1.40 tff(79,plain,
% 1.79/1.40 (hskp31 | hskp19 | hskp10),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[78, 66])).
% 1.79/1.40 tff(80,plain,
% 1.79/1.40 ($false),
% 1.79/1.40 inference(unit_resolution,[status(thm)],[79, 65, 59, 48])).
% 1.79/1.40 tff(81,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.79/1.40 tff(82,plain,
% 1.79/1.40 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)))),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(83,plain,
% 1.79/1.40 ((hskp12 | hskp5 | (~ndr1_0) | c2_1(a471) | c0_1(a471) | (~c3_1(a471))) <=> (hskp12 | hskp5 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)))),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(84,plain,
% 1.79/1.40 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a471) | c0_1(a471) | (~c3_1(a471)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471))))),
% 1.79/1.40 inference(monotonicity,[status(thm)],[83])).
% 1.79/1.40 tff(85,plain,
% 1.79/1.40 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a471) | c0_1(a471) | (~c3_1(a471)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)))),
% 1.79/1.40 inference(transitivity,[status(thm)],[84, 82])).
% 1.79/1.40 tff(86,plain,
% 1.79/1.40 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a471) | c0_1(a471) | (~c3_1(a471)))),
% 1.79/1.40 inference(quant_inst,[status(thm)],[])).
% 1.79/1.40 tff(87,plain,
% 1.79/1.40 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.79/1.40 tff(88,plain,
% 1.79/1.40 (hskp5 | c0_1(a471) | (~c3_1(a471))),
% 1.79/1.40 inference(unit_resolution,[status(thm)],[87, 81, 21, 29, 41])).
% 1.79/1.40 tff(89,plain,
% 1.79/1.40 (~c3_1(a471)),
% 1.79/1.40 inference(unit_resolution,[status(thm)],[88, 31, 30])).
% 1.79/1.40 tff(90,plain,
% 1.79/1.40 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.79/1.40 inference(bind,[status(th)],[])).
% 1.79/1.40 tff(91,plain,
% 1.79/1.40 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.79/1.40 inference(quant_intro,[status(thm)],[90])).
% 1.79/1.40 tff(92,plain,
% 1.79/1.40 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(93,plain,
% 1.79/1.40 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.79/1.40 inference(bind,[status(th)],[])).
% 1.79/1.40 tff(94,plain,
% 1.79/1.40 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.79/1.40 inference(quant_intro,[status(thm)],[93])).
% 1.79/1.40 tff(95,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 1.79/1.40 tff(96,plain,
% 1.79/1.40 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.79/1.40 tff(97,plain,
% 1.79/1.40 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[96, 92])).
% 1.79/1.40 tff(98,plain,(
% 1.79/1.40 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.79/1.40 inference(skolemize,[status(sab)],[97])).
% 1.79/1.40 tff(99,plain,
% 1.79/1.40 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[98, 91])).
% 1.79/1.40 tff(100,plain,
% 1.79/1.40 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 1.79/1.40 inference(bind,[status(th)],[])).
% 1.79/1.40 tff(101,plain,
% 1.79/1.40 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.79/1.40 inference(quant_intro,[status(thm)],[100])).
% 1.79/1.40 tff(102,plain,
% 1.79/1.40 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(103,plain,
% 1.79/1.40 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 1.79/1.40 inference(bind,[status(th)],[])).
% 1.79/1.40 tff(104,plain,
% 1.79/1.40 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.79/1.40 inference(quant_intro,[status(thm)],[103])).
% 1.79/1.40 tff(105,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 1.79/1.40 tff(106,plain,
% 1.79/1.40 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[105, 104])).
% 1.79/1.40 tff(107,plain,
% 1.79/1.40 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[106, 102])).
% 1.79/1.40 tff(108,plain,(
% 1.79/1.40 ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.79/1.40 inference(skolemize,[status(sab)],[107])).
% 1.79/1.40 tff(109,plain,
% 1.79/1.40 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[108, 101])).
% 1.79/1.40 tff(110,assumption,(~hskp16), introduced(assumption)).
% 1.79/1.40 tff(111,assumption,(hskp19), introduced(assumption)).
% 1.79/1.40 tff(112,plain,
% 1.79/1.40 (((~hskp19) | (~c3_1(a500))) <=> ((~hskp19) | (~c3_1(a500)))),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(113,plain,
% 1.79/1.40 (((~c3_1(a500)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a500)))),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(114,axiom,((~c3_1(a500)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 1.79/1.40 tff(115,plain,
% 1.79/1.40 ((~hskp19) | (~c3_1(a500))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.79/1.40 tff(116,plain,
% 1.79/1.40 ((~hskp19) | (~c3_1(a500))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[115, 112])).
% 1.79/1.40 tff(117,plain,
% 1.79/1.40 (~c3_1(a500)),
% 1.79/1.40 inference(unit_resolution,[status(thm)],[116, 111])).
% 1.79/1.40 tff(118,plain,
% 1.79/1.40 (((~hskp19) | (~c2_1(a500))) <=> ((~hskp19) | (~c2_1(a500)))),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(119,plain,
% 1.79/1.40 (((~c2_1(a500)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a500)))),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(120,axiom,((~c2_1(a500)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 1.79/1.40 tff(121,plain,
% 1.79/1.40 ((~hskp19) | (~c2_1(a500))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[120, 119])).
% 1.79/1.40 tff(122,plain,
% 1.79/1.40 ((~hskp19) | (~c2_1(a500))),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[121, 118])).
% 1.79/1.40 tff(123,plain,
% 1.79/1.40 (~c2_1(a500)),
% 1.79/1.40 inference(unit_resolution,[status(thm)],[122, 111])).
% 1.79/1.40 tff(124,plain,
% 1.79/1.40 (((~hskp19) | c1_1(a500)) <=> ((~hskp19) | c1_1(a500))),
% 1.79/1.40 inference(rewrite,[status(thm)],[])).
% 1.79/1.40 tff(125,axiom,((~hskp19) | c1_1(a500)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 1.79/1.40 tff(126,plain,
% 1.79/1.40 ((~hskp19) | c1_1(a500)),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[125, 124])).
% 1.79/1.40 tff(127,plain,
% 1.79/1.40 ((~hskp19) | c1_1(a500)),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[126, 124])).
% 1.79/1.40 tff(128,plain,
% 1.79/1.40 ((~hskp19) | c1_1(a500)),
% 1.79/1.40 inference(modus_ponens,[status(thm)],[127, 124])).
% 1.79/1.41 tff(129,plain,
% 1.79/1.41 ((~hskp19) | c1_1(a500)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[128, 124])).
% 1.79/1.41 tff(130,plain,
% 1.79/1.41 ((~hskp19) | c1_1(a500)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[129, 124])).
% 1.79/1.41 tff(131,plain,
% 1.79/1.41 ((~hskp19) | c1_1(a500)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[130, 124])).
% 1.79/1.41 tff(132,plain,
% 1.79/1.41 ((~hskp19) | c1_1(a500)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[131, 124])).
% 1.79/1.41 tff(133,plain,
% 1.79/1.41 ((~hskp19) | c1_1(a500)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[132, 124])).
% 1.79/1.41 tff(134,plain,
% 1.79/1.41 (c1_1(a500)),
% 1.79/1.41 inference(unit_resolution,[status(thm)],[133, 111])).
% 1.79/1.41 tff(135,assumption,(~c0_1(a500)), introduced(assumption)).
% 1.79/1.41 tff(136,assumption,(~c3_1(a500)), introduced(assumption)).
% 1.79/1.41 tff(137,assumption,(~c2_1(a500)), introduced(assumption)).
% 1.79/1.41 tff(138,assumption,(c1_1(a500)), introduced(assumption)).
% 1.79/1.41 tff(139,plain,
% 1.79/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a500) | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | c0_1(a500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a500) | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | c0_1(a500))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(140,plain,
% 1.79/1.41 (((~ndr1_0) | c0_1(a500) | c3_1(a500) | (~c1_1(a500)) | c0_1(a500) | c2_1(a500) | (~c1_1(a500)) | c3_1(a500) | c0_1(a500) | c2_1(a500)) <=> (c2_1(a500) | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | c0_1(a500))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(141,plain,
% 1.79/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a500) | c3_1(a500) | (~c1_1(a500)) | c0_1(a500) | c2_1(a500) | (~c1_1(a500)) | c3_1(a500) | c0_1(a500) | c2_1(a500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a500) | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | c0_1(a500)))),
% 1.79/1.41 inference(monotonicity,[status(thm)],[140])).
% 1.79/1.41 tff(142,plain,
% 1.79/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a500) | c3_1(a500) | (~c1_1(a500)) | c0_1(a500) | c2_1(a500) | (~c1_1(a500)) | c3_1(a500) | c0_1(a500) | c2_1(a500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a500) | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | c0_1(a500))),
% 1.79/1.41 inference(transitivity,[status(thm)],[141, 139])).
% 1.79/1.41 tff(143,plain,
% 1.79/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a500) | c3_1(a500) | (~c1_1(a500)) | c0_1(a500) | c2_1(a500) | (~c1_1(a500)) | c3_1(a500) | c0_1(a500) | c2_1(a500))),
% 1.79/1.41 inference(quant_inst,[status(thm)],[])).
% 1.79/1.41 tff(144,plain,
% 1.79/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a500) | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | c0_1(a500)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.79/1.41 tff(145,plain,
% 1.79/1.41 ($false),
% 1.79/1.41 inference(unit_resolution,[status(thm)],[144, 81, 138, 137, 136, 10, 135])).
% 1.79/1.41 tff(146,plain,(c0_1(a500) | (~c1_1(a500)) | c2_1(a500) | c3_1(a500)), inference(lemma,lemma(discharge,[]))).
% 1.79/1.41 tff(147,plain,
% 1.79/1.41 (c0_1(a500)),
% 1.79/1.41 inference(unit_resolution,[status(thm)],[146, 134, 123, 117])).
% 1.79/1.41 tff(148,plain,
% 1.79/1.41 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W))))),
% 1.79/1.41 inference(bind,[status(th)],[])).
% 1.79/1.41 tff(149,plain,
% 1.79/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_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)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.79/1.41 inference(quant_intro,[status(thm)],[148])).
% 1.79/1.41 tff(150,plain,
% 1.79/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_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)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(151,plain,
% 1.79/1.41 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))))),
% 1.79/1.41 inference(bind,[status(th)],[])).
% 1.79/1.41 tff(152,plain,
% 1.79/1.41 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.79/1.41 inference(quant_intro,[status(thm)],[151])).
% 1.79/1.41 tff(153,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause208')).
% 1.79/1.41 tff(154,plain,
% 1.79/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[153, 152])).
% 1.79/1.41 tff(155,plain,
% 1.79/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[154, 150])).
% 1.79/1.41 tff(156,plain,(
% 1.79/1.41 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.79/1.41 inference(skolemize,[status(sab)],[155])).
% 1.79/1.41 tff(157,plain,
% 1.79/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[156, 149])).
% 1.79/1.41 tff(158,plain,
% 1.79/1.41 (^[U: $i] : refl((hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.79/1.41 inference(bind,[status(th)],[])).
% 1.79/1.41 tff(159,plain,
% 1.79/1.41 (![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.79/1.41 inference(quant_intro,[status(thm)],[158])).
% 1.79/1.41 tff(160,plain,
% 1.79/1.41 (![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(161,plain,
% 1.79/1.41 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) | hskp12) <=> ((hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp12))), rewrite(((hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp12) <=> (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) | hskp12) <=> (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.79/1.41 inference(bind,[status(th)],[])).
% 1.79/1.41 tff(162,plain,
% 1.79/1.41 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) | hskp12) <=> ![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.79/1.41 inference(quant_intro,[status(thm)],[161])).
% 1.79/1.41 tff(163,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp30) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 1.79/1.41 tff(164,plain,
% 1.79/1.41 (![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[163, 162])).
% 1.79/1.41 tff(165,plain,
% 1.79/1.41 (![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[164, 160])).
% 1.79/1.41 tff(166,plain,(
% 1.79/1.41 ![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.79/1.41 inference(skolemize,[status(sab)],[165])).
% 1.79/1.41 tff(167,plain,
% 1.79/1.41 (![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[166, 159])).
% 1.79/1.41 tff(168,plain,
% 1.79/1.41 (((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)))) <=> ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp12 | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(169,plain,
% 1.79/1.41 ((hskp30 | hskp12 | (~ndr1_0) | c3_1(a500) | (~c1_1(a500)) | (~c0_1(a500))) <=> (hskp30 | hskp12 | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(170,plain,
% 1.79/1.41 (((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | (~ndr1_0) | c3_1(a500) | (~c1_1(a500)) | (~c0_1(a500)))) <=> ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500))))),
% 1.79/1.41 inference(monotonicity,[status(thm)],[169])).
% 1.79/1.41 tff(171,plain,
% 1.79/1.41 (((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | (~ndr1_0) | c3_1(a500) | (~c1_1(a500)) | (~c0_1(a500)))) <=> ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp12 | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)))),
% 1.79/1.41 inference(transitivity,[status(thm)],[170, 168])).
% 1.79/1.41 tff(172,plain,
% 1.79/1.41 ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | (~ndr1_0) | c3_1(a500) | (~c1_1(a500)) | (~c0_1(a500)))),
% 1.79/1.41 inference(quant_inst,[status(thm)],[])).
% 1.79/1.41 tff(173,plain,
% 1.79/1.41 ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp12 | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[172, 171])).
% 1.79/1.41 tff(174,plain,
% 1.79/1.41 (hskp30 | (~c0_1(a500))),
% 1.79/1.41 inference(unit_resolution,[status(thm)],[173, 81, 21, 134, 117, 167])).
% 1.79/1.41 tff(175,plain,
% 1.79/1.41 (hskp30),
% 1.79/1.41 inference(unit_resolution,[status(thm)],[174, 147])).
% 1.79/1.41 tff(176,plain,
% 1.79/1.41 (((~hskp30) | c3_1(a488)) <=> ((~hskp30) | c3_1(a488))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(177,axiom,((~hskp30) | c3_1(a488)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 1.79/1.41 tff(178,plain,
% 1.79/1.41 ((~hskp30) | c3_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[177, 176])).
% 1.79/1.41 tff(179,plain,
% 1.79/1.41 ((~hskp30) | c3_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[178, 176])).
% 1.79/1.41 tff(180,plain,
% 1.79/1.41 ((~hskp30) | c3_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[179, 176])).
% 1.79/1.41 tff(181,plain,
% 1.79/1.41 ((~hskp30) | c3_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[180, 176])).
% 1.79/1.41 tff(182,plain,
% 1.79/1.41 ((~hskp30) | c3_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[181, 176])).
% 1.79/1.41 tff(183,plain,
% 1.79/1.41 ((~hskp30) | c3_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[182, 176])).
% 1.79/1.41 tff(184,plain,
% 1.79/1.41 ((~hskp30) | c3_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[183, 176])).
% 1.79/1.41 tff(185,plain,
% 1.79/1.41 ((~hskp30) | c3_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[184, 176])).
% 1.79/1.41 tff(186,plain,
% 1.79/1.41 (c3_1(a488)),
% 1.79/1.41 inference(unit_resolution,[status(thm)],[185, 175])).
% 1.79/1.41 tff(187,plain,
% 1.79/1.41 (((~hskp30) | c2_1(a488)) <=> ((~hskp30) | c2_1(a488))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(188,axiom,((~hskp30) | c2_1(a488)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 1.79/1.41 tff(189,plain,
% 1.79/1.41 ((~hskp30) | c2_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[188, 187])).
% 1.79/1.41 tff(190,plain,
% 1.79/1.41 ((~hskp30) | c2_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[189, 187])).
% 1.79/1.41 tff(191,plain,
% 1.79/1.41 ((~hskp30) | c2_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[190, 187])).
% 1.79/1.41 tff(192,plain,
% 1.79/1.41 ((~hskp30) | c2_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[191, 187])).
% 1.79/1.41 tff(193,plain,
% 1.79/1.41 ((~hskp30) | c2_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[192, 187])).
% 1.79/1.41 tff(194,plain,
% 1.79/1.41 ((~hskp30) | c2_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[193, 187])).
% 1.79/1.41 tff(195,plain,
% 1.79/1.41 ((~hskp30) | c2_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[194, 187])).
% 1.79/1.41 tff(196,plain,
% 1.79/1.41 ((~hskp30) | c2_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[195, 187])).
% 1.79/1.41 tff(197,plain,
% 1.79/1.41 (c2_1(a488)),
% 1.79/1.41 inference(unit_resolution,[status(thm)],[196, 175])).
% 1.79/1.41 tff(198,plain,
% 1.79/1.41 (((~hskp30) | c1_1(a488)) <=> ((~hskp30) | c1_1(a488))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(199,axiom,((~hskp30) | c1_1(a488)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 1.79/1.41 tff(200,plain,
% 1.79/1.41 ((~hskp30) | c1_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[199, 198])).
% 1.79/1.41 tff(201,plain,
% 1.79/1.41 ((~hskp30) | c1_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[200, 198])).
% 1.79/1.41 tff(202,plain,
% 1.79/1.41 ((~hskp30) | c1_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[201, 198])).
% 1.79/1.41 tff(203,plain,
% 1.79/1.41 ((~hskp30) | c1_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[202, 198])).
% 1.79/1.41 tff(204,plain,
% 1.79/1.41 ((~hskp30) | c1_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[203, 198])).
% 1.79/1.41 tff(205,plain,
% 1.79/1.41 ((~hskp30) | c1_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[204, 198])).
% 1.79/1.41 tff(206,plain,
% 1.79/1.41 ((~hskp30) | c1_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[205, 198])).
% 1.79/1.41 tff(207,plain,
% 1.79/1.41 ((~hskp30) | c1_1(a488)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[206, 198])).
% 1.79/1.41 tff(208,plain,
% 1.79/1.41 (c1_1(a488)),
% 1.79/1.41 inference(unit_resolution,[status(thm)],[207, 175])).
% 1.79/1.41 tff(209,plain,
% 1.79/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(210,plain,
% 1.79/1.41 (((~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c0_1(a488)) | c3_1(a500) | (~c1_1(a500)) | (~c0_1(a500))) <=> (c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(211,plain,
% 1.79/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c0_1(a488)) | c3_1(a500) | (~c1_1(a500)) | (~c0_1(a500)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488))))),
% 1.79/1.41 inference(monotonicity,[status(thm)],[210])).
% 1.79/1.41 tff(212,plain,
% 1.79/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c0_1(a488)) | c3_1(a500) | (~c1_1(a500)) | (~c0_1(a500)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.79/1.41 inference(transitivity,[status(thm)],[211, 209])).
% 1.79/1.41 tff(213,plain,
% 1.79/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c0_1(a488)) | c3_1(a500) | (~c1_1(a500)) | (~c0_1(a500)))),
% 1.79/1.41 inference(quant_inst,[status(thm)],[])).
% 1.79/1.41 tff(214,plain,
% 1.79/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a500) | (~ndr1_0) | (~c1_1(a500)) | (~c0_1(a500)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[213, 212])).
% 1.79/1.41 tff(215,plain,
% 1.79/1.41 (~c0_1(a488)),
% 1.79/1.41 inference(unit_resolution,[status(thm)],[214, 81, 208, 197, 186, 134, 117, 157, 147])).
% 1.79/1.41 tff(216,plain,
% 1.79/1.41 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.79/1.41 inference(bind,[status(th)],[])).
% 1.79/1.41 tff(217,plain,
% 1.79/1.41 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.79/1.41 inference(quant_intro,[status(thm)],[216])).
% 1.79/1.41 tff(218,plain,
% 1.79/1.41 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(219,plain,
% 1.79/1.41 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.79/1.41 inference(bind,[status(th)],[])).
% 1.79/1.41 tff(220,plain,
% 1.79/1.41 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.79/1.41 inference(quant_intro,[status(thm)],[219])).
% 1.79/1.41 tff(221,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 1.79/1.41 tff(222,plain,
% 1.79/1.41 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[221, 220])).
% 1.79/1.41 tff(223,plain,
% 1.79/1.41 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[222, 218])).
% 1.79/1.41 tff(224,plain,(
% 1.79/1.41 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.79/1.41 inference(skolemize,[status(sab)],[223])).
% 1.79/1.41 tff(225,plain,
% 1.79/1.41 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[224, 217])).
% 1.79/1.41 tff(226,plain,
% 1.79/1.41 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c0_1(a488) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | (~ndr1_0) | c0_1(a488) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(227,plain,
% 1.79/1.41 ((hskp16 | (~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | c0_1(a488) | (~c3_1(a488)) | (~c1_1(a488))) <=> (hskp16 | (~ndr1_0) | c0_1(a488) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(228,plain,
% 1.79/1.41 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | c0_1(a488) | (~c3_1(a488)) | (~c1_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c0_1(a488) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488))))),
% 1.79/1.41 inference(monotonicity,[status(thm)],[227])).
% 1.79/1.41 tff(229,plain,
% 1.79/1.41 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | c0_1(a488) | (~c3_1(a488)) | (~c1_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | (~ndr1_0) | c0_1(a488) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.79/1.41 inference(transitivity,[status(thm)],[228, 226])).
% 1.79/1.41 tff(230,plain,
% 1.79/1.41 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | c0_1(a488) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.79/1.41 inference(quant_inst,[status(thm)],[])).
% 1.79/1.41 tff(231,plain,
% 1.79/1.41 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | (~ndr1_0) | c0_1(a488) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[230, 229])).
% 1.79/1.41 tff(232,plain,
% 1.79/1.41 ($false),
% 1.79/1.41 inference(unit_resolution,[status(thm)],[231, 81, 110, 208, 197, 186, 225, 215])).
% 1.79/1.41 tff(233,plain,((~hskp19) | hskp16 | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.79/1.41 tff(234,plain,
% 1.79/1.41 (~hskp19),
% 1.79/1.41 inference(unit_resolution,[status(thm)],[233, 110, 21])).
% 1.79/1.41 tff(235,assumption,(~hskp19), introduced(assumption)).
% 1.79/1.41 tff(236,assumption,(~hskp31), introduced(assumption)).
% 1.79/1.41 tff(237,assumption,(~c2_1(a464)), introduced(assumption)).
% 1.79/1.41 tff(238,assumption,(~c0_1(a464)), introduced(assumption)).
% 1.79/1.41 tff(239,plain,
% 1.79/1.41 (hskp10),
% 1.79/1.41 inference(unit_resolution,[status(thm)],[79, 236, 235])).
% 1.79/1.41 tff(240,plain,
% 1.79/1.41 (((~hskp10) | (~c3_1(a478))) <=> ((~hskp10) | (~c3_1(a478)))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(241,plain,
% 1.79/1.41 (((~c3_1(a478)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a478)))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(242,axiom,((~c3_1(a478)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.79/1.41 tff(243,plain,
% 1.79/1.41 ((~hskp10) | (~c3_1(a478))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[242, 241])).
% 1.79/1.41 tff(244,plain,
% 1.79/1.41 ((~hskp10) | (~c3_1(a478))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[243, 240])).
% 1.79/1.41 tff(245,plain,
% 1.79/1.41 (~c3_1(a478)),
% 1.79/1.41 inference(unit_resolution,[status(thm)],[244, 239])).
% 1.79/1.41 tff(246,plain,
% 1.79/1.41 (((~hskp10) | (~c0_1(a478))) <=> ((~hskp10) | (~c0_1(a478)))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(247,plain,
% 1.79/1.41 (((~c0_1(a478)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a478)))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(248,axiom,((~c0_1(a478)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 1.79/1.41 tff(249,plain,
% 1.79/1.41 ((~hskp10) | (~c0_1(a478))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[248, 247])).
% 1.79/1.41 tff(250,plain,
% 1.79/1.41 ((~hskp10) | (~c0_1(a478))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[249, 246])).
% 1.79/1.41 tff(251,plain,
% 1.79/1.41 (~c0_1(a478)),
% 1.79/1.41 inference(unit_resolution,[status(thm)],[250, 239])).
% 1.79/1.41 tff(252,plain,
% 1.79/1.41 (((~hskp10) | c2_1(a478)) <=> ((~hskp10) | c2_1(a478))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(253,axiom,((~hskp10) | c2_1(a478)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 1.79/1.41 tff(254,plain,
% 1.79/1.41 ((~hskp10) | c2_1(a478)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[253, 252])).
% 1.79/1.41 tff(255,plain,
% 1.79/1.41 ((~hskp10) | c2_1(a478)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[254, 252])).
% 1.79/1.41 tff(256,plain,
% 1.79/1.41 ((~hskp10) | c2_1(a478)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[255, 252])).
% 1.79/1.41 tff(257,plain,
% 1.79/1.41 ((~hskp10) | c2_1(a478)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[256, 252])).
% 1.79/1.41 tff(258,plain,
% 1.79/1.41 ((~hskp10) | c2_1(a478)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[257, 252])).
% 1.79/1.41 tff(259,plain,
% 1.79/1.41 ((~hskp10) | c2_1(a478)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[258, 252])).
% 1.79/1.41 tff(260,plain,
% 1.79/1.41 ((~hskp10) | c2_1(a478)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[259, 252])).
% 1.79/1.41 tff(261,plain,
% 1.79/1.41 ((~hskp10) | c2_1(a478)),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[260, 252])).
% 1.79/1.41 tff(262,plain,
% 1.79/1.41 (c2_1(a478)),
% 1.79/1.41 inference(unit_resolution,[status(thm)],[261, 239])).
% 1.79/1.41 tff(263,assumption,(~c1_1(a465)), introduced(assumption)).
% 1.79/1.41 tff(264,assumption,(~c0_1(a465)), introduced(assumption)).
% 1.79/1.41 tff(265,assumption,(~c3_1(a478)), introduced(assumption)).
% 1.79/1.41 tff(266,assumption,(~c0_1(a478)), introduced(assumption)).
% 1.79/1.41 tff(267,assumption,(c2_1(a478)), introduced(assumption)).
% 1.79/1.41 tff(268,assumption,(~c3_1(a467)), introduced(assumption)).
% 1.79/1.41 tff(269,assumption,(~c1_1(a467)), introduced(assumption)).
% 1.79/1.41 tff(270,plain,
% 1.79/1.41 (^[U: $i] : refl((hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.79/1.41 inference(bind,[status(th)],[])).
% 1.79/1.41 tff(271,plain,
% 1.79/1.41 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.79/1.41 inference(quant_intro,[status(thm)],[270])).
% 1.79/1.41 tff(272,plain,
% 1.79/1.41 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(273,plain,
% 1.79/1.41 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp19) <=> ((hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19))), rewrite(((hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp19) <=> (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.79/1.41 inference(bind,[status(th)],[])).
% 1.79/1.41 tff(274,plain,
% 1.79/1.41 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp19) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.79/1.41 inference(quant_intro,[status(thm)],[273])).
% 1.79/1.41 tff(275,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 1.79/1.41 tff(276,plain,
% 1.79/1.41 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[275, 274])).
% 1.79/1.41 tff(277,plain,
% 1.79/1.41 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[276, 272])).
% 1.79/1.41 tff(278,plain,(
% 1.79/1.41 ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.79/1.41 inference(skolemize,[status(sab)],[277])).
% 1.79/1.41 tff(279,plain,
% 1.79/1.41 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[278, 271])).
% 1.79/1.41 tff(280,plain,
% 1.79/1.41 (((~hskp16) | (~c2_1(a487))) <=> ((~hskp16) | (~c2_1(a487)))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(281,plain,
% 1.79/1.41 (((~c2_1(a487)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a487)))),
% 1.79/1.41 inference(rewrite,[status(thm)],[])).
% 1.79/1.41 tff(282,axiom,((~c2_1(a487)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 1.79/1.41 tff(283,plain,
% 1.79/1.41 ((~hskp16) | (~c2_1(a487))),
% 1.79/1.41 inference(modus_ponens,[status(thm)],[282, 281])).
% 1.79/1.41 tff(284,plain,
% 1.79/1.41 ((~hskp16) | (~c2_1(a487))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[283, 280])).
% 1.79/1.42 tff(285,plain,
% 1.79/1.42 (~c2_1(a487)),
% 1.79/1.42 inference(unit_resolution,[status(thm)],[284, 22])).
% 1.79/1.42 tff(286,plain,
% 1.79/1.42 (((~hskp16) | c0_1(a487)) <=> ((~hskp16) | c0_1(a487))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(287,axiom,((~hskp16) | c0_1(a487)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 1.79/1.42 tff(288,plain,
% 1.79/1.42 ((~hskp16) | c0_1(a487)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[287, 286])).
% 1.79/1.42 tff(289,plain,
% 1.79/1.42 ((~hskp16) | c0_1(a487)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[288, 286])).
% 1.79/1.42 tff(290,plain,
% 1.79/1.42 ((~hskp16) | c0_1(a487)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[289, 286])).
% 1.79/1.42 tff(291,plain,
% 1.79/1.42 ((~hskp16) | c0_1(a487)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[290, 286])).
% 1.79/1.42 tff(292,plain,
% 1.79/1.42 ((~hskp16) | c0_1(a487)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[291, 286])).
% 1.79/1.42 tff(293,plain,
% 1.79/1.42 ((~hskp16) | c0_1(a487)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[292, 286])).
% 1.79/1.42 tff(294,plain,
% 1.79/1.42 ((~hskp16) | c0_1(a487)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[293, 286])).
% 1.79/1.42 tff(295,plain,
% 1.79/1.42 ((~hskp16) | c0_1(a487)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[294, 286])).
% 1.79/1.42 tff(296,plain,
% 1.79/1.42 (c0_1(a487)),
% 1.79/1.42 inference(unit_resolution,[status(thm)],[295, 22])).
% 1.79/1.42 tff(297,plain,
% 1.79/1.42 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(298,plain,
% 1.79/1.42 ((hskp19 | hskp18 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487))) <=> (hskp19 | hskp18 | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(299,plain,
% 1.79/1.42 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487))))),
% 1.79/1.42 inference(monotonicity,[status(thm)],[298])).
% 1.79/1.42 tff(300,plain,
% 1.79/1.42 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)))),
% 1.79/1.42 inference(transitivity,[status(thm)],[299, 297])).
% 1.79/1.42 tff(301,plain,
% 1.79/1.42 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)))),
% 1.79/1.42 inference(quant_inst,[status(thm)],[])).
% 1.79/1.42 tff(302,plain,
% 1.79/1.42 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[301, 300])).
% 1.79/1.42 tff(303,plain,
% 1.79/1.42 (hskp18),
% 1.79/1.42 inference(unit_resolution,[status(thm)],[302, 81, 235, 296, 28, 285, 279])).
% 1.79/1.42 tff(304,plain,
% 1.79/1.42 (((~hskp18) | (~c3_1(a494))) <=> ((~hskp18) | (~c3_1(a494)))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(305,plain,
% 1.79/1.42 (((~c3_1(a494)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a494)))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(306,axiom,((~c3_1(a494)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 1.79/1.42 tff(307,plain,
% 1.79/1.42 ((~hskp18) | (~c3_1(a494))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[306, 305])).
% 1.79/1.42 tff(308,plain,
% 1.79/1.42 ((~hskp18) | (~c3_1(a494))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[307, 304])).
% 1.79/1.42 tff(309,plain,
% 1.79/1.42 (~c3_1(a494)),
% 1.79/1.42 inference(unit_resolution,[status(thm)],[308, 303])).
% 1.79/1.42 tff(310,plain,
% 1.79/1.42 (((~hskp18) | (~c2_1(a494))) <=> ((~hskp18) | (~c2_1(a494)))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(311,plain,
% 1.79/1.42 (((~c2_1(a494)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a494)))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(312,axiom,((~c2_1(a494)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 1.79/1.42 tff(313,plain,
% 1.79/1.42 ((~hskp18) | (~c2_1(a494))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[312, 311])).
% 1.79/1.42 tff(314,plain,
% 1.79/1.42 ((~hskp18) | (~c2_1(a494))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[313, 310])).
% 1.79/1.42 tff(315,plain,
% 1.79/1.42 (~c2_1(a494)),
% 1.79/1.42 inference(unit_resolution,[status(thm)],[314, 303])).
% 1.79/1.42 tff(316,plain,
% 1.79/1.42 (((~hskp18) | c0_1(a494)) <=> ((~hskp18) | c0_1(a494))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(317,axiom,((~hskp18) | c0_1(a494)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 1.79/1.42 tff(318,plain,
% 1.79/1.42 ((~hskp18) | c0_1(a494)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[317, 316])).
% 1.79/1.42 tff(319,plain,
% 1.79/1.42 ((~hskp18) | c0_1(a494)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[318, 316])).
% 1.79/1.42 tff(320,plain,
% 1.79/1.42 ((~hskp18) | c0_1(a494)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[319, 316])).
% 1.79/1.42 tff(321,plain,
% 1.79/1.42 ((~hskp18) | c0_1(a494)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[320, 316])).
% 1.79/1.42 tff(322,plain,
% 1.79/1.42 ((~hskp18) | c0_1(a494)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[321, 316])).
% 1.79/1.42 tff(323,plain,
% 1.79/1.42 ((~hskp18) | c0_1(a494)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[322, 316])).
% 1.79/1.42 tff(324,plain,
% 1.79/1.42 ((~hskp18) | c0_1(a494)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[323, 316])).
% 1.79/1.42 tff(325,plain,
% 1.79/1.42 ((~hskp18) | c0_1(a494)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[324, 316])).
% 1.79/1.42 tff(326,plain,
% 1.79/1.42 (c0_1(a494)),
% 1.79/1.42 inference(unit_resolution,[status(thm)],[325, 303])).
% 1.79/1.42 tff(327,assumption,(~c3_1(a494)), introduced(assumption)).
% 1.79/1.42 tff(328,assumption,(~c2_1(a494)), introduced(assumption)).
% 1.79/1.42 tff(329,assumption,(c0_1(a494)), introduced(assumption)).
% 1.79/1.42 tff(330,assumption,(hskp29), introduced(assumption)).
% 1.79/1.42 tff(331,plain,
% 1.79/1.42 (((~hskp29) | c2_1(a474)) <=> ((~hskp29) | c2_1(a474))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(332,axiom,((~hskp29) | c2_1(a474)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 1.79/1.42 tff(333,plain,
% 1.79/1.42 ((~hskp29) | c2_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[332, 331])).
% 1.79/1.42 tff(334,plain,
% 1.79/1.42 ((~hskp29) | c2_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[333, 331])).
% 1.79/1.42 tff(335,plain,
% 1.79/1.42 ((~hskp29) | c2_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[334, 331])).
% 1.79/1.42 tff(336,plain,
% 1.79/1.42 ((~hskp29) | c2_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[335, 331])).
% 1.79/1.42 tff(337,plain,
% 1.79/1.42 ((~hskp29) | c2_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[336, 331])).
% 1.79/1.42 tff(338,plain,
% 1.79/1.42 ((~hskp29) | c2_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[337, 331])).
% 1.79/1.42 tff(339,plain,
% 1.79/1.42 ((~hskp29) | c2_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[338, 331])).
% 1.79/1.42 tff(340,plain,
% 1.79/1.42 ((~hskp29) | c2_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[339, 331])).
% 1.79/1.42 tff(341,plain,
% 1.79/1.42 (c2_1(a474)),
% 1.79/1.42 inference(unit_resolution,[status(thm)],[340, 330])).
% 1.79/1.42 tff(342,plain,
% 1.79/1.42 (((~hskp29) | c1_1(a474)) <=> ((~hskp29) | c1_1(a474))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(343,axiom,((~hskp29) | c1_1(a474)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 1.79/1.42 tff(344,plain,
% 1.79/1.42 ((~hskp29) | c1_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[343, 342])).
% 1.79/1.42 tff(345,plain,
% 1.79/1.42 ((~hskp29) | c1_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[344, 342])).
% 1.79/1.42 tff(346,plain,
% 1.79/1.42 ((~hskp29) | c1_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[345, 342])).
% 1.79/1.42 tff(347,plain,
% 1.79/1.42 ((~hskp29) | c1_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[346, 342])).
% 1.79/1.42 tff(348,plain,
% 1.79/1.42 ((~hskp29) | c1_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[347, 342])).
% 1.79/1.42 tff(349,plain,
% 1.79/1.42 ((~hskp29) | c1_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[348, 342])).
% 1.79/1.42 tff(350,plain,
% 1.79/1.42 ((~hskp29) | c1_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[349, 342])).
% 1.79/1.42 tff(351,plain,
% 1.79/1.42 ((~hskp29) | c1_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[350, 342])).
% 1.79/1.42 tff(352,plain,
% 1.79/1.42 (c1_1(a474)),
% 1.79/1.42 inference(unit_resolution,[status(thm)],[351, 330])).
% 1.79/1.42 tff(353,plain,
% 1.79/1.42 (((~hskp29) | c0_1(a474)) <=> ((~hskp29) | c0_1(a474))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(354,axiom,((~hskp29) | c0_1(a474)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 1.79/1.42 tff(355,plain,
% 1.79/1.42 ((~hskp29) | c0_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[354, 353])).
% 1.79/1.42 tff(356,plain,
% 1.79/1.42 ((~hskp29) | c0_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[355, 353])).
% 1.79/1.42 tff(357,plain,
% 1.79/1.42 ((~hskp29) | c0_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[356, 353])).
% 1.79/1.42 tff(358,plain,
% 1.79/1.42 ((~hskp29) | c0_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[357, 353])).
% 1.79/1.42 tff(359,plain,
% 1.79/1.42 ((~hskp29) | c0_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[358, 353])).
% 1.79/1.42 tff(360,plain,
% 1.79/1.42 ((~hskp29) | c0_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[359, 353])).
% 1.79/1.42 tff(361,plain,
% 1.79/1.42 ((~hskp29) | c0_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[360, 353])).
% 1.79/1.42 tff(362,plain,
% 1.79/1.42 ((~hskp29) | c0_1(a474)),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[361, 353])).
% 1.79/1.42 tff(363,plain,
% 1.79/1.42 (c0_1(a474)),
% 1.79/1.42 inference(unit_resolution,[status(thm)],[362, 330])).
% 1.79/1.42 tff(364,plain,
% 1.79/1.42 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a494) | c3_1(a494) | (~ndr1_0) | (~c0_1(a494)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a494) | c3_1(a494) | (~ndr1_0) | (~c0_1(a494)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(365,plain,
% 1.79/1.42 (((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a494) | c2_1(a494) | (~c0_1(a494))) <=> (c2_1(a494) | c3_1(a494) | (~ndr1_0) | (~c0_1(a494)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(366,plain,
% 1.79/1.42 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a494) | c2_1(a494) | (~c0_1(a494)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a494) | c3_1(a494) | (~ndr1_0) | (~c0_1(a494)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.79/1.42 inference(monotonicity,[status(thm)],[365])).
% 1.79/1.42 tff(367,plain,
% 1.79/1.42 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a494) | c2_1(a494) | (~c0_1(a494)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a494) | c3_1(a494) | (~ndr1_0) | (~c0_1(a494)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.79/1.42 inference(transitivity,[status(thm)],[366, 364])).
% 1.79/1.42 tff(368,plain,
% 1.79/1.42 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a494) | c2_1(a494) | (~c0_1(a494)))),
% 1.79/1.42 inference(quant_inst,[status(thm)],[])).
% 1.79/1.42 tff(369,plain,
% 1.79/1.42 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a494) | c3_1(a494) | (~ndr1_0) | (~c0_1(a494)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[368, 367])).
% 1.79/1.42 tff(370,plain,
% 1.79/1.42 ($false),
% 1.79/1.42 inference(unit_resolution,[status(thm)],[369, 81, 363, 352, 341, 329, 328, 327, 109])).
% 1.79/1.42 tff(371,plain,((~hskp29) | (~c0_1(a494)) | c2_1(a494) | c3_1(a494)), inference(lemma,lemma(discharge,[]))).
% 1.79/1.42 tff(372,plain,
% 1.79/1.42 (~hskp29),
% 1.79/1.42 inference(unit_resolution,[status(thm)],[371, 326, 315, 309])).
% 1.79/1.42 tff(373,assumption,(c3_1(a465)), introduced(assumption)).
% 1.79/1.42 tff(374,plain,
% 1.79/1.42 (~hskp29),
% 1.79/1.42 inference(unit_resolution,[status(thm)],[371, 329, 328, 327])).
% 1.79/1.42 tff(375,plain,
% 1.79/1.42 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 1.79/1.42 inference(bind,[status(th)],[])).
% 1.79/1.42 tff(376,plain,
% 1.79/1.42 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.79/1.42 inference(quant_intro,[status(thm)],[375])).
% 1.79/1.42 tff(377,plain,
% 1.79/1.42 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(378,plain,
% 1.79/1.42 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp29))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 1.79/1.42 inference(bind,[status(th)],[])).
% 1.79/1.42 tff(379,plain,
% 1.79/1.42 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.79/1.42 inference(quant_intro,[status(thm)],[378])).
% 1.79/1.42 tff(380,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 1.79/1.42 tff(381,plain,
% 1.79/1.42 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[380, 379])).
% 1.79/1.42 tff(382,plain,
% 1.79/1.42 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[381, 377])).
% 1.79/1.42 tff(383,plain,(
% 1.79/1.42 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.79/1.42 inference(skolemize,[status(sab)],[382])).
% 1.79/1.42 tff(384,plain,
% 1.79/1.42 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[383, 376])).
% 1.79/1.42 tff(385,assumption,(~c2_1(a487)), introduced(assumption)).
% 1.79/1.42 tff(386,assumption,(~c1_1(a487)), introduced(assumption)).
% 1.79/1.42 tff(387,assumption,(c0_1(a487)), introduced(assumption)).
% 1.79/1.42 tff(388,plain,
% 1.79/1.42 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c0_1(a487)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c0_1(a487)))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(389,plain,
% 1.79/1.42 ((hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a465) | c2_1(a465) | (~c3_1(a465))) <=> (hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c0_1(a487)))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(390,plain,
% 1.79/1.42 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a465) | c2_1(a465) | (~c3_1(a465)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c0_1(a487))))),
% 1.79/1.42 inference(monotonicity,[status(thm)],[389])).
% 1.79/1.42 tff(391,plain,
% 1.79/1.42 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a465) | c2_1(a465) | (~c3_1(a465)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c0_1(a487)))),
% 1.79/1.42 inference(transitivity,[status(thm)],[390, 388])).
% 1.79/1.42 tff(392,plain,
% 1.79/1.42 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a465) | c2_1(a465) | (~c3_1(a465)))),
% 1.79/1.42 inference(quant_inst,[status(thm)],[])).
% 1.79/1.42 tff(393,plain,
% 1.79/1.42 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c0_1(a487))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[392, 391])).
% 1.79/1.42 tff(394,plain,
% 1.79/1.42 (hskp29 | (~c3_1(a465)) | c2_1(a465)),
% 1.79/1.42 inference(unit_resolution,[status(thm)],[393, 81, 387, 386, 385, 264, 384])).
% 1.79/1.42 tff(395,plain,
% 1.79/1.42 (c2_1(a465)),
% 1.79/1.42 inference(unit_resolution,[status(thm)],[394, 373, 374])).
% 1.79/1.42 tff(396,plain,
% 1.79/1.42 (^[V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.79/1.42 inference(bind,[status(th)],[])).
% 1.79/1.42 tff(397,plain,
% 1.79/1.42 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.79/1.42 inference(quant_intro,[status(thm)],[396])).
% 1.79/1.42 tff(398,plain,
% 1.79/1.42 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(399,plain,
% 1.79/1.42 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.79/1.42 inference(bind,[status(th)],[])).
% 1.79/1.42 tff(400,plain,
% 1.79/1.42 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.79/1.42 inference(quant_intro,[status(thm)],[399])).
% 1.79/1.42 tff(401,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.79/1.42 tff(402,plain,
% 1.79/1.42 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[401, 400])).
% 1.79/1.42 tff(403,plain,
% 1.79/1.42 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[402, 398])).
% 1.79/1.42 tff(404,plain,(
% 1.79/1.42 ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.79/1.42 inference(skolemize,[status(sab)],[403])).
% 1.79/1.42 tff(405,plain,
% 1.79/1.42 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[404, 397])).
% 1.79/1.42 tff(406,plain,
% 1.79/1.42 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c1_1(a487) | c2_1(a487) | c0_1(a478) | (~ndr1_0) | (~c1_1(a478)) | (~c2_1(a478)) | (~c0_1(a487)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c1_1(a487) | c2_1(a487) | c0_1(a478) | (~ndr1_0) | (~c1_1(a478)) | (~c2_1(a478)) | (~c0_1(a487)))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(407,plain,
% 1.79/1.42 (((~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a478) | (~c1_1(a478)) | (~c2_1(a478))) <=> (c1_1(a487) | c2_1(a487) | c0_1(a478) | (~ndr1_0) | (~c1_1(a478)) | (~c2_1(a478)) | (~c0_1(a487)))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(408,plain,
% 1.79/1.42 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a478) | (~c1_1(a478)) | (~c2_1(a478)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c1_1(a487) | c2_1(a487) | c0_1(a478) | (~ndr1_0) | (~c1_1(a478)) | (~c2_1(a478)) | (~c0_1(a487))))),
% 1.79/1.42 inference(monotonicity,[status(thm)],[407])).
% 1.79/1.42 tff(409,plain,
% 1.79/1.42 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a478) | (~c1_1(a478)) | (~c2_1(a478)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c1_1(a487) | c2_1(a487) | c0_1(a478) | (~ndr1_0) | (~c1_1(a478)) | (~c2_1(a478)) | (~c0_1(a487)))),
% 1.79/1.42 inference(transitivity,[status(thm)],[408, 406])).
% 1.79/1.42 tff(410,plain,
% 1.79/1.42 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a478) | (~c1_1(a478)) | (~c2_1(a478)))),
% 1.79/1.42 inference(quant_inst,[status(thm)],[])).
% 1.79/1.42 tff(411,plain,
% 1.79/1.42 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c1_1(a487) | c2_1(a487) | c0_1(a478) | (~ndr1_0) | (~c1_1(a478)) | (~c2_1(a478)) | (~c0_1(a487))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[410, 409])).
% 1.79/1.42 tff(412,plain,
% 1.79/1.42 (~c1_1(a478)),
% 1.79/1.42 inference(unit_resolution,[status(thm)],[411, 81, 387, 267, 386, 385, 266, 405])).
% 1.79/1.42 tff(413,plain,
% 1.79/1.42 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.79/1.42 inference(bind,[status(th)],[])).
% 1.79/1.42 tff(414,plain,
% 1.79/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.79/1.42 inference(quant_intro,[status(thm)],[413])).
% 1.79/1.42 tff(415,plain,
% 1.79/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(416,plain,
% 1.79/1.42 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.79/1.42 inference(bind,[status(th)],[])).
% 1.79/1.42 tff(417,plain,
% 1.79/1.42 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.79/1.42 inference(quant_intro,[status(thm)],[416])).
% 1.79/1.42 tff(418,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause203')).
% 1.79/1.42 tff(419,plain,
% 1.79/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[418, 417])).
% 1.79/1.42 tff(420,plain,
% 1.79/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[419, 415])).
% 1.79/1.42 tff(421,plain,(
% 1.79/1.42 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.79/1.42 inference(skolemize,[status(sab)],[420])).
% 1.79/1.42 tff(422,plain,
% 1.79/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[421, 414])).
% 1.79/1.42 tff(423,plain,
% 1.79/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a494) | c3_1(a494) | c0_1(a478) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | (~c2_1(a478)) | (~c0_1(a494)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a494) | c3_1(a494) | c0_1(a478) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | (~c2_1(a478)) | (~c0_1(a494)))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(424,plain,
% 1.79/1.42 (((~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | c0_1(a478) | (~c2_1(a478))) <=> (c2_1(a494) | c3_1(a494) | c0_1(a478) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | (~c2_1(a478)) | (~c0_1(a494)))),
% 1.79/1.42 inference(rewrite,[status(thm)],[])).
% 1.79/1.42 tff(425,plain,
% 1.79/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | c0_1(a478) | (~c2_1(a478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a494) | c3_1(a494) | c0_1(a478) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | (~c2_1(a478)) | (~c0_1(a494))))),
% 1.79/1.42 inference(monotonicity,[status(thm)],[424])).
% 1.79/1.42 tff(426,plain,
% 1.79/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | c0_1(a478) | (~c2_1(a478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a494) | c3_1(a494) | c0_1(a478) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | (~c2_1(a478)) | (~c0_1(a494)))),
% 1.79/1.42 inference(transitivity,[status(thm)],[425, 423])).
% 1.79/1.42 tff(427,plain,
% 1.79/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | c0_1(a478) | (~c2_1(a478)))),
% 1.79/1.42 inference(quant_inst,[status(thm)],[])).
% 1.79/1.42 tff(428,plain,
% 1.79/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a494) | c3_1(a494) | c0_1(a478) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a478) | (~c2_1(a478)) | (~c0_1(a494))),
% 1.79/1.42 inference(modus_ponens,[status(thm)],[427, 426])).
% 1.79/1.42 tff(429,plain,
% 1.79/1.42 ((~c3_1(a465)) | (~c2_1(a465))),
% 1.79/1.42 inference(unit_resolution,[status(thm)],[428, 81, 329, 267, 328, 327, 266, 263, 422, 412])).
% 1.79/1.42 tff(430,plain,
% 1.79/1.42 ($false),
% 1.79/1.42 inference(unit_resolution,[status(thm)],[429, 395, 373])).
% 1.79/1.42 tff(431,plain,((~c3_1(a465)) | (~c0_1(a494)) | (~c2_1(a478)) | c2_1(a494) | c3_1(a494) | c0_1(a478) | c1_1(a465) | (~c0_1(a487)) | c1_1(a487) | c2_1(a487) | c0_1(a465)), inference(lemma,lemma(discharge,[]))).
% 1.79/1.42 tff(432,plain,
% 1.79/1.42 (~c3_1(a465)),
% 1.79/1.42 inference(unit_resolution,[status(thm)],[431, 326, 267, 315, 309, 266, 263, 296, 28, 285, 264])).
% 1.79/1.42 tff(433,plain,
% 1.79/1.42 (((~hskp3) | c3_1(a465)) <=> ((~hskp3) | c3_1(a465))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(434,axiom,((~hskp3) | c3_1(a465)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 1.79/1.43 tff(435,plain,
% 1.79/1.43 ((~hskp3) | c3_1(a465)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[434, 433])).
% 1.79/1.43 tff(436,plain,
% 1.79/1.43 ((~hskp3) | c3_1(a465)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[435, 433])).
% 1.79/1.43 tff(437,plain,
% 1.79/1.43 ((~hskp3) | c3_1(a465)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[436, 433])).
% 1.79/1.43 tff(438,plain,
% 1.79/1.43 ((~hskp3) | c3_1(a465)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[437, 433])).
% 1.79/1.43 tff(439,plain,
% 1.79/1.43 ((~hskp3) | c3_1(a465)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[438, 433])).
% 1.79/1.43 tff(440,plain,
% 1.79/1.43 ((~hskp3) | c3_1(a465)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[439, 433])).
% 1.79/1.43 tff(441,plain,
% 1.79/1.43 ((~hskp3) | c3_1(a465)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[440, 433])).
% 1.79/1.43 tff(442,plain,
% 1.79/1.43 ((~hskp3) | c3_1(a465)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[441, 433])).
% 1.79/1.43 tff(443,plain,
% 1.79/1.43 (~hskp3),
% 1.79/1.43 inference(unit_resolution,[status(thm)],[442, 432])).
% 1.79/1.43 tff(444,plain,
% 1.79/1.43 ((hskp29 | hskp12 | hskp3) <=> (hskp29 | hskp12 | hskp3)),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(445,plain,
% 1.79/1.43 (((hskp29 | hskp12) | hskp3) <=> (hskp29 | hskp12 | hskp3)),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(446,plain,
% 1.79/1.43 ((hskp29 | hskp12) <=> (hskp29 | hskp12)),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(447,plain,
% 1.79/1.43 (((hskp29 | hskp12) | hskp3) <=> ((hskp29 | hskp12) | hskp3)),
% 1.79/1.43 inference(monotonicity,[status(thm)],[446])).
% 1.79/1.43 tff(448,plain,
% 1.79/1.43 (((hskp29 | hskp12) | hskp3) <=> (hskp29 | hskp12 | hskp3)),
% 1.79/1.43 inference(transitivity,[status(thm)],[447, 445])).
% 1.79/1.43 tff(449,axiom,((hskp29 | hskp12) | hskp3), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 1.79/1.43 tff(450,plain,
% 1.79/1.43 (hskp29 | hskp12 | hskp3),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[449, 448])).
% 1.79/1.43 tff(451,plain,
% 1.79/1.43 (hskp29 | hskp12 | hskp3),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[450, 444])).
% 1.79/1.43 tff(452,plain,
% 1.79/1.43 (hskp29 | hskp12 | hskp3),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[451, 444])).
% 1.79/1.43 tff(453,plain,
% 1.79/1.43 (hskp29 | hskp12 | hskp3),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[452, 444])).
% 1.79/1.43 tff(454,plain,
% 1.79/1.43 (hskp29 | hskp12 | hskp3),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[453, 444])).
% 1.79/1.43 tff(455,plain,
% 1.79/1.43 (hskp29 | hskp12 | hskp3),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[454, 444])).
% 1.79/1.43 tff(456,plain,
% 1.79/1.43 (hskp29 | hskp12 | hskp3),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[455, 444])).
% 1.79/1.43 tff(457,plain,
% 1.79/1.43 (hskp29 | hskp12 | hskp3),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[456, 444])).
% 1.79/1.43 tff(458,plain,
% 1.79/1.43 (hskp12),
% 1.79/1.43 inference(unit_resolution,[status(thm)],[457, 443, 372])).
% 1.79/1.43 tff(459,plain,
% 1.79/1.43 (((~hskp12) | (~c3_1(a481))) <=> ((~hskp12) | (~c3_1(a481)))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(460,plain,
% 1.79/1.43 (((~c3_1(a481)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a481)))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(461,axiom,((~c3_1(a481)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 1.79/1.43 tff(462,plain,
% 1.79/1.43 ((~hskp12) | (~c3_1(a481))),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[461, 460])).
% 1.79/1.43 tff(463,plain,
% 1.79/1.43 ((~hskp12) | (~c3_1(a481))),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[462, 459])).
% 1.79/1.43 tff(464,plain,
% 1.79/1.43 (~c3_1(a481)),
% 1.79/1.43 inference(unit_resolution,[status(thm)],[463, 458])).
% 1.79/1.43 tff(465,plain,
% 1.79/1.43 (((~hskp12) | (~c0_1(a481))) <=> ((~hskp12) | (~c0_1(a481)))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(466,plain,
% 1.79/1.43 (((~c0_1(a481)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a481)))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(467,axiom,((~c0_1(a481)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.79/1.43 tff(468,plain,
% 1.79/1.43 ((~hskp12) | (~c0_1(a481))),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[467, 466])).
% 1.79/1.43 tff(469,plain,
% 1.79/1.43 ((~hskp12) | (~c0_1(a481))),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[468, 465])).
% 1.79/1.43 tff(470,plain,
% 1.79/1.43 (~c0_1(a481)),
% 1.79/1.43 inference(unit_resolution,[status(thm)],[469, 458])).
% 1.79/1.43 tff(471,plain,
% 1.79/1.43 (((~hskp12) | c1_1(a481)) <=> ((~hskp12) | c1_1(a481))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(472,axiom,((~hskp12) | c1_1(a481)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 1.79/1.43 tff(473,plain,
% 1.79/1.43 ((~hskp12) | c1_1(a481)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[472, 471])).
% 1.79/1.43 tff(474,plain,
% 1.79/1.43 ((~hskp12) | c1_1(a481)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[473, 471])).
% 1.79/1.43 tff(475,plain,
% 1.79/1.43 ((~hskp12) | c1_1(a481)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[474, 471])).
% 1.79/1.43 tff(476,plain,
% 1.79/1.43 ((~hskp12) | c1_1(a481)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[475, 471])).
% 1.79/1.43 tff(477,plain,
% 1.79/1.43 ((~hskp12) | c1_1(a481)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[476, 471])).
% 1.79/1.43 tff(478,plain,
% 1.79/1.43 ((~hskp12) | c1_1(a481)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[477, 471])).
% 1.79/1.43 tff(479,plain,
% 1.79/1.43 ((~hskp12) | c1_1(a481)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[478, 471])).
% 1.79/1.43 tff(480,plain,
% 1.79/1.43 ((~hskp12) | c1_1(a481)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[479, 471])).
% 1.79/1.43 tff(481,plain,
% 1.79/1.43 (c1_1(a481)),
% 1.79/1.43 inference(unit_resolution,[status(thm)],[480, 458])).
% 1.79/1.43 tff(482,plain,
% 1.79/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(483,plain,
% 1.79/1.43 (((~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c1_1(a481)) | c0_1(a481) | c2_1(a481) | (~c1_1(a481)) | c3_1(a481) | c0_1(a481) | c2_1(a481)) <=> (c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(484,plain,
% 1.79/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c1_1(a481)) | c0_1(a481) | c2_1(a481) | (~c1_1(a481)) | c3_1(a481) | c0_1(a481) | c2_1(a481))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481)))),
% 1.79/1.43 inference(monotonicity,[status(thm)],[483])).
% 1.79/1.43 tff(485,plain,
% 1.79/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c1_1(a481)) | c0_1(a481) | c2_1(a481) | (~c1_1(a481)) | c3_1(a481) | c0_1(a481) | c2_1(a481))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481))),
% 1.79/1.43 inference(transitivity,[status(thm)],[484, 482])).
% 1.79/1.43 tff(486,plain,
% 1.79/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c1_1(a481)) | c0_1(a481) | c2_1(a481) | (~c1_1(a481)) | c3_1(a481) | c0_1(a481) | c2_1(a481))),
% 1.79/1.43 inference(quant_inst,[status(thm)],[])).
% 1.79/1.43 tff(487,plain,
% 1.79/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[486, 485])).
% 1.79/1.43 tff(488,plain,
% 1.79/1.43 (c2_1(a481)),
% 1.79/1.43 inference(unit_resolution,[status(thm)],[487, 81, 481, 470, 464, 10])).
% 1.79/1.43 tff(489,plain,
% 1.79/1.43 (~c1_1(a478)),
% 1.79/1.43 inference(unit_resolution,[status(thm)],[411, 81, 296, 267, 28, 285, 266, 405])).
% 1.79/1.43 tff(490,plain,
% 1.79/1.43 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.79/1.43 inference(bind,[status(th)],[])).
% 1.79/1.43 tff(491,plain,
% 1.79/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.79/1.43 inference(quant_intro,[status(thm)],[490])).
% 1.79/1.43 tff(492,plain,
% 1.79/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(493,plain,
% 1.79/1.43 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.79/1.43 inference(bind,[status(th)],[])).
% 1.79/1.43 tff(494,plain,
% 1.79/1.43 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.79/1.43 inference(quant_intro,[status(thm)],[493])).
% 1.79/1.43 tff(495,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause204')).
% 1.79/1.43 tff(496,plain,
% 1.79/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[495, 494])).
% 1.79/1.43 tff(497,plain,
% 1.79/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[496, 492])).
% 1.79/1.43 tff(498,plain,(
% 1.79/1.43 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.79/1.43 inference(skolemize,[status(sab)],[497])).
% 1.79/1.43 tff(499,plain,
% 1.79/1.43 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[498, 491])).
% 1.79/1.43 tff(500,plain,
% 1.79/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a494) | c0_1(a481) | c3_1(a481) | c3_1(a478) | (~ndr1_0) | c1_1(a478) | (~c2_1(a478)) | (~c1_1(a481)) | (~c1_1(a494)) | (~c0_1(a494)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a494) | c0_1(a481) | c3_1(a481) | c3_1(a478) | (~ndr1_0) | c1_1(a478) | (~c2_1(a478)) | (~c1_1(a481)) | (~c1_1(a494)) | (~c0_1(a494)))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(501,plain,
% 1.79/1.43 (((~ndr1_0) | c2_1(a494) | (~c1_1(a494)) | (~c0_1(a494)) | c3_1(a478) | c1_1(a478) | (~c2_1(a478)) | c3_1(a481) | c0_1(a481) | (~c1_1(a481))) <=> (c2_1(a494) | c0_1(a481) | c3_1(a481) | c3_1(a478) | (~ndr1_0) | c1_1(a478) | (~c2_1(a478)) | (~c1_1(a481)) | (~c1_1(a494)) | (~c0_1(a494)))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(502,plain,
% 1.79/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a494) | (~c1_1(a494)) | (~c0_1(a494)) | c3_1(a478) | c1_1(a478) | (~c2_1(a478)) | c3_1(a481) | c0_1(a481) | (~c1_1(a481)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a494) | c0_1(a481) | c3_1(a481) | c3_1(a478) | (~ndr1_0) | c1_1(a478) | (~c2_1(a478)) | (~c1_1(a481)) | (~c1_1(a494)) | (~c0_1(a494))))),
% 1.79/1.43 inference(monotonicity,[status(thm)],[501])).
% 1.79/1.43 tff(503,plain,
% 1.79/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a494) | (~c1_1(a494)) | (~c0_1(a494)) | c3_1(a478) | c1_1(a478) | (~c2_1(a478)) | c3_1(a481) | c0_1(a481) | (~c1_1(a481)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a494) | c0_1(a481) | c3_1(a481) | c3_1(a478) | (~ndr1_0) | c1_1(a478) | (~c2_1(a478)) | (~c1_1(a481)) | (~c1_1(a494)) | (~c0_1(a494)))),
% 1.79/1.43 inference(transitivity,[status(thm)],[502, 500])).
% 1.79/1.43 tff(504,plain,
% 1.79/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a494) | (~c1_1(a494)) | (~c0_1(a494)) | c3_1(a478) | c1_1(a478) | (~c2_1(a478)) | c3_1(a481) | c0_1(a481) | (~c1_1(a481)))),
% 1.79/1.43 inference(quant_inst,[status(thm)],[])).
% 1.79/1.43 tff(505,plain,
% 1.79/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a494) | c0_1(a481) | c3_1(a481) | c3_1(a478) | (~ndr1_0) | c1_1(a478) | (~c2_1(a478)) | (~c1_1(a481)) | (~c1_1(a494)) | (~c0_1(a494))),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[504, 503])).
% 1.79/1.43 tff(506,plain,
% 1.79/1.43 (~c1_1(a494)),
% 1.79/1.43 inference(unit_resolution,[status(thm)],[505, 81, 326, 481, 267, 315, 470, 464, 265, 499, 489])).
% 1.79/1.43 tff(507,plain,
% 1.79/1.43 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c2_1(a494) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | c1_1(a494) | (~c0_1(a494)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c2_1(a494) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | c1_1(a494) | (~c0_1(a494)))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(508,plain,
% 1.79/1.43 (((~ndr1_0) | c2_1(a494) | c1_1(a494) | (~c0_1(a494)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481))) <=> (c2_1(a494) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | c1_1(a494) | (~c0_1(a494)))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(509,plain,
% 1.79/1.43 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a494) | c1_1(a494) | (~c0_1(a494)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c2_1(a494) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | c1_1(a494) | (~c0_1(a494))))),
% 1.79/1.43 inference(monotonicity,[status(thm)],[508])).
% 1.79/1.43 tff(510,plain,
% 1.79/1.43 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a494) | c1_1(a494) | (~c0_1(a494)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c2_1(a494) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | c1_1(a494) | (~c0_1(a494)))),
% 1.79/1.43 inference(transitivity,[status(thm)],[509, 507])).
% 1.79/1.43 tff(511,plain,
% 1.79/1.43 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a494) | c1_1(a494) | (~c0_1(a494)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.79/1.43 inference(quant_inst,[status(thm)],[])).
% 1.79/1.43 tff(512,plain,
% 1.79/1.43 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c2_1(a494) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | c1_1(a494) | (~c0_1(a494))),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[511, 510])).
% 1.79/1.43 tff(513,plain,
% 1.79/1.43 ($false),
% 1.79/1.43 inference(unit_resolution,[status(thm)],[512, 81, 326, 481, 315, 470, 405, 506, 488])).
% 1.79/1.43 tff(514,plain,((~hskp16) | (~c2_1(a478)) | c3_1(a478) | c0_1(a478) | c1_1(a465) | c0_1(a465) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.79/1.43 tff(515,plain,
% 1.79/1.43 (~hskp16),
% 1.79/1.43 inference(unit_resolution,[status(thm)],[514, 264, 265, 266, 263, 267, 235])).
% 1.79/1.43 tff(516,plain,
% 1.79/1.43 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a478) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a478) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(517,plain,
% 1.79/1.43 ((hskp16 | hskp7 | (~ndr1_0) | c0_1(a478) | c3_1(a478) | (~c2_1(a478))) <=> (hskp16 | hskp7 | c0_1(a478) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(518,plain,
% 1.79/1.43 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a478) | c3_1(a478) | (~c2_1(a478)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a478) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478))))),
% 1.79/1.43 inference(monotonicity,[status(thm)],[517])).
% 1.79/1.43 tff(519,plain,
% 1.79/1.43 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a478) | c3_1(a478) | (~c2_1(a478)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a478) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478)))),
% 1.79/1.43 inference(transitivity,[status(thm)],[518, 516])).
% 1.79/1.43 tff(520,plain,
% 1.79/1.43 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a478) | c3_1(a478) | (~c2_1(a478)))),
% 1.79/1.43 inference(quant_inst,[status(thm)],[])).
% 1.79/1.43 tff(521,plain,
% 1.79/1.43 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a478) | c3_1(a478) | (~ndr1_0) | (~c2_1(a478))),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[520, 519])).
% 1.79/1.43 tff(522,plain,
% 1.79/1.43 (hskp16 | hskp7),
% 1.79/1.43 inference(unit_resolution,[status(thm)],[521, 81, 267, 266, 265, 20])).
% 1.79/1.43 tff(523,plain,
% 1.79/1.43 (hskp7),
% 1.79/1.43 inference(unit_resolution,[status(thm)],[522, 515])).
% 1.79/1.43 tff(524,plain,
% 1.79/1.43 (((~hskp7) | (~c2_1(a471))) <=> ((~hskp7) | (~c2_1(a471)))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(525,plain,
% 1.79/1.43 (((~c2_1(a471)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a471)))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(526,axiom,((~c2_1(a471)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 1.79/1.43 tff(527,plain,
% 1.79/1.43 ((~hskp7) | (~c2_1(a471))),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[526, 525])).
% 1.79/1.43 tff(528,plain,
% 1.79/1.43 ((~hskp7) | (~c2_1(a471))),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[527, 524])).
% 1.79/1.43 tff(529,plain,
% 1.79/1.43 (~c2_1(a471)),
% 1.79/1.43 inference(unit_resolution,[status(thm)],[528, 523])).
% 1.79/1.43 tff(530,plain,
% 1.79/1.43 (((~hskp7) | c3_1(a471)) <=> ((~hskp7) | c3_1(a471))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(531,axiom,((~hskp7) | c3_1(a471)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 1.79/1.43 tff(532,plain,
% 1.79/1.43 ((~hskp7) | c3_1(a471)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[531, 530])).
% 1.79/1.43 tff(533,plain,
% 1.79/1.43 ((~hskp7) | c3_1(a471)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[532, 530])).
% 1.79/1.43 tff(534,plain,
% 1.79/1.43 ((~hskp7) | c3_1(a471)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[533, 530])).
% 1.79/1.43 tff(535,plain,
% 1.79/1.43 ((~hskp7) | c3_1(a471)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[534, 530])).
% 1.79/1.43 tff(536,plain,
% 1.79/1.43 ((~hskp7) | c3_1(a471)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[535, 530])).
% 1.79/1.43 tff(537,plain,
% 1.79/1.43 ((~hskp7) | c3_1(a471)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[536, 530])).
% 1.79/1.43 tff(538,plain,
% 1.79/1.43 ((~hskp7) | c3_1(a471)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[537, 530])).
% 1.79/1.43 tff(539,plain,
% 1.79/1.43 ((~hskp7) | c3_1(a471)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[538, 530])).
% 1.79/1.43 tff(540,plain,
% 1.79/1.43 (c3_1(a471)),
% 1.79/1.43 inference(unit_resolution,[status(thm)],[539, 523])).
% 1.79/1.43 tff(541,plain,
% 1.79/1.43 (((~hskp7) | c0_1(a471)) <=> ((~hskp7) | c0_1(a471))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(542,axiom,((~hskp7) | c0_1(a471)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.79/1.43 tff(543,plain,
% 1.79/1.43 ((~hskp7) | c0_1(a471)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[542, 541])).
% 1.79/1.43 tff(544,plain,
% 1.79/1.43 ((~hskp7) | c0_1(a471)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[543, 541])).
% 1.79/1.43 tff(545,plain,
% 1.79/1.43 ((~hskp7) | c0_1(a471)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[544, 541])).
% 1.79/1.43 tff(546,plain,
% 1.79/1.43 ((~hskp7) | c0_1(a471)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[545, 541])).
% 1.79/1.43 tff(547,plain,
% 1.79/1.43 ((~hskp7) | c0_1(a471)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[546, 541])).
% 1.79/1.43 tff(548,plain,
% 1.79/1.43 ((~hskp7) | c0_1(a471)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[547, 541])).
% 1.79/1.43 tff(549,plain,
% 1.79/1.43 ((~hskp7) | c0_1(a471)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[548, 541])).
% 1.79/1.43 tff(550,plain,
% 1.79/1.43 ((~hskp7) | c0_1(a471)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[549, 541])).
% 1.79/1.43 tff(551,plain,
% 1.79/1.43 (c0_1(a471)),
% 1.79/1.43 inference(unit_resolution,[status(thm)],[550, 523])).
% 1.79/1.43 tff(552,assumption,(c0_1(a471)), introduced(assumption)).
% 1.79/1.43 tff(553,assumption,(c3_1(a471)), introduced(assumption)).
% 1.79/1.43 tff(554,assumption,(c0_1(a467)), introduced(assumption)).
% 1.79/1.43 tff(555,plain,
% 1.79/1.43 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 1.79/1.43 inference(bind,[status(th)],[])).
% 1.79/1.43 tff(556,plain,
% 1.79/1.43 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.79/1.43 inference(quant_intro,[status(thm)],[555])).
% 1.79/1.43 tff(557,plain,
% 1.79/1.43 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(558,plain,
% 1.79/1.43 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp16) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp16))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 1.79/1.43 inference(bind,[status(th)],[])).
% 1.79/1.43 tff(559,plain,
% 1.79/1.43 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.79/1.43 inference(quant_intro,[status(thm)],[558])).
% 1.79/1.43 tff(560,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 1.79/1.43 tff(561,plain,
% 1.79/1.43 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[560, 559])).
% 1.79/1.43 tff(562,plain,
% 1.79/1.43 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[561, 557])).
% 1.79/1.43 tff(563,plain,(
% 1.79/1.43 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.79/1.43 inference(skolemize,[status(sab)],[562])).
% 1.79/1.43 tff(564,plain,
% 1.79/1.43 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[563, 556])).
% 1.79/1.43 tff(565,plain,
% 1.79/1.43 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(566,plain,
% 1.79/1.43 ((hskp16 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c0_1(a467)) | c3_1(a467) | c1_1(a467) | c2_1(a467)) <=> (hskp16 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(567,plain,
% 1.79/1.43 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c0_1(a467)) | c3_1(a467) | c1_1(a467) | c2_1(a467))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467)))),
% 1.79/1.43 inference(monotonicity,[status(thm)],[566])).
% 1.79/1.43 tff(568,plain,
% 1.79/1.43 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c0_1(a467)) | c3_1(a467) | c1_1(a467) | c2_1(a467))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467))),
% 1.79/1.43 inference(transitivity,[status(thm)],[567, 565])).
% 1.79/1.43 tff(569,plain,
% 1.79/1.43 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c0_1(a467)) | c3_1(a467) | c1_1(a467) | c2_1(a467))),
% 1.79/1.43 inference(quant_inst,[status(thm)],[])).
% 1.79/1.43 tff(570,plain,
% 1.79/1.43 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467)),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[569, 568])).
% 1.79/1.43 tff(571,plain,
% 1.79/1.43 (hskp16 | (~c0_1(a467)) | c2_1(a467)),
% 1.79/1.43 inference(unit_resolution,[status(thm)],[570, 81, 269, 268, 564])).
% 1.79/1.43 tff(572,plain,
% 1.79/1.43 (c2_1(a467)),
% 1.79/1.43 inference(unit_resolution,[status(thm)],[571, 554, 110])).
% 1.79/1.43 tff(573,plain,
% 1.79/1.43 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.79/1.43 inference(bind,[status(th)],[])).
% 1.79/1.43 tff(574,plain,
% 1.79/1.43 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.79/1.43 inference(quant_intro,[status(thm)],[573])).
% 1.79/1.43 tff(575,plain,
% 1.79/1.43 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.79/1.43 inference(rewrite,[status(thm)],[])).
% 1.79/1.43 tff(576,plain,
% 1.79/1.43 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.79/1.43 inference(bind,[status(th)],[])).
% 1.79/1.43 tff(577,plain,
% 1.79/1.43 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.79/1.43 inference(quant_intro,[status(thm)],[576])).
% 1.79/1.43 tff(578,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 1.79/1.43 tff(579,plain,
% 1.79/1.43 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[578, 577])).
% 1.79/1.43 tff(580,plain,
% 1.79/1.43 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.79/1.43 inference(modus_ponens,[status(thm)],[579, 575])).
% 1.79/1.44 tff(581,plain,(
% 1.79/1.44 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.79/1.44 inference(skolemize,[status(sab)],[580])).
% 1.79/1.44 tff(582,plain,
% 1.79/1.44 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[581, 574])).
% 1.79/1.44 tff(583,plain,
% 1.79/1.44 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a471) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a471)) | (~c3_1(a471)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a471) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a471)) | (~c3_1(a471)))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(584,plain,
% 1.79/1.44 ((hskp12 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467))) <=> (hskp12 | c2_1(a471) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a471)) | (~c3_1(a471)))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(585,plain,
% 1.79/1.44 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a471) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a471)) | (~c3_1(a471))))),
% 1.79/1.44 inference(monotonicity,[status(thm)],[584])).
% 1.79/1.44 tff(586,plain,
% 1.79/1.44 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a471) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a471)) | (~c3_1(a471)))),
% 1.79/1.44 inference(transitivity,[status(thm)],[585, 583])).
% 1.79/1.44 tff(587,plain,
% 1.79/1.44 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))),
% 1.79/1.44 inference(quant_inst,[status(thm)],[])).
% 1.79/1.44 tff(588,plain,
% 1.79/1.44 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a471) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a471)) | (~c3_1(a471))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[587, 586])).
% 1.79/1.44 tff(589,plain,
% 1.79/1.44 (hskp12 | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a471)) | (~c3_1(a471))),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[588, 81, 29, 269, 582])).
% 1.79/1.44 tff(590,plain,
% 1.79/1.44 ($false),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[589, 572, 554, 553, 552, 21])).
% 1.79/1.44 tff(591,plain,((~c0_1(a467)) | (~c3_1(a471)) | (~c0_1(a471)) | hskp12 | c2_1(a471) | c1_1(a467) | hskp16 | c3_1(a467)), inference(lemma,lemma(discharge,[]))).
% 1.79/1.44 tff(592,plain,
% 1.79/1.44 (~c0_1(a467)),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[591, 21, 551, 540, 529, 269, 515, 268])).
% 1.79/1.44 tff(593,plain,
% 1.79/1.44 (((~hskp5) | c0_1(a467)) <=> ((~hskp5) | c0_1(a467))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(594,axiom,((~hskp5) | c0_1(a467)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 1.79/1.44 tff(595,plain,
% 1.79/1.44 ((~hskp5) | c0_1(a467)),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[594, 593])).
% 1.79/1.44 tff(596,plain,
% 1.79/1.44 ((~hskp5) | c0_1(a467)),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[595, 593])).
% 1.79/1.44 tff(597,plain,
% 1.79/1.44 ((~hskp5) | c0_1(a467)),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[596, 593])).
% 1.79/1.44 tff(598,plain,
% 1.79/1.44 ((~hskp5) | c0_1(a467)),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[597, 593])).
% 1.79/1.44 tff(599,plain,
% 1.79/1.44 ((~hskp5) | c0_1(a467)),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[598, 593])).
% 1.79/1.44 tff(600,plain,
% 1.79/1.44 ((~hskp5) | c0_1(a467)),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[599, 593])).
% 1.79/1.44 tff(601,plain,
% 1.79/1.44 ((~hskp5) | c0_1(a467)),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[600, 593])).
% 1.79/1.44 tff(602,plain,
% 1.79/1.44 ((~hskp5) | c0_1(a467)),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[601, 593])).
% 1.79/1.44 tff(603,plain,
% 1.79/1.44 (~hskp5),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[602, 592])).
% 1.79/1.44 tff(604,plain,
% 1.79/1.44 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.79/1.44 inference(bind,[status(th)],[])).
% 1.79/1.44 tff(605,plain,
% 1.79/1.44 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.79/1.44 inference(quant_intro,[status(thm)],[604])).
% 1.79/1.44 tff(606,plain,
% 1.79/1.44 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(607,plain,
% 1.79/1.44 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.79/1.44 inference(bind,[status(th)],[])).
% 1.79/1.44 tff(608,plain,
% 1.79/1.44 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.79/1.44 inference(quant_intro,[status(thm)],[607])).
% 1.79/1.44 tff(609,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 1.79/1.44 tff(610,plain,
% 1.79/1.44 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[609, 608])).
% 1.79/1.44 tff(611,plain,
% 1.79/1.44 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[610, 606])).
% 1.79/1.44 tff(612,plain,(
% 1.79/1.44 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.79/1.44 inference(skolemize,[status(sab)],[611])).
% 1.79/1.44 tff(613,plain,
% 1.79/1.44 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[612, 605])).
% 1.79/1.44 tff(614,plain,
% 1.79/1.44 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a467) | c1_1(a467) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a467) | c1_1(a467) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(615,plain,
% 1.79/1.44 ((hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c1_1(a464)) | c3_1(a467) | c1_1(a467) | c0_1(a467)) <=> (hskp5 | c0_1(a467) | c1_1(a467) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(616,plain,
% 1.79/1.44 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c1_1(a464)) | c3_1(a467) | c1_1(a467) | c0_1(a467))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a467) | c1_1(a467) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464))))),
% 1.79/1.44 inference(monotonicity,[status(thm)],[615])).
% 1.79/1.44 tff(617,plain,
% 1.79/1.44 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c1_1(a464)) | c3_1(a467) | c1_1(a467) | c0_1(a467))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a467) | c1_1(a467) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.79/1.44 inference(transitivity,[status(thm)],[616, 614])).
% 1.79/1.44 tff(618,plain,
% 1.79/1.44 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c1_1(a464)) | c3_1(a467) | c1_1(a467) | c0_1(a467))),
% 1.79/1.44 inference(quant_inst,[status(thm)],[])).
% 1.79/1.44 tff(619,plain,
% 1.79/1.44 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a467) | c1_1(a467) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[618, 617])).
% 1.79/1.44 tff(620,plain,
% 1.79/1.44 (hskp5 | c0_1(a467) | c1_1(a467) | (~c1_1(a464))),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[619, 81, 268, 238, 237, 613])).
% 1.79/1.44 tff(621,plain,
% 1.79/1.44 (~c1_1(a464)),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[620, 603, 269, 592])).
% 1.79/1.44 tff(622,plain,
% 1.79/1.44 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(623,plain,
% 1.79/1.44 ((hskp12 | hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c3_1(a464))) <=> (hskp12 | hskp5 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(624,plain,
% 1.79/1.44 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c3_1(a464)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464))))),
% 1.79/1.44 inference(monotonicity,[status(thm)],[623])).
% 1.79/1.44 tff(625,plain,
% 1.79/1.44 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c3_1(a464)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)))),
% 1.79/1.44 inference(transitivity,[status(thm)],[624, 622])).
% 1.79/1.44 tff(626,plain,
% 1.79/1.44 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c3_1(a464)))),
% 1.79/1.44 inference(quant_inst,[status(thm)],[])).
% 1.79/1.44 tff(627,plain,
% 1.79/1.44 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[626, 625])).
% 1.79/1.44 tff(628,plain,
% 1.79/1.44 (hskp12 | hskp5 | c0_1(a464) | (~c3_1(a464))),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[627, 81, 237, 41])).
% 1.79/1.44 tff(629,plain,
% 1.79/1.44 (~c3_1(a464)),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[628, 603, 21, 238])).
% 1.79/1.44 tff(630,plain,
% 1.79/1.44 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(631,plain,
% 1.79/1.44 ((hskp12 | hskp5 | (~ndr1_0) | c2_1(a465) | c0_1(a465) | (~c3_1(a465))) <=> (hskp12 | hskp5 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(632,plain,
% 1.79/1.44 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a465) | c0_1(a465) | (~c3_1(a465)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465)))),
% 1.79/1.44 inference(monotonicity,[status(thm)],[631])).
% 1.79/1.44 tff(633,plain,
% 1.79/1.44 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a465) | c0_1(a465) | (~c3_1(a465)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465))),
% 1.79/1.44 inference(transitivity,[status(thm)],[632, 630])).
% 1.79/1.44 tff(634,plain,
% 1.79/1.44 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a465) | c0_1(a465) | (~c3_1(a465)))),
% 1.79/1.44 inference(quant_inst,[status(thm)],[])).
% 1.79/1.44 tff(635,plain,
% 1.79/1.44 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465)),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[634, 633])).
% 1.79/1.44 tff(636,plain,
% 1.79/1.44 (hskp12 | hskp5 | (~c3_1(a465)) | c2_1(a465)),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[635, 81, 264, 41])).
% 1.79/1.44 tff(637,plain,
% 1.79/1.44 (c2_1(a465)),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[636, 373, 21, 31])).
% 1.79/1.44 tff(638,assumption,(~c1_1(a464)), introduced(assumption)).
% 1.79/1.44 tff(639,plain,
% 1.79/1.44 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 1.79/1.44 inference(bind,[status(th)],[])).
% 1.79/1.44 tff(640,plain,
% 1.79/1.44 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.79/1.44 inference(quant_intro,[status(thm)],[639])).
% 1.79/1.44 tff(641,plain,
% 1.79/1.44 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(642,plain,
% 1.79/1.44 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 1.79/1.44 inference(bind,[status(th)],[])).
% 1.79/1.44 tff(643,plain,
% 1.79/1.44 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.79/1.44 inference(quant_intro,[status(thm)],[642])).
% 1.79/1.44 tff(644,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 1.79/1.44 tff(645,plain,
% 1.79/1.44 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[644, 643])).
% 1.79/1.44 tff(646,plain,
% 1.79/1.44 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[645, 641])).
% 1.79/1.44 tff(647,plain,(
% 1.79/1.44 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.79/1.44 inference(skolemize,[status(sab)],[646])).
% 1.79/1.44 tff(648,plain,
% 1.79/1.44 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[647, 640])).
% 1.79/1.44 tff(649,assumption,(~c3_1(a464)), introduced(assumption)).
% 1.79/1.44 tff(650,plain,
% 1.79/1.44 (((~hskp2) | c3_1(a464)) <=> ((~hskp2) | c3_1(a464))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(651,axiom,((~hskp2) | c3_1(a464)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 1.79/1.44 tff(652,plain,
% 1.79/1.44 ((~hskp2) | c3_1(a464)),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[651, 650])).
% 1.79/1.44 tff(653,plain,
% 1.79/1.44 ((~hskp2) | c3_1(a464)),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[652, 650])).
% 1.79/1.44 tff(654,plain,
% 1.79/1.44 ((~hskp2) | c3_1(a464)),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[653, 650])).
% 1.79/1.44 tff(655,plain,
% 1.79/1.44 ((~hskp2) | c3_1(a464)),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[654, 650])).
% 1.79/1.44 tff(656,plain,
% 1.79/1.44 ((~hskp2) | c3_1(a464)),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[655, 650])).
% 1.79/1.44 tff(657,plain,
% 1.79/1.44 ((~hskp2) | c3_1(a464)),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[656, 650])).
% 1.79/1.44 tff(658,plain,
% 1.79/1.44 ((~hskp2) | c3_1(a464)),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[657, 650])).
% 1.79/1.44 tff(659,plain,
% 1.79/1.44 ((~hskp2) | c3_1(a464)),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[658, 650])).
% 1.79/1.44 tff(660,plain,
% 1.79/1.44 (~hskp2),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[659, 649])).
% 1.79/1.44 tff(661,plain,
% 1.79/1.44 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c3_1(a464) | c1_1(a465) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a465)) | (~c2_1(a465)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c3_1(a464) | c1_1(a465) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a465)) | (~c2_1(a465)))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(662,plain,
% 1.79/1.44 ((hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a464) | c1_1(a464) | c2_1(a464)) <=> (hskp2 | c3_1(a464) | c1_1(a465) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a465)) | (~c2_1(a465)))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(663,plain,
% 1.79/1.44 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c3_1(a464) | c1_1(a465) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a465)) | (~c2_1(a465))))),
% 1.79/1.44 inference(monotonicity,[status(thm)],[662])).
% 1.79/1.44 tff(664,plain,
% 1.79/1.44 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c3_1(a464) | c1_1(a465) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a465)) | (~c2_1(a465)))),
% 1.79/1.44 inference(transitivity,[status(thm)],[663, 661])).
% 1.79/1.44 tff(665,plain,
% 1.79/1.44 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a464) | c1_1(a464) | c2_1(a464))),
% 1.79/1.44 inference(quant_inst,[status(thm)],[])).
% 1.79/1.44 tff(666,plain,
% 1.79/1.44 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c3_1(a464) | c1_1(a465) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a465)) | (~c2_1(a465))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[665, 664])).
% 1.79/1.44 tff(667,plain,
% 1.79/1.44 ((~c3_1(a465)) | (~c2_1(a465))),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[666, 81, 660, 649, 263, 237, 648, 638])).
% 1.79/1.44 tff(668,plain,
% 1.79/1.44 ($false),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[667, 637, 373])).
% 1.79/1.44 tff(669,plain,((~c3_1(a465)) | c3_1(a464) | c1_1(a465) | c2_1(a464) | c1_1(a464) | hskp12 | hskp5 | c0_1(a465)), inference(lemma,lemma(discharge,[]))).
% 1.79/1.44 tff(670,plain,
% 1.79/1.44 (~c3_1(a465)),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[669, 629, 263, 237, 621, 21, 603, 264])).
% 1.79/1.44 tff(671,plain,
% 1.79/1.44 (~hskp3),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[442, 670])).
% 1.79/1.44 tff(672,plain,
% 1.79/1.44 (^[U: $i] : refl((hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 1.79/1.44 inference(bind,[status(th)],[])).
% 1.79/1.44 tff(673,plain,
% 1.79/1.44 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.79/1.44 inference(quant_intro,[status(thm)],[672])).
% 1.79/1.44 tff(674,plain,
% 1.79/1.44 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(675,plain,
% 1.79/1.44 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 1.79/1.44 inference(bind,[status(th)],[])).
% 1.79/1.44 tff(676,plain,
% 1.79/1.44 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.79/1.44 inference(quant_intro,[status(thm)],[675])).
% 1.79/1.44 tff(677,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 1.79/1.44 tff(678,plain,
% 1.79/1.44 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[677, 676])).
% 1.79/1.44 tff(679,plain,
% 1.79/1.44 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[678, 674])).
% 1.79/1.44 tff(680,plain,(
% 1.79/1.44 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.79/1.44 inference(skolemize,[status(sab)],[679])).
% 1.79/1.44 tff(681,plain,
% 1.79/1.44 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[680, 673])).
% 1.79/1.44 tff(682,plain,
% 1.79/1.44 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(683,plain,
% 1.79/1.44 ((hskp4 | hskp3 | (~ndr1_0) | c2_1(a464) | c1_1(a464) | c0_1(a464)) <=> (hskp4 | hskp3 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(684,plain,
% 1.79/1.44 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c2_1(a464) | c1_1(a464) | c0_1(a464))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464)))),
% 1.79/1.44 inference(monotonicity,[status(thm)],[683])).
% 1.79/1.44 tff(685,plain,
% 1.79/1.44 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c2_1(a464) | c1_1(a464) | c0_1(a464))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464))),
% 1.79/1.44 inference(transitivity,[status(thm)],[684, 682])).
% 1.79/1.44 tff(686,plain,
% 1.79/1.44 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c2_1(a464) | c1_1(a464) | c0_1(a464))),
% 1.79/1.44 inference(quant_inst,[status(thm)],[])).
% 1.79/1.44 tff(687,plain,
% 1.79/1.44 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464)),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[686, 685])).
% 1.79/1.44 tff(688,plain,
% 1.79/1.44 (hskp4 | hskp3 | c0_1(a464) | c1_1(a464)),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[687, 81, 237, 681])).
% 1.79/1.44 tff(689,plain,
% 1.79/1.44 (hskp4),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[688, 671, 238, 621])).
% 1.79/1.44 tff(690,plain,
% 1.79/1.44 (((~hskp4) | (~c0_1(a466))) <=> ((~hskp4) | (~c0_1(a466)))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(691,plain,
% 1.79/1.44 (((~c0_1(a466)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a466)))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(692,axiom,((~c0_1(a466)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 1.79/1.44 tff(693,plain,
% 1.79/1.44 ((~hskp4) | (~c0_1(a466))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[692, 691])).
% 1.79/1.44 tff(694,plain,
% 1.79/1.44 ((~hskp4) | (~c0_1(a466))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[693, 690])).
% 1.79/1.44 tff(695,plain,
% 1.79/1.44 (~c0_1(a466)),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[694, 689])).
% 1.79/1.44 tff(696,plain,
% 1.79/1.44 (((~hskp4) | (~c1_1(a466))) <=> ((~hskp4) | (~c1_1(a466)))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(697,plain,
% 1.79/1.44 (((~c1_1(a466)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a466)))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(698,axiom,((~c1_1(a466)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.79/1.44 tff(699,plain,
% 1.79/1.44 ((~hskp4) | (~c1_1(a466))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[698, 697])).
% 1.79/1.44 tff(700,plain,
% 1.79/1.44 ((~hskp4) | (~c1_1(a466))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[699, 696])).
% 1.79/1.44 tff(701,plain,
% 1.79/1.44 (~c1_1(a466)),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[700, 689])).
% 1.79/1.44 tff(702,plain,
% 1.79/1.44 (((~hskp4) | (~c3_1(a466))) <=> ((~hskp4) | (~c3_1(a466)))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(703,plain,
% 1.79/1.44 (((~c3_1(a466)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a466)))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(704,axiom,((~c3_1(a466)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 1.79/1.44 tff(705,plain,
% 1.79/1.44 ((~hskp4) | (~c3_1(a466))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[704, 703])).
% 1.79/1.44 tff(706,plain,
% 1.79/1.44 ((~hskp4) | (~c3_1(a466))),
% 1.79/1.44 inference(modus_ponens,[status(thm)],[705, 702])).
% 1.79/1.44 tff(707,plain,
% 1.79/1.44 (~c3_1(a466)),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[706, 689])).
% 1.79/1.44 tff(708,assumption,(~c3_1(a466)), introduced(assumption)).
% 1.79/1.44 tff(709,assumption,(~c0_1(a466)), introduced(assumption)).
% 1.79/1.44 tff(710,assumption,(~c1_1(a466)), introduced(assumption)).
% 1.79/1.44 tff(711,plain,
% 1.79/1.44 (hskp7),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[522, 110])).
% 1.79/1.44 tff(712,plain,
% 1.79/1.44 (c0_1(a471)),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[550, 711])).
% 1.79/1.44 tff(713,plain,
% 1.79/1.44 (c3_1(a471)),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[539, 711])).
% 1.79/1.44 tff(714,plain,
% 1.79/1.44 (~c0_1(a467)),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[591, 712, 21, 713, 29, 269, 110, 268])).
% 1.79/1.44 tff(715,plain,
% 1.79/1.44 (~hskp5),
% 1.79/1.44 inference(unit_resolution,[status(thm)],[602, 714])).
% 1.79/1.44 tff(716,plain,
% 1.79/1.44 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a466) | c1_1(a466) | c3_1(a466) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a466) | c1_1(a466) | c3_1(a466) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.79/1.44 inference(rewrite,[status(thm)],[])).
% 1.79/1.44 tff(717,plain,
% 1.79/1.44 ((hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c1_1(a464)) | c3_1(a466) | c1_1(a466) | c0_1(a466)) <=> (hskp5 | c0_1(a466) | c1_1(a466) | c3_1(a466) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(718,plain,
% 1.79/1.45 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c1_1(a464)) | c3_1(a466) | c1_1(a466) | c0_1(a466))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a466) | c1_1(a466) | c3_1(a466) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464))))),
% 1.79/1.45 inference(monotonicity,[status(thm)],[717])).
% 1.79/1.45 tff(719,plain,
% 1.79/1.45 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c1_1(a464)) | c3_1(a466) | c1_1(a466) | c0_1(a466))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a466) | c1_1(a466) | c3_1(a466) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.79/1.45 inference(transitivity,[status(thm)],[718, 716])).
% 1.79/1.45 tff(720,plain,
% 1.79/1.45 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c2_1(a464) | c0_1(a464) | (~c1_1(a464)) | c3_1(a466) | c1_1(a466) | c0_1(a466))),
% 1.79/1.45 inference(quant_inst,[status(thm)],[])).
% 1.79/1.45 tff(721,plain,
% 1.79/1.45 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a466) | c1_1(a466) | c3_1(a466) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[720, 719])).
% 1.79/1.45 tff(722,plain,
% 1.79/1.45 (hskp5 | c0_1(a466) | c1_1(a466) | (~c1_1(a464))),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[721, 81, 708, 238, 237, 613])).
% 1.79/1.45 tff(723,plain,
% 1.79/1.45 (~c1_1(a464)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[722, 715, 710, 709])).
% 1.79/1.45 tff(724,plain,
% 1.79/1.45 (^[U: $i] : refl((hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.79/1.45 inference(bind,[status(th)],[])).
% 1.79/1.45 tff(725,plain,
% 1.79/1.45 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.79/1.45 inference(quant_intro,[status(thm)],[724])).
% 1.79/1.45 tff(726,plain,
% 1.79/1.45 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(727,plain,
% 1.79/1.45 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp17) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp17))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp17) <=> (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp17) <=> (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.79/1.45 inference(bind,[status(th)],[])).
% 1.79/1.45 tff(728,plain,
% 1.79/1.45 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp17) <=> ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.79/1.45 inference(quant_intro,[status(thm)],[727])).
% 1.79/1.45 tff(729,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 1.79/1.45 tff(730,plain,
% 1.79/1.45 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[729, 728])).
% 1.79/1.45 tff(731,plain,
% 1.79/1.45 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[730, 726])).
% 1.79/1.45 tff(732,plain,(
% 1.79/1.45 ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.79/1.45 inference(skolemize,[status(sab)],[731])).
% 1.79/1.45 tff(733,plain,
% 1.79/1.45 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[732, 725])).
% 1.79/1.45 tff(734,plain,
% 1.79/1.45 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c3_1(a471)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c3_1(a471)))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(735,plain,
% 1.79/1.45 ((hskp17 | hskp5 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471))) <=> (hskp17 | hskp5 | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c3_1(a471)))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(736,plain,
% 1.79/1.45 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c3_1(a471))))),
% 1.79/1.45 inference(monotonicity,[status(thm)],[735])).
% 1.79/1.45 tff(737,plain,
% 1.79/1.45 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c3_1(a471)))),
% 1.79/1.45 inference(transitivity,[status(thm)],[736, 734])).
% 1.79/1.45 tff(738,plain,
% 1.79/1.45 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)))),
% 1.79/1.45 inference(quant_inst,[status(thm)],[])).
% 1.79/1.45 tff(739,plain,
% 1.79/1.45 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c3_1(a471))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[738, 737])).
% 1.79/1.45 tff(740,plain,
% 1.79/1.45 (hskp17 | hskp5 | (~c0_1(a471)) | (~c3_1(a471))),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[739, 81, 29, 733])).
% 1.79/1.45 tff(741,plain,
% 1.79/1.45 (hskp17),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[740, 715, 712, 713])).
% 1.79/1.45 tff(742,plain,
% 1.79/1.45 (((~hskp17) | c2_1(a493)) <=> ((~hskp17) | c2_1(a493))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(743,axiom,((~hskp17) | c2_1(a493)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 1.79/1.45 tff(744,plain,
% 1.79/1.45 ((~hskp17) | c2_1(a493)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[743, 742])).
% 1.79/1.45 tff(745,plain,
% 1.79/1.45 ((~hskp17) | c2_1(a493)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[744, 742])).
% 1.79/1.45 tff(746,plain,
% 1.79/1.45 ((~hskp17) | c2_1(a493)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[745, 742])).
% 1.79/1.45 tff(747,plain,
% 1.79/1.45 ((~hskp17) | c2_1(a493)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[746, 742])).
% 1.79/1.45 tff(748,plain,
% 1.79/1.45 ((~hskp17) | c2_1(a493)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[747, 742])).
% 1.79/1.45 tff(749,plain,
% 1.79/1.45 ((~hskp17) | c2_1(a493)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[748, 742])).
% 1.79/1.45 tff(750,plain,
% 1.79/1.45 ((~hskp17) | c2_1(a493)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[749, 742])).
% 1.79/1.45 tff(751,plain,
% 1.79/1.45 ((~hskp17) | c2_1(a493)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[750, 742])).
% 1.79/1.45 tff(752,plain,
% 1.79/1.45 (c2_1(a493)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[751, 741])).
% 1.79/1.45 tff(753,plain,
% 1.79/1.45 (((~hskp17) | (~c0_1(a493))) <=> ((~hskp17) | (~c0_1(a493)))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(754,plain,
% 1.79/1.45 (((~c0_1(a493)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a493)))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(755,axiom,((~c0_1(a493)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 1.79/1.45 tff(756,plain,
% 1.79/1.45 ((~hskp17) | (~c0_1(a493))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[755, 754])).
% 1.79/1.45 tff(757,plain,
% 1.79/1.45 ((~hskp17) | (~c0_1(a493))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[756, 753])).
% 1.79/1.45 tff(758,plain,
% 1.79/1.45 (~c0_1(a493)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[757, 741])).
% 1.79/1.45 tff(759,plain,
% 1.79/1.45 (((~hskp17) | c3_1(a493)) <=> ((~hskp17) | c3_1(a493))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(760,axiom,((~hskp17) | c3_1(a493)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 1.79/1.45 tff(761,plain,
% 1.79/1.45 ((~hskp17) | c3_1(a493)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[760, 759])).
% 1.79/1.45 tff(762,plain,
% 1.79/1.45 ((~hskp17) | c3_1(a493)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[761, 759])).
% 1.79/1.45 tff(763,plain,
% 1.79/1.45 ((~hskp17) | c3_1(a493)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[762, 759])).
% 1.79/1.45 tff(764,plain,
% 1.79/1.45 ((~hskp17) | c3_1(a493)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[763, 759])).
% 1.79/1.45 tff(765,plain,
% 1.79/1.45 ((~hskp17) | c3_1(a493)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[764, 759])).
% 1.79/1.45 tff(766,plain,
% 1.79/1.45 ((~hskp17) | c3_1(a493)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[765, 759])).
% 1.79/1.45 tff(767,plain,
% 1.79/1.45 ((~hskp17) | c3_1(a493)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[766, 759])).
% 1.79/1.45 tff(768,plain,
% 1.79/1.45 ((~hskp17) | c3_1(a493)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[767, 759])).
% 1.79/1.45 tff(769,plain,
% 1.79/1.45 (c3_1(a493)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[768, 741])).
% 1.79/1.45 tff(770,plain,
% 1.79/1.45 (~c0_1(a467)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[591, 552, 21, 553, 29, 269, 110, 268])).
% 1.79/1.45 tff(771,plain,
% 1.79/1.45 (~hskp5),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[602, 770])).
% 1.79/1.45 tff(772,plain,
% 1.79/1.45 (hskp17),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[740, 771, 552, 553])).
% 1.79/1.45 tff(773,plain,
% 1.79/1.45 (~c0_1(a493)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[757, 772])).
% 1.79/1.45 tff(774,assumption,(hskp26), introduced(assumption)).
% 1.79/1.45 tff(775,plain,
% 1.79/1.45 (((~hskp26) | (~c3_1(a559))) <=> ((~hskp26) | (~c3_1(a559)))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(776,plain,
% 1.79/1.45 (((~c3_1(a559)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a559)))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(777,axiom,((~c3_1(a559)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 1.79/1.45 tff(778,plain,
% 1.79/1.45 ((~hskp26) | (~c3_1(a559))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[777, 776])).
% 1.79/1.45 tff(779,plain,
% 1.79/1.45 ((~hskp26) | (~c3_1(a559))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[778, 775])).
% 1.79/1.45 tff(780,plain,
% 1.79/1.45 (~c3_1(a559)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[779, 774])).
% 1.79/1.45 tff(781,plain,
% 1.79/1.45 (c3_1(a493)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[768, 772])).
% 1.79/1.45 tff(782,plain,
% 1.79/1.45 (c2_1(a493)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[751, 772])).
% 1.79/1.45 tff(783,plain,
% 1.79/1.45 (((~hskp26) | c0_1(a559)) <=> ((~hskp26) | c0_1(a559))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(784,axiom,((~hskp26) | c0_1(a559)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 1.79/1.45 tff(785,plain,
% 1.79/1.45 ((~hskp26) | c0_1(a559)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[784, 783])).
% 1.79/1.45 tff(786,plain,
% 1.79/1.45 ((~hskp26) | c0_1(a559)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[785, 783])).
% 1.79/1.45 tff(787,plain,
% 1.79/1.45 ((~hskp26) | c0_1(a559)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[786, 783])).
% 1.79/1.45 tff(788,plain,
% 1.79/1.45 ((~hskp26) | c0_1(a559)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[787, 783])).
% 1.79/1.45 tff(789,plain,
% 1.79/1.45 ((~hskp26) | c0_1(a559)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[788, 783])).
% 1.79/1.45 tff(790,plain,
% 1.79/1.45 ((~hskp26) | c0_1(a559)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[789, 783])).
% 1.79/1.45 tff(791,plain,
% 1.79/1.45 ((~hskp26) | c0_1(a559)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[790, 783])).
% 1.79/1.45 tff(792,plain,
% 1.79/1.45 ((~hskp26) | c0_1(a559)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[791, 783])).
% 1.79/1.45 tff(793,plain,
% 1.79/1.45 (c0_1(a559)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[792, 774])).
% 1.79/1.45 tff(794,plain,
% 1.79/1.45 (((~hskp26) | c1_1(a559)) <=> ((~hskp26) | c1_1(a559))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(795,axiom,((~hskp26) | c1_1(a559)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 1.79/1.45 tff(796,plain,
% 1.79/1.45 ((~hskp26) | c1_1(a559)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[795, 794])).
% 1.79/1.45 tff(797,plain,
% 1.79/1.45 ((~hskp26) | c1_1(a559)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[796, 794])).
% 1.79/1.45 tff(798,plain,
% 1.79/1.45 ((~hskp26) | c1_1(a559)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[797, 794])).
% 1.79/1.45 tff(799,plain,
% 1.79/1.45 ((~hskp26) | c1_1(a559)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[798, 794])).
% 1.79/1.45 tff(800,plain,
% 1.79/1.45 ((~hskp26) | c1_1(a559)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[799, 794])).
% 1.79/1.45 tff(801,plain,
% 1.79/1.45 ((~hskp26) | c1_1(a559)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[800, 794])).
% 1.79/1.45 tff(802,plain,
% 1.79/1.45 ((~hskp26) | c1_1(a559)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[801, 794])).
% 1.79/1.45 tff(803,plain,
% 1.79/1.45 ((~hskp26) | c1_1(a559)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[802, 794])).
% 1.79/1.45 tff(804,plain,
% 1.79/1.45 (c1_1(a559)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[803, 774])).
% 1.79/1.45 tff(805,plain,
% 1.79/1.45 (~c0_1(a467)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[591, 21, 552, 553, 29, 269, 110, 268])).
% 1.79/1.45 tff(806,plain,
% 1.79/1.45 (~hskp5),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[602, 805])).
% 1.79/1.45 tff(807,plain,
% 1.79/1.45 (~c1_1(a464)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[722, 806, 710, 709])).
% 1.79/1.45 tff(808,plain,
% 1.79/1.45 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))),
% 1.79/1.45 inference(bind,[status(th)],[])).
% 1.79/1.45 tff(809,plain,
% 1.79/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.79/1.45 inference(quant_intro,[status(thm)],[808])).
% 1.79/1.45 tff(810,plain,
% 1.79/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(811,plain,
% 1.79/1.45 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))))),
% 1.79/1.45 inference(bind,[status(th)],[])).
% 1.79/1.45 tff(812,plain,
% 1.79/1.45 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.79/1.45 inference(quant_intro,[status(thm)],[811])).
% 1.79/1.45 tff(813,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause205')).
% 1.79/1.45 tff(814,plain,
% 1.79/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[813, 812])).
% 1.79/1.45 tff(815,plain,
% 1.79/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[814, 810])).
% 1.79/1.45 tff(816,plain,(
% 1.79/1.45 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.79/1.45 inference(skolemize,[status(sab)],[815])).
% 1.79/1.45 tff(817,plain,
% 1.79/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[816, 809])).
% 1.79/1.45 tff(818,assumption,(~c0_1(a493)), introduced(assumption)).
% 1.79/1.45 tff(819,assumption,(~c3_1(a559)), introduced(assumption)).
% 1.79/1.45 tff(820,plain,
% 1.79/1.45 (~c3_1(a464)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[628, 806, 21, 238])).
% 1.79/1.45 tff(821,assumption,(c3_1(a493)), introduced(assumption)).
% 1.79/1.45 tff(822,assumption,(c2_1(a493)), introduced(assumption)).
% 1.79/1.45 tff(823,assumption,(c1_1(a559)), introduced(assumption)).
% 1.79/1.45 tff(824,assumption,(c0_1(a559)), introduced(assumption)).
% 1.79/1.45 tff(825,plain,
% 1.79/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a464) | c3_1(a559) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a559)) | (~c0_1(a559)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c3_1(a559) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a559)) | (~c0_1(a559)))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(826,plain,
% 1.79/1.45 (((~ndr1_0) | c3_1(a559) | (~c1_1(a559)) | (~c0_1(a559)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464)) <=> (c3_1(a464) | c3_1(a559) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a559)) | (~c0_1(a559)))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(827,plain,
% 1.79/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a559) | (~c1_1(a559)) | (~c0_1(a559)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a464) | c3_1(a559) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a559)) | (~c0_1(a559))))),
% 1.79/1.45 inference(monotonicity,[status(thm)],[826])).
% 1.79/1.45 tff(828,plain,
% 1.79/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a559) | (~c1_1(a559)) | (~c0_1(a559)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c3_1(a559) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a559)) | (~c0_1(a559)))),
% 1.79/1.45 inference(transitivity,[status(thm)],[827, 825])).
% 1.79/1.45 tff(829,plain,
% 1.79/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a559) | (~c1_1(a559)) | (~c0_1(a559)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))),
% 1.79/1.45 inference(quant_inst,[status(thm)],[])).
% 1.79/1.45 tff(830,plain,
% 1.79/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c3_1(a559) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a559)) | (~c0_1(a559))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[829, 828])).
% 1.79/1.45 tff(831,plain,
% 1.79/1.45 ($false),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[830, 81, 824, 823, 822, 821, 820, 819, 818, 237, 817, 807])).
% 1.79/1.45 tff(832,plain,(hskp12 | (~c0_1(a559)) | (~c1_1(a559)) | (~c2_1(a493)) | (~c3_1(a493)) | c3_1(a559) | c0_1(a493) | c2_1(a464) | c0_1(a464) | c1_1(a466) | c0_1(a466) | c3_1(a466) | (~c0_1(a471)) | (~c3_1(a471)) | c2_1(a471) | c1_1(a467) | hskp16 | c3_1(a467)), inference(lemma,lemma(discharge,[]))).
% 1.79/1.45 tff(833,plain,
% 1.79/1.45 ($false),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[832, 804, 793, 21, 782, 781, 780, 773, 237, 238, 710, 709, 708, 552, 553, 29, 269, 110, 268])).
% 1.79/1.45 tff(834,plain,((~hskp26) | hskp12 | c2_1(a464) | c0_1(a464) | c1_1(a466) | c0_1(a466) | c3_1(a466) | (~c0_1(a471)) | (~c3_1(a471)) | c2_1(a471) | c1_1(a467) | hskp16 | c3_1(a467)), inference(lemma,lemma(discharge,[]))).
% 1.79/1.45 tff(835,plain,
% 1.79/1.45 (~hskp26),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[834, 712, 237, 238, 710, 709, 708, 21, 713, 29, 269, 110, 268])).
% 1.79/1.45 tff(836,plain,
% 1.79/1.45 ((hskp26 | hskp16 | hskp13) <=> (hskp26 | hskp16 | hskp13)),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(837,plain,
% 1.79/1.45 (((hskp26 | hskp16) | hskp13) <=> (hskp26 | hskp16 | hskp13)),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(838,plain,
% 1.79/1.45 ((hskp26 | hskp16) <=> (hskp26 | hskp16)),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(839,plain,
% 1.79/1.45 (((hskp26 | hskp16) | hskp13) <=> ((hskp26 | hskp16) | hskp13)),
% 1.79/1.45 inference(monotonicity,[status(thm)],[838])).
% 1.79/1.45 tff(840,plain,
% 1.79/1.45 (((hskp26 | hskp16) | hskp13) <=> (hskp26 | hskp16 | hskp13)),
% 1.79/1.45 inference(transitivity,[status(thm)],[839, 837])).
% 1.79/1.45 tff(841,axiom,((hskp26 | hskp16) | hskp13), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 1.79/1.45 tff(842,plain,
% 1.79/1.45 (hskp26 | hskp16 | hskp13),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[841, 840])).
% 1.79/1.45 tff(843,plain,
% 1.79/1.45 (hskp26 | hskp16 | hskp13),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[842, 836])).
% 1.79/1.45 tff(844,plain,
% 1.79/1.45 (hskp26 | hskp16 | hskp13),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[843, 836])).
% 1.79/1.45 tff(845,plain,
% 1.79/1.45 (hskp26 | hskp16 | hskp13),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[844, 836])).
% 1.79/1.45 tff(846,plain,
% 1.79/1.45 (hskp26 | hskp16 | hskp13),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[845, 836])).
% 1.79/1.45 tff(847,plain,
% 1.79/1.45 (hskp26 | hskp16 | hskp13),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[846, 836])).
% 1.79/1.45 tff(848,plain,
% 1.79/1.45 (hskp26 | hskp16 | hskp13),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[847, 836])).
% 1.79/1.45 tff(849,plain,
% 1.79/1.45 (hskp26 | hskp16 | hskp13),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[848, 836])).
% 1.79/1.45 tff(850,plain,
% 1.79/1.45 (hskp13),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[849, 835, 110])).
% 1.79/1.45 tff(851,plain,
% 1.79/1.45 (((~hskp13) | (~c2_1(a482))) <=> ((~hskp13) | (~c2_1(a482)))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(852,plain,
% 1.79/1.45 (((~c2_1(a482)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a482)))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(853,axiom,((~c2_1(a482)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 1.79/1.45 tff(854,plain,
% 1.79/1.45 ((~hskp13) | (~c2_1(a482))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[853, 852])).
% 1.79/1.45 tff(855,plain,
% 1.79/1.45 ((~hskp13) | (~c2_1(a482))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[854, 851])).
% 1.79/1.45 tff(856,plain,
% 1.79/1.45 (~c2_1(a482)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[855, 850])).
% 1.79/1.45 tff(857,assumption,(~c0_1(a482)), introduced(assumption)).
% 1.79/1.45 tff(858,assumption,(~c2_1(a482)), introduced(assumption)).
% 1.79/1.45 tff(859,plain,
% 1.79/1.45 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c2_1(a482) | (~ndr1_0) | c0_1(a482) | (~c3_1(a482)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c2_1(a482) | (~ndr1_0) | c0_1(a482) | (~c3_1(a482)))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(860,plain,
% 1.79/1.45 ((hskp12 | hskp5 | (~ndr1_0) | c2_1(a482) | c0_1(a482) | (~c3_1(a482))) <=> (hskp12 | hskp5 | c2_1(a482) | (~ndr1_0) | c0_1(a482) | (~c3_1(a482)))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(861,plain,
% 1.79/1.45 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a482) | c0_1(a482) | (~c3_1(a482)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c2_1(a482) | (~ndr1_0) | c0_1(a482) | (~c3_1(a482))))),
% 1.79/1.45 inference(monotonicity,[status(thm)],[860])).
% 1.79/1.45 tff(862,plain,
% 1.79/1.45 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a482) | c0_1(a482) | (~c3_1(a482)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c2_1(a482) | (~ndr1_0) | c0_1(a482) | (~c3_1(a482)))),
% 1.79/1.45 inference(transitivity,[status(thm)],[861, 859])).
% 1.79/1.45 tff(863,plain,
% 1.79/1.45 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a482) | c0_1(a482) | (~c3_1(a482)))),
% 1.79/1.45 inference(quant_inst,[status(thm)],[])).
% 1.79/1.45 tff(864,plain,
% 1.79/1.45 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c2_1(a482) | (~ndr1_0) | c0_1(a482) | (~c3_1(a482))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[863, 862])).
% 1.79/1.45 tff(865,plain,
% 1.79/1.45 (hskp12 | hskp5 | c0_1(a482) | (~c3_1(a482))),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[864, 81, 858, 41])).
% 1.79/1.45 tff(866,plain,
% 1.79/1.45 (~c3_1(a482)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[865, 806, 857, 21])).
% 1.79/1.45 tff(867,plain,
% 1.79/1.45 (((~hskp13) | c3_1(a482)) <=> ((~hskp13) | c3_1(a482))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(868,axiom,((~hskp13) | c3_1(a482)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 1.79/1.45 tff(869,plain,
% 1.79/1.45 ((~hskp13) | c3_1(a482)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[868, 867])).
% 1.79/1.45 tff(870,plain,
% 1.79/1.45 ((~hskp13) | c3_1(a482)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[869, 867])).
% 1.79/1.45 tff(871,plain,
% 1.79/1.45 ((~hskp13) | c3_1(a482)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[870, 867])).
% 1.79/1.45 tff(872,plain,
% 1.79/1.45 ((~hskp13) | c3_1(a482)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[871, 867])).
% 1.79/1.45 tff(873,plain,
% 1.79/1.45 ((~hskp13) | c3_1(a482)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[872, 867])).
% 1.79/1.45 tff(874,plain,
% 1.79/1.45 ((~hskp13) | c3_1(a482)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[873, 867])).
% 1.79/1.45 tff(875,plain,
% 1.79/1.45 ((~hskp13) | c3_1(a482)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[874, 867])).
% 1.79/1.45 tff(876,plain,
% 1.79/1.45 ((~hskp13) | c3_1(a482)),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[875, 867])).
% 1.79/1.45 tff(877,plain,
% 1.79/1.45 (~hskp13),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[876, 866])).
% 1.79/1.45 tff(878,plain,
% 1.79/1.45 (hskp26),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[849, 877, 110])).
% 1.79/1.45 tff(879,plain,
% 1.79/1.45 (~c3_1(a559)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[779, 878])).
% 1.79/1.45 tff(880,plain,
% 1.79/1.45 (c1_1(a559)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[803, 878])).
% 1.79/1.45 tff(881,plain,
% 1.79/1.45 (c0_1(a559)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[792, 878])).
% 1.79/1.45 tff(882,plain,
% 1.79/1.45 ($false),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[830, 81, 881, 880, 822, 821, 820, 879, 818, 237, 817, 807])).
% 1.79/1.45 tff(883,plain,(hskp12 | (~c2_1(a493)) | (~c3_1(a493)) | c0_1(a493) | c2_1(a464) | hskp16 | c0_1(a482) | c2_1(a482) | c0_1(a464) | c1_1(a466) | c0_1(a466) | c3_1(a466) | (~c0_1(a471)) | (~c3_1(a471)) | c2_1(a471) | c1_1(a467) | c3_1(a467)), inference(lemma,lemma(discharge,[]))).
% 1.79/1.45 tff(884,plain,
% 1.79/1.45 (c0_1(a482)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[883, 856, 21, 713, 237, 110, 769, 758, 238, 710, 709, 708, 712, 752, 29, 269, 268])).
% 1.79/1.45 tff(885,plain,
% 1.79/1.45 (((~hskp13) | (~c1_1(a482))) <=> ((~hskp13) | (~c1_1(a482)))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(886,plain,
% 1.79/1.45 (((~c1_1(a482)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a482)))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(887,axiom,((~c1_1(a482)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 1.79/1.45 tff(888,plain,
% 1.79/1.45 ((~hskp13) | (~c1_1(a482))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[887, 886])).
% 1.79/1.45 tff(889,plain,
% 1.79/1.45 ((~hskp13) | (~c1_1(a482))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[888, 885])).
% 1.79/1.45 tff(890,plain,
% 1.79/1.45 (~c1_1(a482)),
% 1.79/1.45 inference(unit_resolution,[status(thm)],[889, 850])).
% 1.79/1.45 tff(891,plain,
% 1.79/1.45 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c1_1(a482) | c2_1(a482) | (~ndr1_0) | (~c0_1(a482)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a482) | c2_1(a482) | (~ndr1_0) | (~c0_1(a482)))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(892,plain,
% 1.79/1.45 ((hskp19 | hskp18 | (~ndr1_0) | c2_1(a482) | c1_1(a482) | (~c0_1(a482))) <=> (hskp19 | hskp18 | c1_1(a482) | c2_1(a482) | (~ndr1_0) | (~c0_1(a482)))),
% 1.79/1.45 inference(rewrite,[status(thm)],[])).
% 1.79/1.45 tff(893,plain,
% 1.79/1.45 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a482) | c1_1(a482) | (~c0_1(a482)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c1_1(a482) | c2_1(a482) | (~ndr1_0) | (~c0_1(a482))))),
% 1.79/1.45 inference(monotonicity,[status(thm)],[892])).
% 1.79/1.45 tff(894,plain,
% 1.79/1.45 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a482) | c1_1(a482) | (~c0_1(a482)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a482) | c2_1(a482) | (~ndr1_0) | (~c0_1(a482)))),
% 1.79/1.45 inference(transitivity,[status(thm)],[893, 891])).
% 1.79/1.45 tff(895,plain,
% 1.79/1.45 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a482) | c1_1(a482) | (~c0_1(a482)))),
% 1.79/1.45 inference(quant_inst,[status(thm)],[])).
% 1.79/1.45 tff(896,plain,
% 1.79/1.45 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c1_1(a482) | c2_1(a482) | (~ndr1_0) | (~c0_1(a482))),
% 1.79/1.45 inference(modus_ponens,[status(thm)],[895, 894])).
% 1.79/1.46 tff(897,plain,
% 1.79/1.46 (hskp18),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[896, 81, 235, 890, 856, 279, 884])).
% 1.79/1.46 tff(898,plain,
% 1.79/1.46 (~c2_1(a494)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[314, 897])).
% 1.79/1.46 tff(899,plain,
% 1.79/1.46 (~c3_1(a494)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[308, 897])).
% 1.79/1.46 tff(900,assumption,(~c0_1(a494)), introduced(assumption)).
% 1.79/1.46 tff(901,plain,
% 1.79/1.46 (~hskp18),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[325, 900])).
% 1.79/1.46 tff(902,plain,
% 1.79/1.46 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)))),
% 1.79/1.46 inference(rewrite,[status(thm)],[])).
% 1.79/1.46 tff(903,plain,
% 1.79/1.46 ((hskp19 | hskp18 | (~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471))) <=> (hskp19 | hskp18 | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)))),
% 1.79/1.46 inference(rewrite,[status(thm)],[])).
% 1.79/1.46 tff(904,plain,
% 1.79/1.46 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471))))),
% 1.79/1.46 inference(monotonicity,[status(thm)],[903])).
% 1.79/1.46 tff(905,plain,
% 1.79/1.46 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)))),
% 1.79/1.46 inference(transitivity,[status(thm)],[904, 902])).
% 1.79/1.46 tff(906,plain,
% 1.79/1.46 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)))),
% 1.79/1.46 inference(quant_inst,[status(thm)],[])).
% 1.79/1.46 tff(907,plain,
% 1.79/1.46 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471))),
% 1.79/1.46 inference(modus_ponens,[status(thm)],[906, 905])).
% 1.79/1.46 tff(908,plain,
% 1.79/1.46 (hskp18 | c1_1(a471) | (~c0_1(a471))),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[907, 81, 235, 29, 279])).
% 1.79/1.46 tff(909,plain,
% 1.79/1.46 (c1_1(a471)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[908, 901, 552])).
% 1.79/1.46 tff(910,plain,
% 1.79/1.46 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 1.79/1.46 inference(bind,[status(th)],[])).
% 1.79/1.46 tff(911,plain,
% 1.79/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.79/1.46 inference(quant_intro,[status(thm)],[910])).
% 1.79/1.46 tff(912,plain,
% 1.79/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.79/1.46 inference(rewrite,[status(thm)],[])).
% 1.79/1.46 tff(913,plain,
% 1.79/1.46 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_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))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 1.79/1.46 inference(bind,[status(th)],[])).
% 1.79/1.46 tff(914,plain,
% 1.79/1.46 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.79/1.46 inference(quant_intro,[status(thm)],[913])).
% 1.79/1.46 tff(915,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause207')).
% 1.79/1.46 tff(916,plain,
% 1.79/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.79/1.46 inference(modus_ponens,[status(thm)],[915, 914])).
% 1.79/1.46 tff(917,plain,
% 1.79/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.79/1.46 inference(modus_ponens,[status(thm)],[916, 912])).
% 1.79/1.46 tff(918,plain,(
% 1.79/1.46 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.79/1.46 inference(skolemize,[status(sab)],[917])).
% 1.79/1.46 tff(919,plain,
% 1.79/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.79/1.46 inference(modus_ponens,[status(thm)],[918, 911])).
% 1.79/1.46 tff(920,plain,
% 1.79/1.46 (hskp17),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[740, 31, 552, 553])).
% 1.79/1.46 tff(921,plain,
% 1.79/1.46 (~c0_1(a493)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[757, 920])).
% 1.79/1.46 tff(922,plain,
% 1.79/1.46 (c3_1(a493)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[768, 920])).
% 1.79/1.46 tff(923,plain,
% 1.79/1.46 (c2_1(a493)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[751, 920])).
% 1.79/1.46 tff(924,plain,
% 1.79/1.46 (~c3_1(a464)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[628, 31, 21, 238])).
% 1.79/1.46 tff(925,plain,
% 1.79/1.46 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a494) | c3_1(a464) | c2_1(a494) | c0_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a494) | c3_1(a464) | c2_1(a494) | c0_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a494)))),
% 1.79/1.46 inference(rewrite,[status(thm)],[])).
% 1.79/1.46 tff(926,plain,
% 1.79/1.46 ((hskp5 | (~ndr1_0) | c2_1(a494) | c0_1(a494) | (~c1_1(a494)) | c3_1(a464) | c1_1(a464) | c0_1(a464)) <=> (hskp5 | c0_1(a494) | c3_1(a464) | c2_1(a494) | c0_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a494)))),
% 1.79/1.46 inference(rewrite,[status(thm)],[])).
% 1.79/1.46 tff(927,plain,
% 1.79/1.46 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c2_1(a494) | c0_1(a494) | (~c1_1(a494)) | c3_1(a464) | c1_1(a464) | c0_1(a464))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a494) | c3_1(a464) | c2_1(a494) | c0_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a494))))),
% 1.79/1.46 inference(monotonicity,[status(thm)],[926])).
% 1.79/1.46 tff(928,plain,
% 1.79/1.46 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c2_1(a494) | c0_1(a494) | (~c1_1(a494)) | c3_1(a464) | c1_1(a464) | c0_1(a464))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a494) | c3_1(a464) | c2_1(a494) | c0_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a494)))),
% 1.79/1.46 inference(transitivity,[status(thm)],[927, 925])).
% 1.79/1.46 tff(929,plain,
% 1.79/1.46 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c2_1(a494) | c0_1(a494) | (~c1_1(a494)) | c3_1(a464) | c1_1(a464) | c0_1(a464))),
% 1.79/1.46 inference(quant_inst,[status(thm)],[])).
% 1.79/1.46 tff(930,plain,
% 1.79/1.46 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a494) | c3_1(a464) | c2_1(a494) | c0_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a494))),
% 1.79/1.46 inference(modus_ponens,[status(thm)],[929, 928])).
% 1.79/1.46 tff(931,plain,
% 1.79/1.46 (c0_1(a494) | (~c1_1(a494))),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[930, 81, 31, 924, 328, 238, 613, 638])).
% 1.79/1.46 tff(932,plain,
% 1.79/1.46 (~c1_1(a494)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[931, 900])).
% 1.79/1.46 tff(933,assumption,(~c1_1(a494)), introduced(assumption)).
% 1.79/1.46 tff(934,plain,
% 1.79/1.46 (c2_1(a465)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[636, 21, 373, 31])).
% 1.79/1.46 tff(935,plain,
% 1.79/1.46 (~c3_1(a464)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[628, 21, 31, 238])).
% 1.79/1.46 tff(936,plain,
% 1.79/1.46 (~hskp2),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[659, 935])).
% 1.79/1.46 tff(937,plain,
% 1.79/1.46 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c2_1(a494) | c3_1(a494) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a494))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c2_1(a494) | c3_1(a494) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a494))),
% 1.79/1.46 inference(rewrite,[status(thm)],[])).
% 1.79/1.46 tff(938,plain,
% 1.79/1.46 ((hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a494) | c1_1(a494) | c2_1(a494)) <=> (hskp2 | c2_1(a494) | c3_1(a494) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a494))),
% 1.79/1.46 inference(rewrite,[status(thm)],[])).
% 1.79/1.46 tff(939,plain,
% 1.79/1.46 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a494) | c1_1(a494) | c2_1(a494))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c2_1(a494) | c3_1(a494) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a494)))),
% 1.79/1.46 inference(monotonicity,[status(thm)],[938])).
% 1.79/1.46 tff(940,plain,
% 1.79/1.46 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a494) | c1_1(a494) | c2_1(a494))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c2_1(a494) | c3_1(a494) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a494))),
% 1.79/1.46 inference(transitivity,[status(thm)],[939, 937])).
% 1.79/1.46 tff(941,plain,
% 1.79/1.46 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a494) | c1_1(a494) | c2_1(a494))),
% 1.79/1.46 inference(quant_inst,[status(thm)],[])).
% 1.79/1.46 tff(942,plain,
% 1.79/1.46 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c2_1(a494) | c3_1(a494) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a494)),
% 1.79/1.46 inference(modus_ponens,[status(thm)],[941, 940])).
% 1.79/1.46 tff(943,plain,
% 1.79/1.46 (hskp2 | c2_1(a494) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a494)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[942, 81, 327, 263, 648])).
% 1.79/1.46 tff(944,plain,
% 1.79/1.46 ($false),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[943, 936, 934, 328, 373, 933])).
% 1.79/1.46 tff(945,plain,(hskp12 | c2_1(a494) | (~c3_1(a465)) | c1_1(a494) | c3_1(a494) | c1_1(a465) | hskp5 | c0_1(a465) | c0_1(a464) | c2_1(a464)), inference(lemma,lemma(discharge,[]))).
% 1.79/1.46 tff(946,plain,
% 1.79/1.46 (~c3_1(a465)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[945, 932, 21, 31, 327, 263, 328, 264, 238, 237])).
% 1.79/1.46 tff(947,plain,
% 1.79/1.46 (~hskp3),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[442, 946])).
% 1.79/1.46 tff(948,plain,
% 1.79/1.46 (hskp29),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[457, 947, 21])).
% 1.79/1.46 tff(949,plain,
% 1.79/1.46 (c2_1(a474)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[340, 948])).
% 1.79/1.46 tff(950,plain,
% 1.79/1.46 (c1_1(a474)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[351, 948])).
% 1.79/1.46 tff(951,plain,
% 1.79/1.46 (c0_1(a474)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[362, 948])).
% 1.79/1.46 tff(952,plain,
% 1.79/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a493) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a493) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.79/1.46 inference(rewrite,[status(thm)],[])).
% 1.79/1.46 tff(953,plain,
% 1.79/1.46 (((~ndr1_0) | (~c1_1(a471)) | (~c3_1(a471)) | (~c0_1(a471)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493))) <=> (c0_1(a493) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.79/1.46 inference(rewrite,[status(thm)],[])).
% 1.79/1.46 tff(954,plain,
% 1.79/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a471)) | (~c3_1(a471)) | (~c0_1(a471)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a493) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.79/1.46 inference(monotonicity,[status(thm)],[953])).
% 1.79/1.46 tff(955,plain,
% 1.79/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a471)) | (~c3_1(a471)) | (~c0_1(a471)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a493) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.79/1.46 inference(transitivity,[status(thm)],[954, 952])).
% 1.79/1.46 tff(956,plain,
% 1.79/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a471)) | (~c3_1(a471)) | (~c0_1(a471)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)))),
% 1.79/1.46 inference(quant_inst,[status(thm)],[])).
% 1.79/1.46 tff(957,plain,
% 1.79/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a493) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.79/1.46 inference(modus_ponens,[status(thm)],[956, 955])).
% 1.79/1.46 tff(958,plain,
% 1.79/1.46 ($false),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[957, 81, 951, 950, 949, 923, 922, 552, 553, 921, 919, 909])).
% 1.79/1.46 tff(959,plain,(c0_1(a494) | (~c0_1(a471)) | (~c3_1(a471)) | hskp12 | hskp5 | c3_1(a494) | c1_1(a465) | c2_1(a494) | c0_1(a465) | c0_1(a464) | c2_1(a464) | hskp19 | c2_1(a471) | c1_1(a464)), inference(lemma,lemma(discharge,[]))).
% 1.79/1.46 tff(960,plain,
% 1.79/1.46 (c0_1(a494)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[959, 328, 553, 21, 31, 327, 263, 552, 264, 238, 237, 235, 29, 638])).
% 1.79/1.46 tff(961,plain,
% 1.79/1.46 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | c2_1(a494) | c3_1(a494) | (~ndr1_0) | c1_1(a494) | (~c0_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c2_1(a494) | c3_1(a494) | (~ndr1_0) | c1_1(a494) | (~c0_1(a494)))),
% 1.79/1.46 inference(rewrite,[status(thm)],[])).
% 1.79/1.46 tff(962,plain,
% 1.79/1.46 ((hskp16 | (~ndr1_0) | c1_1(a494) | c3_1(a494) | (~c0_1(a494)) | c3_1(a494) | c1_1(a494) | c2_1(a494)) <=> (hskp16 | c2_1(a494) | c3_1(a494) | (~ndr1_0) | c1_1(a494) | (~c0_1(a494)))),
% 1.79/1.46 inference(rewrite,[status(thm)],[])).
% 1.79/1.46 tff(963,plain,
% 1.79/1.46 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a494) | c3_1(a494) | (~c0_1(a494)) | c3_1(a494) | c1_1(a494) | c2_1(a494))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | c2_1(a494) | c3_1(a494) | (~ndr1_0) | c1_1(a494) | (~c0_1(a494))))),
% 1.79/1.46 inference(monotonicity,[status(thm)],[962])).
% 1.79/1.46 tff(964,plain,
% 1.79/1.46 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a494) | c3_1(a494) | (~c0_1(a494)) | c3_1(a494) | c1_1(a494) | c2_1(a494))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c2_1(a494) | c3_1(a494) | (~ndr1_0) | c1_1(a494) | (~c0_1(a494)))),
% 1.79/1.46 inference(transitivity,[status(thm)],[963, 961])).
% 1.79/1.46 tff(965,plain,
% 1.79/1.46 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a494) | c3_1(a494) | (~c0_1(a494)) | c3_1(a494) | c1_1(a494) | c2_1(a494))),
% 1.79/1.46 inference(quant_inst,[status(thm)],[])).
% 1.79/1.46 tff(966,plain,
% 1.79/1.46 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c2_1(a494) | c3_1(a494) | (~ndr1_0) | c1_1(a494) | (~c0_1(a494))),
% 1.79/1.46 inference(modus_ponens,[status(thm)],[965, 964])).
% 1.79/1.46 tff(967,plain,
% 1.79/1.46 ($false),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[966, 81, 110, 329, 328, 327, 564, 933])).
% 1.79/1.46 tff(968,plain,(c1_1(a494) | hskp16 | (~c0_1(a494)) | c2_1(a494) | c3_1(a494)), inference(lemma,lemma(discharge,[]))).
% 1.79/1.46 tff(969,plain,
% 1.79/1.46 (c1_1(a494)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[968, 960, 327, 328, 110])).
% 1.79/1.46 tff(970,plain,
% 1.79/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a464) | c3_1(a494) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a494)) | (~c0_1(a494)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c3_1(a494) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a494)) | (~c0_1(a494)))),
% 1.79/1.46 inference(rewrite,[status(thm)],[])).
% 1.79/1.46 tff(971,plain,
% 1.79/1.46 (((~ndr1_0) | c3_1(a494) | (~c1_1(a494)) | (~c0_1(a494)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464)) <=> (c3_1(a464) | c3_1(a494) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a494)) | (~c0_1(a494)))),
% 1.79/1.46 inference(rewrite,[status(thm)],[])).
% 1.79/1.46 tff(972,plain,
% 1.79/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a494) | (~c1_1(a494)) | (~c0_1(a494)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a464) | c3_1(a494) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a494)) | (~c0_1(a494))))),
% 1.79/1.46 inference(monotonicity,[status(thm)],[971])).
% 1.79/1.46 tff(973,plain,
% 1.79/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a494) | (~c1_1(a494)) | (~c0_1(a494)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c3_1(a494) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a494)) | (~c0_1(a494)))),
% 1.79/1.46 inference(transitivity,[status(thm)],[972, 970])).
% 1.79/1.46 tff(974,plain,
% 1.79/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a494) | (~c1_1(a494)) | (~c0_1(a494)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))),
% 1.79/1.46 inference(quant_inst,[status(thm)],[])).
% 1.79/1.46 tff(975,plain,
% 1.79/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c3_1(a494) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | (~c1_1(a494)) | (~c0_1(a494))),
% 1.79/1.46 inference(modus_ponens,[status(thm)],[974, 973])).
% 1.79/1.46 tff(976,plain,
% 1.79/1.46 ((~c1_1(a494)) | (~c0_1(a494))),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[975, 81, 923, 922, 924, 327, 921, 237, 817, 638])).
% 1.79/1.46 tff(977,plain,
% 1.79/1.46 ($false),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[976, 969, 960])).
% 1.79/1.46 tff(978,plain,(c2_1(a494) | c3_1(a494) | c2_1(a464) | c1_1(a464) | hskp16 | (~c3_1(a471)) | hskp12 | hskp5 | c1_1(a465) | (~c0_1(a471)) | c0_1(a465) | c0_1(a464) | hskp19 | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.79/1.46 tff(979,plain,
% 1.79/1.46 ($false),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[978, 899, 898, 237, 723, 110, 713, 21, 715, 263, 712, 264, 238, 235, 29])).
% 1.79/1.46 tff(980,plain,(hskp16 | c2_1(a464) | hskp12 | c1_1(a465) | c0_1(a465) | c0_1(a464) | hskp19 | c2_1(a471) | c1_1(a466) | c0_1(a466) | c3_1(a466) | c1_1(a467) | c3_1(a467) | (~c2_1(a478)) | c0_1(a478) | c3_1(a478)), inference(lemma,lemma(discharge,[]))).
% 1.79/1.46 tff(981,plain,
% 1.79/1.46 (hskp16),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[980, 21, 237, 263, 264, 238, 235, 29, 710, 709, 708, 269, 268, 267, 266, 265])).
% 1.79/1.46 tff(982,plain,
% 1.79/1.46 (~c2_1(a487)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[284, 981])).
% 1.79/1.46 tff(983,plain,
% 1.79/1.46 (~c1_1(a487)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[27, 981])).
% 1.79/1.46 tff(984,plain,
% 1.79/1.46 (c0_1(a487)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[295, 981])).
% 1.79/1.46 tff(985,plain,
% 1.79/1.46 (hskp18),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[302, 81, 235, 984, 983, 982, 279])).
% 1.79/1.46 tff(986,plain,
% 1.79/1.46 (~c3_1(a494)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[308, 985])).
% 1.79/1.46 tff(987,plain,
% 1.79/1.46 (~c2_1(a494)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[314, 985])).
% 1.79/1.46 tff(988,plain,
% 1.79/1.46 (c0_1(a494)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[325, 985])).
% 1.79/1.46 tff(989,plain,
% 1.79/1.46 (~hskp29),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[371, 988, 987, 986])).
% 1.79/1.46 tff(990,plain,
% 1.79/1.46 (hskp3),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[457, 989, 21])).
% 1.79/1.46 tff(991,plain,
% 1.79/1.46 (c3_1(a465)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[442, 990])).
% 1.79/1.46 tff(992,plain,
% 1.79/1.46 (hskp29 | (~c3_1(a465)) | c2_1(a465)),
% 1.79/1.46 inference(unit_resolution,[status(thm)],[393, 81, 984, 983, 982, 264, 384])).
% 1.89/1.46 tff(993,plain,
% 1.89/1.46 (c2_1(a465)),
% 1.89/1.46 inference(unit_resolution,[status(thm)],[992, 991, 989])).
% 1.89/1.46 tff(994,plain,
% 1.89/1.46 (~c1_1(a478)),
% 1.89/1.46 inference(unit_resolution,[status(thm)],[411, 81, 984, 267, 983, 982, 266, 405])).
% 1.89/1.46 tff(995,plain,
% 1.89/1.46 ($false),
% 1.89/1.46 inference(unit_resolution,[status(thm)],[428, 81, 988, 267, 991, 987, 986, 266, 263, 422, 994, 993])).
% 1.89/1.46 tff(996,plain,(hskp12 | (~c2_1(a478)) | c0_1(a478) | c1_1(a465) | c0_1(a465) | hskp19 | c2_1(a464) | c0_1(a464) | c2_1(a471) | c1_1(a466) | c0_1(a466) | c3_1(a466) | c1_1(a467) | c3_1(a467) | c3_1(a478)), inference(lemma,lemma(discharge,[]))).
% 1.89/1.46 tff(997,plain,
% 1.89/1.46 ($false),
% 1.89/1.46 inference(unit_resolution,[status(thm)],[996, 707, 701, 266, 263, 264, 235, 237, 238, 267, 529, 21, 695, 269, 268, 265])).
% 1.89/1.46 tff(998,plain,(hskp12 | c0_1(a478) | c1_1(a465) | c0_1(a465) | hskp19 | c2_1(a464) | c0_1(a464) | (~c2_1(a478)) | c1_1(a467) | c3_1(a467) | c3_1(a478)), inference(lemma,lemma(discharge,[]))).
% 1.89/1.46 tff(999,plain,
% 1.89/1.46 (hskp12),
% 1.89/1.46 inference(unit_resolution,[status(thm)],[998, 269, 263, 264, 235, 237, 238, 267, 266, 268, 265])).
% 1.89/1.46 tff(1000,plain,
% 1.89/1.46 (~c3_1(a481)),
% 1.89/1.46 inference(unit_resolution,[status(thm)],[463, 999])).
% 1.89/1.46 tff(1001,plain,
% 1.89/1.46 (~c0_1(a481)),
% 1.89/1.46 inference(unit_resolution,[status(thm)],[469, 999])).
% 1.89/1.46 tff(1002,plain,
% 1.89/1.46 (c1_1(a481)),
% 1.89/1.46 inference(unit_resolution,[status(thm)],[480, 999])).
% 1.89/1.46 tff(1003,plain,
% 1.89/1.46 (c2_1(a481)),
% 1.89/1.46 inference(unit_resolution,[status(thm)],[487, 81, 1002, 1001, 1000, 10])).
% 1.89/1.46 tff(1004,plain,
% 1.89/1.46 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c0_1(a481) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a481) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.89/1.46 inference(rewrite,[status(thm)],[])).
% 1.89/1.46 tff(1005,plain,
% 1.89/1.46 (((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481))) <=> (c0_1(a481) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.89/1.46 inference(rewrite,[status(thm)],[])).
% 1.89/1.46 tff(1006,plain,
% 1.89/1.46 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c0_1(a481) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481))))),
% 1.89/1.46 inference(monotonicity,[status(thm)],[1005])).
% 1.89/1.46 tff(1007,plain,
% 1.89/1.46 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a481) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.89/1.46 inference(transitivity,[status(thm)],[1006, 1004])).
% 1.89/1.46 tff(1008,plain,
% 1.89/1.46 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.89/1.46 inference(quant_inst,[status(thm)],[])).
% 1.89/1.46 tff(1009,plain,
% 1.89/1.46 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a481) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481))),
% 1.89/1.46 inference(modus_ponens,[status(thm)],[1008, 1007])).
% 1.89/1.46 tff(1010,plain,
% 1.89/1.46 (c1_1(a471)),
% 1.89/1.46 inference(unit_resolution,[status(thm)],[1009, 81, 1002, 551, 1001, 529, 405, 1003])).
% 1.89/1.46 tff(1011,assumption,(~hskp17), introduced(assumption)).
% 1.89/1.46 tff(1012,plain,
% 1.89/1.46 (hskp5),
% 1.89/1.46 inference(unit_resolution,[status(thm)],[740, 712, 1011, 713])).
% 1.89/1.46 tff(1013,plain,
% 1.89/1.46 (c0_1(a467)),
% 1.89/1.46 inference(unit_resolution,[status(thm)],[602, 1012])).
% 1.89/1.47 tff(1014,plain,
% 1.89/1.47 (hskp12),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[591, 1013, 712, 713, 29, 269, 110, 268])).
% 1.89/1.47 tff(1015,plain,
% 1.89/1.47 (c1_1(a481)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[480, 1014])).
% 1.89/1.47 tff(1016,assumption,(~c3_1(a481)), introduced(assumption)).
% 1.89/1.47 tff(1017,assumption,(~c0_1(a481)), introduced(assumption)).
% 1.89/1.47 tff(1018,plain,
% 1.89/1.47 ((~c1_1(a481)) | c2_1(a481)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[487, 81, 1017, 1016, 10])).
% 1.89/1.47 tff(1019,plain,
% 1.89/1.47 (c2_1(a481)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1018, 1015])).
% 1.89/1.47 tff(1020,plain,
% 1.89/1.47 (c2_1(a467)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[571, 1013, 110])).
% 1.89/1.47 tff(1021,plain,
% 1.89/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a481) | c3_1(a481) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a481) | c3_1(a481) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1022,plain,
% 1.89/1.47 (((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a467) | c1_1(a467) | (~c2_1(a467)) | c3_1(a481) | c0_1(a481) | (~c1_1(a481))) <=> (c0_1(a481) | c3_1(a481) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1023,plain,
% 1.89/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a467) | c1_1(a467) | (~c2_1(a467)) | c3_1(a481) | c0_1(a481) | (~c1_1(a481)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a481) | c3_1(a481) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481))))),
% 1.89/1.47 inference(monotonicity,[status(thm)],[1022])).
% 1.89/1.47 tff(1024,plain,
% 1.89/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a467) | c1_1(a467) | (~c2_1(a467)) | c3_1(a481) | c0_1(a481) | (~c1_1(a481)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a481) | c3_1(a481) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)))),
% 1.89/1.47 inference(transitivity,[status(thm)],[1023, 1021])).
% 1.89/1.47 tff(1025,plain,
% 1.89/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a467) | c1_1(a467) | (~c2_1(a467)) | c3_1(a481) | c0_1(a481) | (~c1_1(a481)))),
% 1.89/1.47 inference(quant_inst,[status(thm)],[])).
% 1.89/1.47 tff(1026,plain,
% 1.89/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a481) | c3_1(a481) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481))),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1025, 1024])).
% 1.89/1.47 tff(1027,plain,
% 1.89/1.47 (c0_1(a481) | (~c2_1(a467)) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481))),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1026, 81, 1016, 29, 269, 268, 499])).
% 1.89/1.47 tff(1028,plain,
% 1.89/1.47 (~c1_1(a471)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1027, 1015, 1017, 712, 1020])).
% 1.89/1.47 tff(1029,plain,
% 1.89/1.47 (c1_1(a471) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481))),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1009, 81, 1017, 29, 405])).
% 1.89/1.47 tff(1030,plain,
% 1.89/1.47 ($false),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1029, 1028, 1019, 712, 1015])).
% 1.89/1.47 tff(1031,plain,(hskp16 | c0_1(a481) | c2_1(a471) | c3_1(a481) | c1_1(a467) | c3_1(a467) | hskp17 | (~c2_1(a478)) | c0_1(a478) | c3_1(a478)), inference(lemma,lemma(discharge,[]))).
% 1.89/1.47 tff(1032,plain,
% 1.89/1.47 (hskp17),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1031, 1000, 515, 529, 269, 268, 1001, 267, 266, 265])).
% 1.89/1.47 tff(1033,plain,
% 1.89/1.47 (~c0_1(a493)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[757, 1032])).
% 1.89/1.47 tff(1034,plain,
% 1.89/1.47 (c3_1(a493)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[768, 1032])).
% 1.89/1.47 tff(1035,plain,
% 1.89/1.47 (c2_1(a493)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[751, 1032])).
% 1.89/1.47 tff(1036,plain,
% 1.89/1.47 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.89/1.47 inference(bind,[status(th)],[])).
% 1.89/1.47 tff(1037,plain,
% 1.89/1.47 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.89/1.47 inference(quant_intro,[status(thm)],[1036])).
% 1.89/1.47 tff(1038,plain,
% 1.89/1.47 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1039,plain,
% 1.89/1.47 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.89/1.47 inference(bind,[status(th)],[])).
% 1.89/1.47 tff(1040,plain,
% 1.89/1.47 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.89/1.47 inference(quant_intro,[status(thm)],[1039])).
% 1.89/1.47 tff(1041,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 1.89/1.47 tff(1042,plain,
% 1.89/1.47 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1041, 1040])).
% 1.89/1.47 tff(1043,plain,
% 1.89/1.47 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1042, 1038])).
% 1.89/1.47 tff(1044,plain,(
% 1.89/1.47 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.89/1.47 inference(skolemize,[status(sab)],[1043])).
% 1.89/1.47 tff(1045,plain,
% 1.89/1.47 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1044, 1037])).
% 1.89/1.47 tff(1046,plain,
% 1.89/1.47 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | c3_1(a481) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp29 | c3_1(a481) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1047,plain,
% 1.89/1.47 ((hskp29 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471))) <=> (hskp29 | c3_1(a481) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1048,plain,
% 1.89/1.47 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | c3_1(a481) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481))))),
% 1.89/1.47 inference(monotonicity,[status(thm)],[1047])).
% 1.89/1.47 tff(1049,plain,
% 1.89/1.47 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp29 | c3_1(a481) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.89/1.47 inference(transitivity,[status(thm)],[1048, 1046])).
% 1.89/1.47 tff(1050,plain,
% 1.89/1.47 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)))),
% 1.89/1.47 inference(quant_inst,[status(thm)],[])).
% 1.89/1.47 tff(1051,plain,
% 1.89/1.47 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp29 | c3_1(a481) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c1_1(a481)) | (~c2_1(a481))),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1050, 1049])).
% 1.89/1.47 tff(1052,plain,
% 1.89/1.47 (hskp29 | (~c1_1(a471))),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1051, 81, 1002, 551, 1000, 529, 1045, 1003])).
% 1.89/1.47 tff(1053,plain,
% 1.89/1.47 (hskp29),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1052, 1010])).
% 1.89/1.47 tff(1054,plain,
% 1.89/1.47 (c2_1(a474)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[340, 1053])).
% 1.89/1.47 tff(1055,plain,
% 1.89/1.47 (c1_1(a474)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[351, 1053])).
% 1.89/1.47 tff(1056,plain,
% 1.89/1.47 (c0_1(a474)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[362, 1053])).
% 1.89/1.47 tff(1057,plain,
% 1.89/1.47 ($false),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[957, 81, 1056, 1055, 1054, 1035, 1034, 551, 540, 1033, 919, 1010])).
% 1.89/1.47 tff(1058,plain,(c1_1(a467) | c3_1(a467) | (~c2_1(a478)) | c0_1(a478) | c3_1(a478) | c1_1(a465) | c0_1(a465) | hskp19 | c2_1(a464) | c0_1(a464)), inference(lemma,lemma(discharge,[]))).
% 1.89/1.47 tff(1059,plain,
% 1.89/1.47 (c1_1(a467)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1058, 268, 267, 266, 265, 263, 264, 235, 237, 238])).
% 1.89/1.47 tff(1060,plain,
% 1.89/1.47 (((~hskp5) | (~c1_1(a467))) <=> ((~hskp5) | (~c1_1(a467)))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1061,plain,
% 1.89/1.47 (((~c1_1(a467)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a467)))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1062,axiom,((~c1_1(a467)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 1.89/1.47 tff(1063,plain,
% 1.89/1.47 ((~hskp5) | (~c1_1(a467))),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1062, 1061])).
% 1.89/1.47 tff(1064,plain,
% 1.89/1.47 ((~hskp5) | (~c1_1(a467))),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1063, 1060])).
% 1.89/1.47 tff(1065,plain,
% 1.89/1.47 (~hskp5),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1064, 1059])).
% 1.89/1.47 tff(1066,plain,
% 1.89/1.47 (hskp17 | hskp5),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[739, 81, 551, 540, 529, 733])).
% 1.89/1.47 tff(1067,plain,
% 1.89/1.47 (hskp17),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1066, 1065])).
% 1.89/1.47 tff(1068,plain,
% 1.89/1.47 (~c0_1(a493)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[757, 1067])).
% 1.89/1.47 tff(1069,plain,
% 1.89/1.47 (c3_1(a493)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[768, 1067])).
% 1.89/1.47 tff(1070,plain,
% 1.89/1.47 (c2_1(a493)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[751, 1067])).
% 1.89/1.47 tff(1071,assumption,(c1_1(a467)), introduced(assumption)).
% 1.89/1.47 tff(1072,plain,
% 1.89/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a464) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1073,plain,
% 1.89/1.47 (((~ndr1_0) | c0_1(a464) | c3_1(a464) | (~c1_1(a464)) | c0_1(a464) | c2_1(a464) | (~c1_1(a464)) | c3_1(a464) | c0_1(a464) | c2_1(a464)) <=> (c3_1(a464) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1074,plain,
% 1.89/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a464) | c3_1(a464) | (~c1_1(a464)) | c0_1(a464) | c2_1(a464) | (~c1_1(a464)) | c3_1(a464) | c0_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a464) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464))))),
% 1.89/1.47 inference(monotonicity,[status(thm)],[1073])).
% 1.89/1.47 tff(1075,plain,
% 1.89/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a464) | c3_1(a464) | (~c1_1(a464)) | c0_1(a464) | c2_1(a464) | (~c1_1(a464)) | c3_1(a464) | c0_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.89/1.47 inference(transitivity,[status(thm)],[1074, 1072])).
% 1.89/1.47 tff(1076,plain,
% 1.89/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a464) | c3_1(a464) | (~c1_1(a464)) | c0_1(a464) | c2_1(a464) | (~c1_1(a464)) | c3_1(a464) | c0_1(a464) | c2_1(a464))),
% 1.89/1.47 inference(quant_inst,[status(thm)],[])).
% 1.89/1.47 tff(1077,plain,
% 1.89/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464))),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 1.89/1.47 tff(1078,plain,
% 1.89/1.47 (~c1_1(a464)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1077, 81, 649, 238, 237, 10])).
% 1.89/1.47 tff(1079,plain,
% 1.89/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a464) | c0_1(a493) | (~c1_1(a467)) | c3_1(a467) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c0_1(a467)) | (~c3_1(a493)) | (~c2_1(a493)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a493) | (~c1_1(a467)) | c3_1(a467) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c0_1(a467)) | (~c3_1(a493)) | (~c2_1(a493)))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1080,plain,
% 1.89/1.47 (((~ndr1_0) | c3_1(a467) | (~c1_1(a467)) | (~c0_1(a467)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464)) <=> (c3_1(a464) | c0_1(a493) | (~c1_1(a467)) | c3_1(a467) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c0_1(a467)) | (~c3_1(a493)) | (~c2_1(a493)))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1081,plain,
% 1.89/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a467) | (~c1_1(a467)) | (~c0_1(a467)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a464) | c0_1(a493) | (~c1_1(a467)) | c3_1(a467) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c0_1(a467)) | (~c3_1(a493)) | (~c2_1(a493))))),
% 1.89/1.47 inference(monotonicity,[status(thm)],[1080])).
% 1.89/1.47 tff(1082,plain,
% 1.89/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a467) | (~c1_1(a467)) | (~c0_1(a467)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a493) | (~c1_1(a467)) | c3_1(a467) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c0_1(a467)) | (~c3_1(a493)) | (~c2_1(a493)))),
% 1.89/1.47 inference(transitivity,[status(thm)],[1081, 1079])).
% 1.89/1.47 tff(1083,plain,
% 1.89/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a467) | (~c1_1(a467)) | (~c0_1(a467)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))),
% 1.89/1.47 inference(quant_inst,[status(thm)],[])).
% 1.89/1.47 tff(1084,plain,
% 1.89/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a493) | (~c1_1(a467)) | c3_1(a467) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c0_1(a467)) | (~c3_1(a493)) | (~c2_1(a493))),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1083, 1082])).
% 1.89/1.47 tff(1085,plain,
% 1.89/1.47 (c1_1(a464) | (~c0_1(a467))),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1084, 81, 822, 821, 649, 818, 1071, 268, 237, 817])).
% 1.89/1.47 tff(1086,plain,
% 1.89/1.47 (~c0_1(a467)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1085, 1078])).
% 1.89/1.47 tff(1087,plain,
% 1.89/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a467) | c3_1(a464) | (~c1_1(a467)) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c2_1(a467))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a467) | c3_1(a464) | (~c1_1(a467)) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c2_1(a467))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1088,plain,
% 1.89/1.47 (((~ndr1_0) | c0_1(a467) | c3_1(a467) | (~c1_1(a467)) | c0_1(a467) | c2_1(a467) | (~c1_1(a467)) | c3_1(a464) | c0_1(a464) | c2_1(a464)) <=> (c0_1(a467) | c3_1(a464) | (~c1_1(a467)) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c2_1(a467))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1089,plain,
% 1.89/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a467) | c3_1(a467) | (~c1_1(a467)) | c0_1(a467) | c2_1(a467) | (~c1_1(a467)) | c3_1(a464) | c0_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a467) | c3_1(a464) | (~c1_1(a467)) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c2_1(a467)))),
% 1.89/1.47 inference(monotonicity,[status(thm)],[1088])).
% 1.89/1.47 tff(1090,plain,
% 1.89/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a467) | c3_1(a467) | (~c1_1(a467)) | c0_1(a467) | c2_1(a467) | (~c1_1(a467)) | c3_1(a464) | c0_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a467) | c3_1(a464) | (~c1_1(a467)) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c2_1(a467))),
% 1.89/1.47 inference(transitivity,[status(thm)],[1089, 1087])).
% 1.89/1.47 tff(1091,plain,
% 1.89/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a467) | c3_1(a467) | (~c1_1(a467)) | c0_1(a467) | c2_1(a467) | (~c1_1(a467)) | c3_1(a464) | c0_1(a464) | c2_1(a464))),
% 1.89/1.47 inference(quant_inst,[status(thm)],[])).
% 1.89/1.47 tff(1092,plain,
% 1.89/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a467) | c3_1(a464) | (~c1_1(a467)) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c2_1(a467)),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1091, 1090])).
% 1.89/1.47 tff(1093,plain,
% 1.89/1.47 (c2_1(a467)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1092, 81, 1086, 649, 1071, 268, 238, 237, 10])).
% 1.89/1.47 tff(1094,plain,
% 1.89/1.47 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | (~ndr1_0) | (~c2_1(a467)) | c1_1(a471) | (~c0_1(a471)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | (~ndr1_0) | (~c2_1(a467)) | c1_1(a471) | (~c0_1(a471)))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1095,plain,
% 1.89/1.47 (((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a467) | (~c1_1(a467)) | (~c2_1(a467))) <=> (c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | (~ndr1_0) | (~c2_1(a467)) | c1_1(a471) | (~c0_1(a471)))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1096,plain,
% 1.89/1.47 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a467) | (~c1_1(a467)) | (~c2_1(a467)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | (~ndr1_0) | (~c2_1(a467)) | c1_1(a471) | (~c0_1(a471))))),
% 1.89/1.47 inference(monotonicity,[status(thm)],[1095])).
% 1.89/1.47 tff(1097,plain,
% 1.89/1.47 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a467) | (~c1_1(a467)) | (~c2_1(a467)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | (~ndr1_0) | (~c2_1(a467)) | c1_1(a471) | (~c0_1(a471)))),
% 1.89/1.47 inference(transitivity,[status(thm)],[1096, 1094])).
% 1.89/1.47 tff(1098,plain,
% 1.89/1.47 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a467) | (~c1_1(a467)) | (~c2_1(a467)))),
% 1.89/1.47 inference(quant_inst,[status(thm)],[])).
% 1.89/1.47 tff(1099,plain,
% 1.89/1.47 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | (~ndr1_0) | (~c2_1(a467)) | c1_1(a471) | (~c0_1(a471))),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 1.89/1.47 tff(1100,plain,
% 1.89/1.47 (c1_1(a471)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1099, 81, 552, 1086, 29, 1071, 405, 1093])).
% 1.89/1.47 tff(1101,plain,
% 1.89/1.47 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 1.89/1.47 inference(bind,[status(th)],[])).
% 1.89/1.47 tff(1102,plain,
% 1.89/1.47 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.89/1.47 inference(quant_intro,[status(thm)],[1101])).
% 1.89/1.47 tff(1103,plain,
% 1.89/1.47 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1104,plain,
% 1.89/1.47 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 1.89/1.47 inference(bind,[status(th)],[])).
% 1.89/1.47 tff(1105,plain,
% 1.89/1.47 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.89/1.47 inference(quant_intro,[status(thm)],[1104])).
% 1.89/1.47 tff(1106,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 1.89/1.47 tff(1107,plain,
% 1.89/1.47 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 1.89/1.47 tff(1108,plain,
% 1.89/1.47 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1107, 1103])).
% 1.89/1.47 tff(1109,plain,(
% 1.89/1.47 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.89/1.47 inference(skolemize,[status(sab)],[1108])).
% 1.89/1.47 tff(1110,plain,
% 1.89/1.47 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1109, 1102])).
% 1.89/1.47 tff(1111,plain,
% 1.89/1.47 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1112,plain,
% 1.89/1.47 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a464) | c1_1(a464) | c0_1(a464)) <=> (hskp2 | hskp1 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1113,plain,
% 1.89/1.47 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a464) | c1_1(a464) | c0_1(a464))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464)))),
% 1.89/1.47 inference(monotonicity,[status(thm)],[1112])).
% 1.89/1.47 tff(1114,plain,
% 1.89/1.47 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a464) | c1_1(a464) | c0_1(a464))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464))),
% 1.89/1.47 inference(transitivity,[status(thm)],[1113, 1111])).
% 1.89/1.47 tff(1115,plain,
% 1.89/1.47 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a464) | c1_1(a464) | c0_1(a464))),
% 1.89/1.47 inference(quant_inst,[status(thm)],[])).
% 1.89/1.47 tff(1116,plain,
% 1.89/1.47 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a464) | c2_1(a464) | (~ndr1_0) | c1_1(a464)),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1115, 1114])).
% 1.89/1.47 tff(1117,plain,
% 1.89/1.47 (hskp2 | hskp1 | c0_1(a464) | c1_1(a464)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1116, 81, 237, 1110])).
% 1.89/1.47 tff(1118,plain,
% 1.89/1.47 (hskp1),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1117, 1078, 238, 660])).
% 1.89/1.47 tff(1119,plain,
% 1.89/1.47 (((~hskp1) | (~c3_1(a463))) <=> ((~hskp1) | (~c3_1(a463)))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1120,plain,
% 1.89/1.47 (((~c3_1(a463)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a463)))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1121,axiom,((~c3_1(a463)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 1.89/1.47 tff(1122,plain,
% 1.89/1.47 ((~hskp1) | (~c3_1(a463))),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 1.89/1.47 tff(1123,plain,
% 1.89/1.47 ((~hskp1) | (~c3_1(a463))),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1122, 1119])).
% 1.89/1.47 tff(1124,plain,
% 1.89/1.47 (~c3_1(a463)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1123, 1118])).
% 1.89/1.47 tff(1125,plain,
% 1.89/1.47 (((~hskp1) | (~c1_1(a463))) <=> ((~hskp1) | (~c1_1(a463)))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1126,plain,
% 1.89/1.47 (((~c1_1(a463)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a463)))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1127,axiom,((~c1_1(a463)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 1.89/1.47 tff(1128,plain,
% 1.89/1.47 ((~hskp1) | (~c1_1(a463))),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 1.89/1.47 tff(1129,plain,
% 1.89/1.47 ((~hskp1) | (~c1_1(a463))),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1128, 1125])).
% 1.89/1.47 tff(1130,plain,
% 1.89/1.47 (~c1_1(a463)),
% 1.89/1.47 inference(unit_resolution,[status(thm)],[1129, 1118])).
% 1.89/1.47 tff(1131,plain,
% 1.89/1.47 (((~hskp1) | c2_1(a463)) <=> ((~hskp1) | c2_1(a463))),
% 1.89/1.47 inference(rewrite,[status(thm)],[])).
% 1.89/1.47 tff(1132,axiom,((~hskp1) | c2_1(a463)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 1.89/1.47 tff(1133,plain,
% 1.89/1.47 ((~hskp1) | c2_1(a463)),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1132, 1131])).
% 1.89/1.47 tff(1134,plain,
% 1.89/1.47 ((~hskp1) | c2_1(a463)),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1133, 1131])).
% 1.89/1.47 tff(1135,plain,
% 1.89/1.47 ((~hskp1) | c2_1(a463)),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1134, 1131])).
% 1.89/1.47 tff(1136,plain,
% 1.89/1.47 ((~hskp1) | c2_1(a463)),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1135, 1131])).
% 1.89/1.47 tff(1137,plain,
% 1.89/1.47 ((~hskp1) | c2_1(a463)),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1136, 1131])).
% 1.89/1.47 tff(1138,plain,
% 1.89/1.47 ((~hskp1) | c2_1(a463)),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1137, 1131])).
% 1.89/1.47 tff(1139,plain,
% 1.89/1.47 ((~hskp1) | c2_1(a463)),
% 1.89/1.47 inference(modus_ponens,[status(thm)],[1138, 1131])).
% 1.89/1.48 tff(1140,plain,
% 1.89/1.48 ((~hskp1) | c2_1(a463)),
% 1.89/1.48 inference(modus_ponens,[status(thm)],[1139, 1131])).
% 1.89/1.48 tff(1141,plain,
% 1.89/1.48 (c2_1(a463)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1140, 1118])).
% 1.89/1.48 tff(1142,plain,
% 1.89/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | c3_1(a467) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | c3_1(a467) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1143,plain,
% 1.89/1.48 (((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c3_1(a467) | c0_1(a467) | (~c1_1(a467))) <=> (c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | c3_1(a467) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1144,plain,
% 1.89/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c3_1(a467) | c0_1(a467) | (~c1_1(a467)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | c3_1(a467) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471))))),
% 1.89/1.48 inference(monotonicity,[status(thm)],[1143])).
% 1.89/1.48 tff(1145,plain,
% 1.89/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c3_1(a467) | c0_1(a467) | (~c1_1(a467)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | c3_1(a467) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)))),
% 1.89/1.48 inference(transitivity,[status(thm)],[1144, 1142])).
% 1.89/1.48 tff(1146,plain,
% 1.89/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c3_1(a467) | c0_1(a467) | (~c1_1(a467)))),
% 1.89/1.48 inference(quant_inst,[status(thm)],[])).
% 1.89/1.48 tff(1147,plain,
% 1.89/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a467) | c2_1(a471) | (~c1_1(a467)) | c3_1(a467) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471))),
% 1.89/1.48 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 1.89/1.48 tff(1148,plain,
% 1.89/1.48 ($false),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1147, 81, 552, 1086, 1141, 29, 1071, 268, 1130, 1124, 499, 1100])).
% 1.89/1.48 tff(1149,plain,(c3_1(a464) | (~c0_1(a471)) | c2_1(a471) | (~c1_1(a467)) | c3_1(a467) | c0_1(a464) | c2_1(a464) | (~c2_1(a493)) | (~c3_1(a493)) | c0_1(a493)), inference(lemma,lemma(discharge,[]))).
% 1.89/1.48 tff(1150,plain,
% 1.89/1.48 (c3_1(a464)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1149, 1059, 529, 551, 268, 238, 237, 1070, 1069, 1068])).
% 1.89/1.48 tff(1151,plain,
% 1.89/1.48 (hskp12),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[628, 1150, 1065, 238])).
% 1.89/1.48 tff(1152,plain,
% 1.89/1.48 (~c3_1(a481)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[463, 1151])).
% 1.89/1.48 tff(1153,plain,
% 1.89/1.48 (~c0_1(a481)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[469, 1151])).
% 1.89/1.48 tff(1154,plain,
% 1.89/1.48 (c1_1(a481)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[480, 1151])).
% 1.89/1.48 tff(1155,plain,
% 1.89/1.48 (c2_1(a481)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[487, 81, 1154, 1153, 1152, 10])).
% 1.89/1.48 tff(1156,plain,
% 1.89/1.48 (c1_1(a471)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1009, 81, 1154, 551, 1153, 529, 405, 1155])).
% 1.89/1.48 tff(1157,plain,
% 1.89/1.48 (hskp29 | (~c1_1(a471))),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1051, 81, 1154, 551, 1152, 529, 1045, 1155])).
% 1.89/1.48 tff(1158,plain,
% 1.89/1.48 (hskp29),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1157, 1156])).
% 1.89/1.48 tff(1159,plain,
% 1.89/1.48 (c2_1(a474)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[340, 1158])).
% 1.89/1.48 tff(1160,plain,
% 1.89/1.48 (c1_1(a474)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[351, 1158])).
% 1.89/1.48 tff(1161,plain,
% 1.89/1.48 (c0_1(a474)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[362, 1158])).
% 1.89/1.48 tff(1162,plain,
% 1.89/1.48 ($false),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[957, 81, 1161, 1160, 1159, 1070, 1069, 551, 540, 1068, 919, 1156])).
% 1.89/1.48 tff(1163,plain,(c3_1(a467) | c0_1(a464) | c2_1(a464) | (~c2_1(a478)) | c0_1(a478) | c3_1(a478) | c1_1(a465) | c0_1(a465) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.89/1.48 tff(1164,plain,
% 1.89/1.48 (c3_1(a467)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1163, 264, 237, 267, 266, 265, 263, 238, 235])).
% 1.89/1.48 tff(1165,plain,
% 1.89/1.48 (((~hskp5) | (~c3_1(a467))) <=> ((~hskp5) | (~c3_1(a467)))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1166,plain,
% 1.89/1.48 (((~c3_1(a467)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a467)))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1167,axiom,((~c3_1(a467)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.89/1.48 tff(1168,plain,
% 1.89/1.48 ((~hskp5) | (~c3_1(a467))),
% 1.89/1.48 inference(modus_ponens,[status(thm)],[1167, 1166])).
% 1.89/1.48 tff(1169,plain,
% 1.89/1.48 ((~hskp5) | (~c3_1(a467))),
% 1.89/1.48 inference(modus_ponens,[status(thm)],[1168, 1165])).
% 1.89/1.48 tff(1170,plain,
% 1.89/1.48 (~hskp5),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1169, 1164])).
% 1.89/1.48 tff(1171,plain,
% 1.89/1.48 (hskp17),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1066, 1170])).
% 1.89/1.48 tff(1172,plain,
% 1.89/1.48 (~c0_1(a493)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[757, 1171])).
% 1.89/1.48 tff(1173,plain,
% 1.89/1.48 (c3_1(a493)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[768, 1171])).
% 1.89/1.48 tff(1174,plain,
% 1.89/1.48 (c2_1(a493)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[751, 1171])).
% 1.89/1.48 tff(1175,plain,
% 1.89/1.48 (~c1_1(a464)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1077, 81, 935, 238, 237, 10])).
% 1.89/1.48 tff(1176,plain,
% 1.89/1.48 (~c3_1(a465)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[669, 1175, 263, 237, 935, 21, 31, 264])).
% 1.89/1.48 tff(1177,plain,
% 1.89/1.48 (~hskp3),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[442, 1176])).
% 1.89/1.48 tff(1178,plain,
% 1.89/1.48 (hskp29),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[457, 1177, 21])).
% 1.89/1.48 tff(1179,plain,
% 1.89/1.48 (c2_1(a474)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[340, 1178])).
% 1.89/1.48 tff(1180,plain,
% 1.89/1.48 (c1_1(a474)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[351, 1178])).
% 1.89/1.48 tff(1181,plain,
% 1.89/1.48 (c0_1(a474)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[362, 1178])).
% 1.89/1.48 tff(1182,plain,
% 1.89/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1183,plain,
% 1.89/1.48 (((~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493))) <=> (c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1184,plain,
% 1.89/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.89/1.48 inference(monotonicity,[status(thm)],[1183])).
% 1.89/1.48 tff(1185,plain,
% 1.89/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.89/1.48 inference(transitivity,[status(thm)],[1184, 1182])).
% 1.89/1.48 tff(1186,plain,
% 1.89/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)))),
% 1.89/1.48 inference(quant_inst,[status(thm)],[])).
% 1.89/1.48 tff(1187,plain,
% 1.89/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.89/1.48 inference(modus_ponens,[status(thm)],[1186, 1185])).
% 1.89/1.48 tff(1188,plain,
% 1.89/1.48 (~c3_1(a474)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1187, 81, 1181, 1180, 1179, 822, 821, 818, 919])).
% 1.89/1.48 tff(1189,plain,
% 1.89/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a464) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1190,plain,
% 1.89/1.48 (((~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464)) <=> (c3_1(a464) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1191,plain,
% 1.89/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a464) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.89/1.48 inference(monotonicity,[status(thm)],[1190])).
% 1.89/1.48 tff(1192,plain,
% 1.89/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.89/1.48 inference(transitivity,[status(thm)],[1191, 1189])).
% 1.89/1.48 tff(1193,plain,
% 1.89/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a464) | c1_1(a464) | c2_1(a464))),
% 1.89/1.48 inference(quant_inst,[status(thm)],[])).
% 1.89/1.48 tff(1194,plain,
% 1.89/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a493) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.89/1.48 inference(modus_ponens,[status(thm)],[1193, 1192])).
% 1.89/1.48 tff(1195,plain,
% 1.89/1.48 ($false),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1194, 81, 1181, 1180, 822, 821, 935, 818, 237, 817, 1175, 1188])).
% 1.89/1.48 tff(1196,plain,(hskp12 | (~c2_1(a493)) | (~c3_1(a493)) | c0_1(a493) | c2_1(a464) | c1_1(a465) | hskp5 | c0_1(a465) | c0_1(a464)), inference(lemma,lemma(discharge,[]))).
% 1.89/1.48 tff(1197,plain,
% 1.89/1.48 (hskp12),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1196, 1174, 1173, 1172, 237, 263, 1170, 264, 238])).
% 1.89/1.48 tff(1198,plain,
% 1.89/1.48 (~c3_1(a481)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[463, 1197])).
% 1.89/1.48 tff(1199,plain,
% 1.89/1.48 (~c0_1(a481)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[469, 1197])).
% 1.89/1.48 tff(1200,plain,
% 1.89/1.48 (c1_1(a481)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[480, 1197])).
% 1.89/1.48 tff(1201,plain,
% 1.89/1.48 (c2_1(a481)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[487, 81, 1200, 1199, 1198, 10])).
% 1.89/1.48 tff(1202,plain,
% 1.89/1.48 (c1_1(a471)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1009, 81, 1200, 551, 1199, 529, 405, 1201])).
% 1.89/1.48 tff(1203,plain,
% 1.89/1.48 (hskp29),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1051, 81, 1200, 551, 1198, 529, 1045, 1202, 1201])).
% 1.89/1.48 tff(1204,plain,
% 1.89/1.48 (c2_1(a474)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[340, 1203])).
% 1.89/1.48 tff(1205,plain,
% 1.89/1.48 (c1_1(a474)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[351, 1203])).
% 1.89/1.48 tff(1206,plain,
% 1.89/1.48 (c0_1(a474)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[362, 1203])).
% 1.89/1.48 tff(1207,plain,
% 1.89/1.48 ($false),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[957, 81, 1206, 1205, 1204, 1174, 1173, 551, 540, 1172, 919, 1202])).
% 1.89/1.48 tff(1208,plain,(c0_1(a465) | c2_1(a464) | c1_1(a465) | c0_1(a464) | (~c2_1(a478)) | c0_1(a478) | c3_1(a478) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.89/1.48 tff(1209,plain,
% 1.89/1.48 (c0_1(a465)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1208, 263, 237, 238, 262, 251, 245, 235])).
% 1.89/1.48 tff(1210,plain,
% 1.89/1.48 (((~hskp3) | (~c0_1(a465))) <=> ((~hskp3) | (~c0_1(a465)))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1211,plain,
% 1.89/1.48 (((~c0_1(a465)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a465)))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1212,axiom,((~c0_1(a465)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 1.89/1.48 tff(1213,plain,
% 1.89/1.48 ((~hskp3) | (~c0_1(a465))),
% 1.89/1.48 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 1.89/1.48 tff(1214,plain,
% 1.89/1.48 ((~hskp3) | (~c0_1(a465))),
% 1.89/1.48 inference(modus_ponens,[status(thm)],[1213, 1210])).
% 1.89/1.48 tff(1215,plain,
% 1.89/1.48 (~hskp3),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1214, 1209])).
% 1.89/1.48 tff(1216,assumption,(~hskp3), introduced(assumption)).
% 1.89/1.48 tff(1217,plain,
% 1.89/1.48 (~hskp29),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[371, 315, 326, 309])).
% 1.89/1.48 tff(1218,plain,
% 1.89/1.48 (hskp12),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[457, 1217, 1216])).
% 1.89/1.48 tff(1219,plain,
% 1.89/1.48 (~c3_1(a481)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[463, 1218])).
% 1.89/1.48 tff(1220,plain,
% 1.89/1.48 (~c0_1(a481)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[469, 1218])).
% 1.89/1.48 tff(1221,plain,
% 1.89/1.48 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c0_1(a487)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c0_1(a487)))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1222,plain,
% 1.89/1.48 ((hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464))) <=> (hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c0_1(a487)))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1223,plain,
% 1.89/1.48 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c0_1(a487))))),
% 1.89/1.48 inference(monotonicity,[status(thm)],[1222])).
% 1.89/1.48 tff(1224,plain,
% 1.89/1.48 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c0_1(a487)))),
% 1.89/1.48 inference(transitivity,[status(thm)],[1223, 1221])).
% 1.89/1.48 tff(1225,plain,
% 1.89/1.48 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464)))),
% 1.89/1.48 inference(quant_inst,[status(thm)],[])).
% 1.89/1.48 tff(1226,plain,
% 1.89/1.48 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a487) | c2_1(a487) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c0_1(a487))),
% 1.89/1.48 inference(modus_ponens,[status(thm)],[1225, 1224])).
% 1.89/1.48 tff(1227,plain,
% 1.89/1.48 (hskp29 | (~c3_1(a464))),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1226, 81, 296, 28, 285, 238, 237, 384])).
% 1.89/1.48 tff(1228,plain,
% 1.89/1.48 (~c3_1(a464)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1227, 1217])).
% 1.89/1.48 tff(1229,plain,
% 1.89/1.48 (c1_1(a481)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[480, 1218])).
% 1.89/1.48 tff(1230,plain,
% 1.89/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a464) | c0_1(a481) | c3_1(a481) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a481) | c3_1(a481) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1231,plain,
% 1.89/1.48 (((~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c1_1(a481)) | c0_1(a481) | c2_1(a481) | (~c1_1(a481)) | c3_1(a464) | c0_1(a464) | c2_1(a464)) <=> (c3_1(a464) | c0_1(a481) | c3_1(a481) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1232,plain,
% 1.89/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c1_1(a481)) | c0_1(a481) | c2_1(a481) | (~c1_1(a481)) | c3_1(a464) | c0_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a464) | c0_1(a481) | c3_1(a481) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481)))),
% 1.89/1.48 inference(monotonicity,[status(thm)],[1231])).
% 1.89/1.48 tff(1233,plain,
% 1.89/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c1_1(a481)) | c0_1(a481) | c2_1(a481) | (~c1_1(a481)) | c3_1(a464) | c0_1(a464) | c2_1(a464))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a481) | c3_1(a481) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481))),
% 1.89/1.48 inference(transitivity,[status(thm)],[1232, 1230])).
% 1.89/1.48 tff(1234,plain,
% 1.89/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c1_1(a481)) | c0_1(a481) | c2_1(a481) | (~c1_1(a481)) | c3_1(a464) | c0_1(a464) | c2_1(a464))),
% 1.89/1.48 inference(quant_inst,[status(thm)],[])).
% 1.89/1.48 tff(1235,plain,
% 1.89/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a464) | c0_1(a481) | c3_1(a481) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a481)) | c2_1(a481)),
% 1.89/1.48 inference(modus_ponens,[status(thm)],[1234, 1233])).
% 1.89/1.48 tff(1236,plain,
% 1.89/1.48 (c2_1(a481)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1235, 81, 1229, 1228, 1220, 1219, 238, 237, 10])).
% 1.89/1.48 tff(1237,plain,
% 1.89/1.48 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c1_1(a487) | c2_1(a487) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | (~c0_1(a487)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c1_1(a487) | c2_1(a487) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | (~c0_1(a487)))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1238,plain,
% 1.89/1.48 (((~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481))) <=> (c1_1(a487) | c2_1(a487) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | (~c0_1(a487)))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1239,plain,
% 1.89/1.48 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c1_1(a487) | c2_1(a487) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | (~c0_1(a487))))),
% 1.89/1.48 inference(monotonicity,[status(thm)],[1238])).
% 1.89/1.48 tff(1240,plain,
% 1.89/1.48 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c1_1(a487) | c2_1(a487) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | (~c0_1(a487)))),
% 1.89/1.48 inference(transitivity,[status(thm)],[1239, 1237])).
% 1.89/1.48 tff(1241,plain,
% 1.89/1.48 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.89/1.48 inference(quant_inst,[status(thm)],[])).
% 1.89/1.48 tff(1242,plain,
% 1.89/1.48 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c1_1(a487) | c2_1(a487) | c0_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)) | (~c0_1(a487))),
% 1.89/1.48 inference(modus_ponens,[status(thm)],[1241, 1240])).
% 1.89/1.48 tff(1243,plain,
% 1.89/1.48 ($false),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1242, 81, 296, 1229, 28, 285, 1220, 405, 1236])).
% 1.89/1.48 tff(1244,plain,((~hskp16) | c0_1(a464) | c2_1(a464) | hskp3 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.89/1.48 tff(1245,plain,
% 1.89/1.48 (~hskp16),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1244, 1215, 237, 238, 235])).
% 1.89/1.48 tff(1246,plain,
% 1.89/1.48 (hskp16 | hskp7),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[521, 81, 262, 251, 245, 20])).
% 1.89/1.48 tff(1247,plain,
% 1.89/1.48 (hskp7),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1246, 1245])).
% 1.89/1.48 tff(1248,plain,
% 1.89/1.48 (~c2_1(a471)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[528, 1247])).
% 1.89/1.48 tff(1249,plain,
% 1.89/1.48 (c0_1(a471)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[550, 1247])).
% 1.89/1.48 tff(1250,plain,
% 1.89/1.48 (c3_1(a471)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[539, 1247])).
% 1.89/1.48 tff(1251,assumption,(c0_1(a465)), introduced(assumption)).
% 1.89/1.48 tff(1252,plain,
% 1.89/1.48 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a471) | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | (~c2_1(a465)) | (~c0_1(a471)) | (~c3_1(a471)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a471) | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | (~c2_1(a465)) | (~c0_1(a471)) | (~c3_1(a471)))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1253,plain,
% 1.89/1.48 ((hskp12 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)) | c1_1(a465) | (~c2_1(a465)) | (~c0_1(a465))) <=> (hskp12 | c2_1(a471) | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | (~c2_1(a465)) | (~c0_1(a471)) | (~c3_1(a471)))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1254,plain,
% 1.89/1.48 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)) | c1_1(a465) | (~c2_1(a465)) | (~c0_1(a465)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a471) | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | (~c2_1(a465)) | (~c0_1(a471)) | (~c3_1(a471))))),
% 1.89/1.48 inference(monotonicity,[status(thm)],[1253])).
% 1.89/1.48 tff(1255,plain,
% 1.89/1.48 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)) | c1_1(a465) | (~c2_1(a465)) | (~c0_1(a465)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a471) | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | (~c2_1(a465)) | (~c0_1(a471)) | (~c3_1(a471)))),
% 1.89/1.48 inference(transitivity,[status(thm)],[1254, 1252])).
% 1.89/1.48 tff(1256,plain,
% 1.89/1.48 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a471) | (~c3_1(a471)) | (~c0_1(a471)) | c1_1(a465) | (~c2_1(a465)) | (~c0_1(a465)))),
% 1.89/1.48 inference(quant_inst,[status(thm)],[])).
% 1.89/1.48 tff(1257,plain,
% 1.89/1.48 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a471) | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | (~c2_1(a465)) | (~c0_1(a471)) | (~c3_1(a471))),
% 1.89/1.48 inference(modus_ponens,[status(thm)],[1256, 1255])).
% 1.89/1.48 tff(1258,plain,
% 1.89/1.48 (hskp12 | (~c2_1(a465)) | (~c0_1(a471)) | (~c3_1(a471))),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1257, 81, 29, 1251, 263, 582])).
% 1.89/1.48 tff(1259,plain,
% 1.89/1.48 (~c2_1(a465)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1258, 21, 553, 552])).
% 1.89/1.48 tff(1260,plain,
% 1.89/1.48 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | c2_1(a465))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | c2_1(a465))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1261,plain,
% 1.89/1.48 ((hskp19 | hskp18 | (~ndr1_0) | c2_1(a465) | c1_1(a465) | (~c0_1(a465))) <=> (hskp19 | hskp18 | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | c2_1(a465))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1262,plain,
% 1.89/1.48 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a465) | c1_1(a465) | (~c0_1(a465)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | c2_1(a465)))),
% 1.89/1.48 inference(monotonicity,[status(thm)],[1261])).
% 1.89/1.48 tff(1263,plain,
% 1.89/1.48 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a465) | c1_1(a465) | (~c0_1(a465)))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | c2_1(a465))),
% 1.89/1.48 inference(transitivity,[status(thm)],[1262, 1260])).
% 1.89/1.48 tff(1264,plain,
% 1.89/1.48 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a465) | c1_1(a465) | (~c0_1(a465)))),
% 1.89/1.48 inference(quant_inst,[status(thm)],[])).
% 1.89/1.48 tff(1265,plain,
% 1.89/1.48 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp18 | (~c0_1(a465)) | c1_1(a465) | (~ndr1_0) | c2_1(a465)),
% 1.89/1.48 inference(modus_ponens,[status(thm)],[1264, 1263])).
% 1.89/1.48 tff(1266,plain,
% 1.89/1.48 (hskp18 | (~c0_1(a465)) | c2_1(a465)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1265, 81, 235, 263, 279])).
% 1.89/1.48 tff(1267,plain,
% 1.89/1.48 (hskp18),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1266, 1259, 1251])).
% 1.89/1.48 tff(1268,plain,
% 1.89/1.48 (~c3_1(a494)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[308, 1267])).
% 1.89/1.48 tff(1269,plain,
% 1.89/1.48 (~hskp3),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1214, 1251])).
% 1.89/1.48 tff(1270,plain,
% 1.89/1.48 (hskp29),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[457, 21, 1269])).
% 1.89/1.48 tff(1271,plain,
% 1.89/1.48 (c0_1(a494)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[325, 1267])).
% 1.89/1.48 tff(1272,plain,
% 1.89/1.48 (~c2_1(a494)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[314, 1267])).
% 1.89/1.48 tff(1273,plain,
% 1.89/1.48 ($false),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[371, 1272, 1271, 1270, 1268])).
% 1.89/1.48 tff(1274,plain,(hskp12 | (~c0_1(a465)) | hskp19 | c1_1(a465) | (~c3_1(a471)) | (~c0_1(a471)) | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.89/1.48 tff(1275,plain,
% 1.89/1.48 (hskp12),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1274, 1250, 235, 263, 1209, 1249, 1248])).
% 1.89/1.48 tff(1276,plain,
% 1.89/1.48 (~c3_1(a481)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[463, 1275])).
% 1.89/1.48 tff(1277,plain,
% 1.89/1.48 (~c0_1(a481)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[469, 1275])).
% 1.89/1.48 tff(1278,plain,
% 1.89/1.48 (c1_1(a481)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[480, 1275])).
% 1.89/1.48 tff(1279,plain,
% 1.89/1.48 (c2_1(a481)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[487, 81, 1278, 1277, 1276, 10])).
% 1.89/1.48 tff(1280,plain,
% 1.89/1.48 (c1_1(a471)),
% 1.89/1.48 inference(unit_resolution,[status(thm)],[1009, 81, 1278, 1249, 1277, 1248, 405, 1279])).
% 1.89/1.48 tff(1281,plain,
% 1.89/1.48 (^[V: $i, U: $i] : refl((hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))),
% 1.89/1.48 inference(bind,[status(th)],[])).
% 1.89/1.48 tff(1282,plain,
% 1.89/1.48 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.89/1.48 inference(quant_intro,[status(thm)],[1281])).
% 1.89/1.48 tff(1283,plain,
% 1.89/1.48 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.89/1.48 inference(rewrite,[status(thm)],[])).
% 1.89/1.48 tff(1284,plain,
% 1.89/1.48 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_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))) | hskp31) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | hskp31))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | hskp31) <=> (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_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))) | hskp31) <=> (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.89/1.49 inference(bind,[status(th)],[])).
% 1.89/1.49 tff(1285,plain,
% 1.89/1.49 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp31) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.89/1.49 inference(quant_intro,[status(thm)],[1284])).
% 1.89/1.49 tff(1286,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))) | hskp31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause200')).
% 1.89/1.49 tff(1287,plain,
% 1.89/1.49 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.89/1.49 inference(modus_ponens,[status(thm)],[1286, 1285])).
% 1.89/1.49 tff(1288,plain,
% 1.89/1.49 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.89/1.49 inference(modus_ponens,[status(thm)],[1287, 1283])).
% 1.89/1.49 tff(1289,plain,(
% 1.89/1.49 ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.89/1.49 inference(skolemize,[status(sab)],[1288])).
% 1.89/1.49 tff(1290,plain,
% 1.89/1.49 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 1.89/1.49 inference(modus_ponens,[status(thm)],[1289, 1282])).
% 1.89/1.49 tff(1291,plain,
% 1.89/1.49 (hskp29),
% 1.89/1.49 inference(unit_resolution,[status(thm)],[1051, 81, 1278, 1249, 1276, 1248, 1045, 1280, 1279])).
% 1.89/1.49 tff(1292,plain,
% 1.89/1.49 (c2_1(a474)),
% 1.89/1.49 inference(unit_resolution,[status(thm)],[340, 1291])).
% 1.89/1.49 tff(1293,plain,
% 1.89/1.49 (c1_1(a474)),
% 1.89/1.49 inference(unit_resolution,[status(thm)],[351, 1291])).
% 1.89/1.49 tff(1294,plain,
% 1.89/1.49 (c0_1(a474)),
% 1.89/1.49 inference(unit_resolution,[status(thm)],[362, 1291])).
% 1.89/1.49 tff(1295,plain,
% 1.89/1.49 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1296,plain,
% 1.92/1.49 ((hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c3_1(a471)) | (~c0_1(a471)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474))) <=> (hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1297,plain,
% 1.92/1.49 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c3_1(a471)) | (~c0_1(a471)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.92/1.49 inference(monotonicity,[status(thm)],[1296])).
% 1.92/1.49 tff(1298,plain,
% 1.92/1.49 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c3_1(a471)) | (~c0_1(a471)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.92/1.49 inference(transitivity,[status(thm)],[1297, 1295])).
% 1.92/1.49 tff(1299,plain,
% 1.92/1.49 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c3_1(a471)) | (~c0_1(a471)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))),
% 1.92/1.49 inference(quant_inst,[status(thm)],[])).
% 1.92/1.49 tff(1300,plain,
% 1.92/1.49 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~ndr1_0) | (~c1_1(a471)) | (~c0_1(a471)) | (~c3_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 1.92/1.49 tff(1301,plain,
% 1.92/1.49 ($false),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1300, 236, 81, 1294, 1293, 1292, 1249, 1250, 1290, 1280])).
% 1.92/1.49 tff(1302,plain,(c1_1(a465) | hskp31 | hskp19 | c2_1(a464) | c0_1(a464)), inference(lemma,lemma(discharge,[]))).
% 1.92/1.49 tff(1303,plain,
% 1.92/1.49 (c1_1(a465)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1302, 238, 235, 237, 236])).
% 1.92/1.49 tff(1304,plain,
% 1.92/1.49 (((~hskp3) | (~c1_1(a465))) <=> ((~hskp3) | (~c1_1(a465)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1305,plain,
% 1.92/1.49 (((~c1_1(a465)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a465)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1306,axiom,((~c1_1(a465)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 1.92/1.49 tff(1307,plain,
% 1.92/1.49 ((~hskp3) | (~c1_1(a465))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1306, 1305])).
% 1.92/1.49 tff(1308,plain,
% 1.92/1.49 ((~hskp3) | (~c1_1(a465))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1307, 1304])).
% 1.92/1.49 tff(1309,plain,
% 1.92/1.49 (~hskp3),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1308, 1303])).
% 1.92/1.49 tff(1310,plain,
% 1.92/1.49 (~hskp16),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1244, 1309, 237, 238, 235])).
% 1.92/1.49 tff(1311,plain,
% 1.92/1.49 (hskp29),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[457, 21, 1216])).
% 1.92/1.49 tff(1312,plain,
% 1.92/1.49 (c2_1(a474)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[340, 1311])).
% 1.92/1.49 tff(1313,plain,
% 1.92/1.49 (c1_1(a474)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[351, 1311])).
% 1.92/1.49 tff(1314,plain,
% 1.92/1.49 (c0_1(a474)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[362, 1311])).
% 1.92/1.49 tff(1315,plain,
% 1.92/1.49 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~ndr1_0) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1316,plain,
% 1.92/1.49 ((hskp31 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474))) <=> (hskp31 | (~ndr1_0) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1317,plain,
% 1.92/1.49 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.92/1.49 inference(monotonicity,[status(thm)],[1316])).
% 1.92/1.49 tff(1318,plain,
% 1.92/1.49 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~ndr1_0) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.92/1.49 inference(transitivity,[status(thm)],[1317, 1315])).
% 1.92/1.49 tff(1319,plain,
% 1.92/1.49 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))),
% 1.92/1.49 inference(quant_inst,[status(thm)],[])).
% 1.92/1.49 tff(1320,plain,
% 1.92/1.49 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~ndr1_0) | (~c3_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1319, 1318])).
% 1.92/1.49 tff(1321,plain,
% 1.92/1.49 (~c3_1(a474)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1320, 236, 81, 1314, 1313, 1312, 1290])).
% 1.92/1.49 tff(1322,plain,
% 1.92/1.49 (((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1323,plain,
% 1.92/1.49 ((hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474))) <=> (hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1324,plain,
% 1.92/1.49 (((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)))) <=> ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.92/1.49 inference(monotonicity,[status(thm)],[1323])).
% 1.92/1.49 tff(1325,plain,
% 1.92/1.49 (((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)))) <=> ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.92/1.49 inference(transitivity,[status(thm)],[1324, 1322])).
% 1.92/1.49 tff(1326,plain,
% 1.92/1.49 ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)))),
% 1.92/1.49 inference(quant_inst,[status(thm)],[])).
% 1.92/1.49 tff(1327,plain,
% 1.92/1.49 ((~![U: $i] : (hskp30 | hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp30 | hskp12 | (~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1326, 1325])).
% 1.92/1.49 tff(1328,plain,
% 1.92/1.49 (hskp30 | c3_1(a474)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1327, 81, 21, 1314, 1313, 167])).
% 1.92/1.49 tff(1329,plain,
% 1.92/1.49 (hskp30),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1328, 1321])).
% 1.92/1.49 tff(1330,plain,
% 1.92/1.49 (c3_1(a488)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[185, 1329])).
% 1.92/1.49 tff(1331,plain,
% 1.92/1.49 (c2_1(a488)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[196, 1329])).
% 1.92/1.49 tff(1332,plain,
% 1.92/1.49 (c1_1(a488)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[207, 1329])).
% 1.92/1.49 tff(1333,plain,
% 1.92/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1334,plain,
% 1.92/1.49 (((~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c0_1(a488)) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474))) <=> ((~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1335,plain,
% 1.92/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c0_1(a488)) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488))))),
% 1.92/1.49 inference(monotonicity,[status(thm)],[1334])).
% 1.92/1.49 tff(1336,plain,
% 1.92/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c0_1(a488)) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.92/1.49 inference(transitivity,[status(thm)],[1335, 1333])).
% 1.92/1.49 tff(1337,plain,
% 1.92/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | (~c0_1(a488)) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)))),
% 1.92/1.49 inference(quant_inst,[status(thm)],[])).
% 1.92/1.49 tff(1338,plain,
% 1.92/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (~ndr1_0) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)) | (~c0_1(a488)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1337, 1336])).
% 1.92/1.49 tff(1339,plain,
% 1.92/1.49 (~c0_1(a488)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1338, 81, 1332, 1331, 1330, 1314, 1313, 157, 1321])).
% 1.92/1.49 tff(1340,plain,
% 1.92/1.49 ($false),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[231, 81, 110, 1332, 1331, 1330, 225, 1339])).
% 1.92/1.49 tff(1341,plain,(hskp12 | hskp16 | hskp31 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.92/1.49 tff(1342,plain,
% 1.92/1.49 (hskp12),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1341, 1310, 236, 1309])).
% 1.92/1.49 tff(1343,plain,
% 1.92/1.49 (~c3_1(a481)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[463, 1342])).
% 1.92/1.49 tff(1344,plain,
% 1.92/1.49 (~c0_1(a481)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[469, 1342])).
% 1.92/1.49 tff(1345,plain,
% 1.92/1.49 (c1_1(a481)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[480, 1342])).
% 1.92/1.49 tff(1346,plain,
% 1.92/1.49 (c2_1(a481)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[487, 81, 1345, 1344, 1343, 10])).
% 1.92/1.49 tff(1347,plain,
% 1.92/1.49 (hskp7),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1246, 1310])).
% 1.92/1.49 tff(1348,plain,
% 1.92/1.49 (~c2_1(a471)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[528, 1347])).
% 1.92/1.49 tff(1349,plain,
% 1.92/1.49 (c0_1(a471)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[550, 1347])).
% 1.92/1.49 tff(1350,plain,
% 1.92/1.49 (c1_1(a471)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1009, 81, 1345, 1349, 1344, 1348, 405, 1346])).
% 1.92/1.49 tff(1351,plain,
% 1.92/1.49 (c3_1(a471)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[539, 1347])).
% 1.92/1.49 tff(1352,plain,
% 1.92/1.49 (hskp29),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1051, 81, 1345, 1349, 1343, 1348, 1045, 1350, 1346])).
% 1.92/1.49 tff(1353,plain,
% 1.92/1.49 (c2_1(a474)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[340, 1352])).
% 1.92/1.49 tff(1354,plain,
% 1.92/1.49 (c1_1(a474)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[351, 1352])).
% 1.92/1.49 tff(1355,plain,
% 1.92/1.49 (c0_1(a474)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[362, 1352])).
% 1.92/1.49 tff(1356,plain,
% 1.92/1.49 ($false),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1300, 236, 81, 1355, 1354, 1353, 1349, 1351, 1290, 1350])).
% 1.92/1.49 tff(1357,plain,(c0_1(a464) | hskp31 | c2_1(a464) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.92/1.49 tff(1358,plain,
% 1.92/1.49 (c0_1(a464)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1357, 237, 236, 235])).
% 1.92/1.49 tff(1359,plain,
% 1.92/1.49 (((~hskp2) | (~c0_1(a464))) <=> ((~hskp2) | (~c0_1(a464)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1360,plain,
% 1.92/1.49 (((~c0_1(a464)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a464)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1361,axiom,((~c0_1(a464)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 1.92/1.49 tff(1362,plain,
% 1.92/1.49 ((~hskp2) | (~c0_1(a464))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1361, 1360])).
% 1.92/1.49 tff(1363,plain,
% 1.92/1.49 ((~hskp2) | (~c0_1(a464))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1362, 1359])).
% 1.92/1.49 tff(1364,plain,
% 1.92/1.49 (~hskp2),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1363, 1358])).
% 1.92/1.49 tff(1365,plain,
% 1.92/1.49 (hskp3),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[457, 1217, 21])).
% 1.92/1.49 tff(1366,plain,
% 1.92/1.49 (~c1_1(a465)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1308, 1365])).
% 1.92/1.49 tff(1367,plain,
% 1.92/1.49 (c3_1(a465)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[442, 1365])).
% 1.92/1.49 tff(1368,plain,
% 1.92/1.49 (~c0_1(a465)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1214, 1365])).
% 1.92/1.49 tff(1369,plain,
% 1.92/1.49 ($false),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[431, 1368, 1367, 267, 296, 28, 266, 1366, 309, 326, 285, 315])).
% 1.92/1.49 tff(1370,plain,((~hskp16) | (~c2_1(a478)) | c0_1(a478) | hskp12 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.92/1.49 tff(1371,plain,
% 1.92/1.49 (~hskp16),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1370, 21, 251, 262, 235])).
% 1.92/1.49 tff(1372,plain,
% 1.92/1.49 (hskp7),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1246, 1371])).
% 1.92/1.49 tff(1373,assumption,(~hskp2), introduced(assumption)).
% 1.92/1.49 tff(1374,plain,
% 1.92/1.49 (hskp3),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1341, 110, 236, 21])).
% 1.92/1.49 tff(1375,plain,
% 1.92/1.49 (~c1_1(a465)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1308, 1374])).
% 1.92/1.49 tff(1376,plain,
% 1.92/1.49 (~c0_1(a465)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1214, 1374])).
% 1.92/1.49 tff(1377,plain,
% 1.92/1.49 (c3_1(a465)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[442, 1374])).
% 1.92/1.49 tff(1378,plain,
% 1.92/1.49 (hskp5 | c2_1(a465)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[635, 81, 21, 373, 264, 41])).
% 1.92/1.49 tff(1379,plain,
% 1.92/1.49 (c2_1(a465)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1378, 31])).
% 1.92/1.49 tff(1380,assumption,(hskp6), introduced(assumption)).
% 1.92/1.49 tff(1381,plain,
% 1.92/1.49 (((~hskp6) | (~c2_1(a470))) <=> ((~hskp6) | (~c2_1(a470)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1382,plain,
% 1.92/1.49 (((~c2_1(a470)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a470)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1383,axiom,((~c2_1(a470)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.92/1.49 tff(1384,plain,
% 1.92/1.49 ((~hskp6) | (~c2_1(a470))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1383, 1382])).
% 1.92/1.49 tff(1385,plain,
% 1.92/1.49 ((~hskp6) | (~c2_1(a470))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1384, 1381])).
% 1.92/1.49 tff(1386,plain,
% 1.92/1.49 (~c2_1(a470)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1385, 1380])).
% 1.92/1.49 tff(1387,plain,
% 1.92/1.49 (((~hskp6) | (~c0_1(a470))) <=> ((~hskp6) | (~c0_1(a470)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1388,plain,
% 1.92/1.49 (((~c0_1(a470)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a470)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1389,axiom,((~c0_1(a470)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 1.92/1.49 tff(1390,plain,
% 1.92/1.49 ((~hskp6) | (~c0_1(a470))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 1.92/1.49 tff(1391,plain,
% 1.92/1.49 ((~hskp6) | (~c0_1(a470))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1390, 1387])).
% 1.92/1.49 tff(1392,plain,
% 1.92/1.49 (~c0_1(a470)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1391, 1380])).
% 1.92/1.49 tff(1393,plain,
% 1.92/1.49 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c0_1(a470) | c2_1(a470) | (~ndr1_0) | (~c3_1(a470)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a470) | c2_1(a470) | (~ndr1_0) | (~c3_1(a470)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1394,plain,
% 1.92/1.49 ((hskp12 | hskp5 | (~ndr1_0) | c2_1(a470) | c0_1(a470) | (~c3_1(a470))) <=> (hskp12 | hskp5 | c0_1(a470) | c2_1(a470) | (~ndr1_0) | (~c3_1(a470)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1395,plain,
% 1.92/1.49 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a470) | c0_1(a470) | (~c3_1(a470)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c0_1(a470) | c2_1(a470) | (~ndr1_0) | (~c3_1(a470))))),
% 1.92/1.49 inference(monotonicity,[status(thm)],[1394])).
% 1.92/1.49 tff(1396,plain,
% 1.92/1.49 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a470) | c0_1(a470) | (~c3_1(a470)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a470) | c2_1(a470) | (~ndr1_0) | (~c3_1(a470)))),
% 1.92/1.49 inference(transitivity,[status(thm)],[1395, 1393])).
% 1.92/1.49 tff(1397,plain,
% 1.92/1.49 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a470) | c0_1(a470) | (~c3_1(a470)))),
% 1.92/1.49 inference(quant_inst,[status(thm)],[])).
% 1.92/1.49 tff(1398,plain,
% 1.92/1.49 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c0_1(a470) | c2_1(a470) | (~ndr1_0) | (~c3_1(a470))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1397, 1396])).
% 1.92/1.49 tff(1399,plain,
% 1.92/1.49 (~c3_1(a470)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1398, 81, 21, 31, 1392, 1386, 41])).
% 1.92/1.49 tff(1400,assumption,(c2_1(a465)), introduced(assumption)).
% 1.92/1.49 tff(1401,plain,
% 1.92/1.49 (((~hskp6) | (~c1_1(a470))) <=> ((~hskp6) | (~c1_1(a470)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1402,plain,
% 1.92/1.49 (((~c1_1(a470)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a470)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1403,axiom,((~c1_1(a470)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.92/1.49 tff(1404,plain,
% 1.92/1.49 ((~hskp6) | (~c1_1(a470))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 1.92/1.49 tff(1405,plain,
% 1.92/1.49 ((~hskp6) | (~c1_1(a470))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1404, 1401])).
% 1.92/1.49 tff(1406,plain,
% 1.92/1.49 (~c1_1(a470)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1405, 1380])).
% 1.92/1.49 tff(1407,plain,
% 1.92/1.49 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c1_1(a470) | c2_1(a470) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c1_1(a470) | c2_1(a470) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1408,plain,
% 1.92/1.49 ((hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470) | c1_1(a470) | c2_1(a470)) <=> (hskp2 | c1_1(a470) | c2_1(a470) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1409,plain,
% 1.92/1.49 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470) | c1_1(a470) | c2_1(a470))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c1_1(a470) | c2_1(a470) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470)))),
% 1.92/1.49 inference(monotonicity,[status(thm)],[1408])).
% 1.92/1.49 tff(1410,plain,
% 1.92/1.49 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470) | c1_1(a470) | c2_1(a470))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c1_1(a470) | c2_1(a470) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470))),
% 1.92/1.49 inference(transitivity,[status(thm)],[1409, 1407])).
% 1.92/1.49 tff(1411,plain,
% 1.92/1.49 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470) | c1_1(a470) | c2_1(a470))),
% 1.92/1.49 inference(quant_inst,[status(thm)],[])).
% 1.92/1.49 tff(1412,plain,
% 1.92/1.49 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c1_1(a470) | c2_1(a470) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a470)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1411, 1410])).
% 1.92/1.49 tff(1413,plain,
% 1.92/1.49 ($false),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1412, 81, 1373, 373, 1406, 1386, 263, 648, 1400, 1399])).
% 1.92/1.49 tff(1414,plain,((~hskp6) | hskp2 | (~c3_1(a465)) | c1_1(a465) | (~c2_1(a465)) | hskp12 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.92/1.49 tff(1415,plain,
% 1.92/1.49 (~hskp6),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1414, 1379, 373, 263, 1373, 21, 31])).
% 1.92/1.49 tff(1416,plain,
% 1.92/1.49 (^[U: $i] : refl((hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.92/1.49 inference(bind,[status(th)],[])).
% 1.92/1.49 tff(1417,plain,
% 1.92/1.49 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.92/1.49 inference(quant_intro,[status(thm)],[1416])).
% 1.92/1.49 tff(1418,plain,
% 1.92/1.49 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1419,plain,
% 1.92/1.49 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp18) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp18))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp18) | hskp6) <=> ((hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp6))), rewrite(((hskp18 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp6) <=> (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp18) | hskp6) <=> (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.92/1.49 inference(bind,[status(th)],[])).
% 1.92/1.49 tff(1420,plain,
% 1.92/1.49 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp18) | hskp6) <=> ![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.92/1.49 inference(quant_intro,[status(thm)],[1419])).
% 1.92/1.49 tff(1421,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp18) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 1.92/1.49 tff(1422,plain,
% 1.92/1.49 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 1.92/1.49 tff(1423,plain,
% 1.92/1.49 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1422, 1418])).
% 1.92/1.49 tff(1424,plain,(
% 1.92/1.49 ![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.92/1.49 inference(skolemize,[status(sab)],[1423])).
% 1.92/1.49 tff(1425,plain,
% 1.92/1.49 (![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1424, 1417])).
% 1.92/1.49 tff(1426,plain,
% 1.92/1.49 (((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp6 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)))) <=> ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp6 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1427,plain,
% 1.92/1.49 ((hskp18 | hskp6 | (~ndr1_0) | c0_1(a465) | (~c3_1(a465)) | (~c2_1(a465))) <=> (hskp18 | hskp6 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1428,plain,
% 1.92/1.49 (((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | c0_1(a465) | (~c3_1(a465)) | (~c2_1(a465)))) <=> ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp6 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465))))),
% 1.92/1.49 inference(monotonicity,[status(thm)],[1427])).
% 1.92/1.49 tff(1429,plain,
% 1.92/1.49 (((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | c0_1(a465) | (~c3_1(a465)) | (~c2_1(a465)))) <=> ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp6 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)))),
% 1.92/1.49 inference(transitivity,[status(thm)],[1428, 1426])).
% 1.92/1.49 tff(1430,plain,
% 1.92/1.49 ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp6 | (~ndr1_0) | c0_1(a465) | (~c3_1(a465)) | (~c2_1(a465)))),
% 1.92/1.49 inference(quant_inst,[status(thm)],[])).
% 1.92/1.49 tff(1431,plain,
% 1.92/1.49 ((~![U: $i] : (hskp18 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp6 | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[1430, 1429])).
% 1.92/1.49 tff(1432,plain,
% 1.92/1.49 (hskp18 | hskp6 | (~c2_1(a465))),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1431, 81, 373, 264, 1425])).
% 1.92/1.49 tff(1433,plain,
% 1.92/1.49 (hskp18),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[1432, 1415, 1379])).
% 1.92/1.49 tff(1434,plain,
% 1.92/1.49 (~c3_1(a494)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[308, 1433])).
% 1.92/1.49 tff(1435,plain,
% 1.92/1.49 (~c2_1(a494)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[314, 1433])).
% 1.92/1.49 tff(1436,plain,
% 1.92/1.49 (c0_1(a494)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[325, 1433])).
% 1.92/1.49 tff(1437,plain,
% 1.92/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a494) | c3_1(a494) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a494)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a494) | c3_1(a494) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a494)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(1438,plain,
% 1.92/1.49 (((~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465))) <=> (c2_1(a494) | c3_1(a494) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a494)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1439,plain,
% 1.92/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a494) | c3_1(a494) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a494))))),
% 1.92/1.50 inference(monotonicity,[status(thm)],[1438])).
% 1.92/1.50 tff(1440,plain,
% 1.92/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a494) | c3_1(a494) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a494)))),
% 1.92/1.50 inference(transitivity,[status(thm)],[1439, 1437])).
% 1.92/1.50 tff(1441,plain,
% 1.92/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a494) | c3_1(a494) | (~c0_1(a494)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))),
% 1.92/1.50 inference(quant_inst,[status(thm)],[])).
% 1.92/1.50 tff(1442,plain,
% 1.92/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a494) | c3_1(a494) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a494))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1441, 1440])).
% 1.92/1.50 tff(1443,plain,
% 1.92/1.50 ($false),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1442, 81, 1436, 373, 1435, 1434, 264, 263, 422, 1379])).
% 1.92/1.50 tff(1444,plain,(hskp5 | (~c3_1(a465)) | c0_1(a465) | c1_1(a465) | hskp2 | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.92/1.50 tff(1445,plain,
% 1.92/1.50 (hskp5),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1444, 1377, 1376, 1375, 1373, 21])).
% 1.92/1.50 tff(1446,plain,
% 1.92/1.50 (~c3_1(a467)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1169, 1445])).
% 1.92/1.50 tff(1447,plain,
% 1.92/1.50 (c0_1(a467)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[602, 1445])).
% 1.92/1.50 tff(1448,plain,
% 1.92/1.50 (~c1_1(a467)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1064, 1445])).
% 1.92/1.50 tff(1449,plain,
% 1.92/1.50 ($false),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[591, 1448, 1447, 21, 713, 29, 1446, 110, 712])).
% 1.92/1.50 tff(1450,plain,(hskp16 | hskp12 | c2_1(a471) | hskp2 | hskp31 | (~c2_1(a478)) | c0_1(a478) | c3_1(a478)), inference(lemma,lemma(discharge,[]))).
% 1.92/1.50 tff(1451,plain,
% 1.92/1.50 (c2_1(a471)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1450, 1371, 21, 1373, 236, 262, 251, 245])).
% 1.92/1.50 tff(1452,plain,
% 1.92/1.50 ($false),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[528, 1451, 1372])).
% 1.92/1.50 tff(1453,plain,(hskp12 | hskp2 | hskp31 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.92/1.50 tff(1454,plain,
% 1.92/1.50 (hskp12),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1453, 1364, 236, 235])).
% 1.92/1.50 tff(1455,plain,
% 1.92/1.50 (~c3_1(a481)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[463, 1454])).
% 1.92/1.50 tff(1456,plain,
% 1.92/1.50 (~c0_1(a481)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[469, 1454])).
% 1.92/1.50 tff(1457,plain,
% 1.92/1.50 (c1_1(a481)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[480, 1454])).
% 1.92/1.50 tff(1458,plain,
% 1.92/1.50 (c2_1(a481)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[487, 81, 1457, 1456, 1455, 10])).
% 1.92/1.50 tff(1459,plain,
% 1.92/1.50 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c0_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1460,plain,
% 1.92/1.50 (((~ndr1_0) | c2_1(a464) | c1_1(a464) | (~c0_1(a464)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481))) <=> (c0_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1461,plain,
% 1.92/1.50 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a464) | c1_1(a464) | (~c0_1(a464)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c0_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a481)) | (~c2_1(a481))))),
% 1.92/1.50 inference(monotonicity,[status(thm)],[1460])).
% 1.92/1.50 tff(1462,plain,
% 1.92/1.50 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a464) | c1_1(a464) | (~c0_1(a464)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.92/1.50 inference(transitivity,[status(thm)],[1461, 1459])).
% 1.92/1.50 tff(1463,plain,
% 1.92/1.50 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a464) | c1_1(a464) | (~c0_1(a464)) | c0_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.92/1.50 inference(quant_inst,[status(thm)],[])).
% 1.92/1.50 tff(1464,plain,
% 1.92/1.50 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | c1_1(a464) | (~c1_1(a481)) | (~c2_1(a481))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1463, 1462])).
% 1.92/1.50 tff(1465,plain,
% 1.92/1.50 (c1_1(a464)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1464, 81, 1457, 1456, 1358, 237, 405, 1458])).
% 1.92/1.50 tff(1466,plain,
% 1.92/1.50 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | c3_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp29 | c3_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1467,plain,
% 1.92/1.50 ((hskp29 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)) | c2_1(a464) | (~c1_1(a464)) | (~c0_1(a464))) <=> (hskp29 | c3_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1468,plain,
% 1.92/1.50 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)) | c2_1(a464) | (~c1_1(a464)) | (~c0_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | c3_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)) | (~c1_1(a481)) | (~c2_1(a481))))),
% 1.92/1.50 inference(monotonicity,[status(thm)],[1467])).
% 1.92/1.50 tff(1469,plain,
% 1.92/1.50 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)) | c2_1(a464) | (~c1_1(a464)) | (~c0_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp29 | c3_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.92/1.50 inference(transitivity,[status(thm)],[1468, 1466])).
% 1.92/1.50 tff(1470,plain,
% 1.92/1.50 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)) | c2_1(a464) | (~c1_1(a464)) | (~c0_1(a464)))),
% 1.92/1.50 inference(quant_inst,[status(thm)],[])).
% 1.92/1.50 tff(1471,plain,
% 1.92/1.50 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp29 | c3_1(a481) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)) | (~c1_1(a481)) | (~c2_1(a481))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1470, 1469])).
% 1.92/1.50 tff(1472,plain,
% 1.92/1.50 (hskp29),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1471, 81, 1457, 1455, 1358, 237, 1045, 1465, 1458])).
% 1.92/1.50 tff(1473,plain,
% 1.92/1.50 (c2_1(a474)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[340, 1472])).
% 1.92/1.50 tff(1474,plain,
% 1.92/1.50 (c1_1(a474)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[351, 1472])).
% 1.92/1.50 tff(1475,plain,
% 1.92/1.50 (c0_1(a474)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[362, 1472])).
% 1.92/1.50 tff(1476,plain,
% 1.92/1.50 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~c0_1(a464)) | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~c0_1(a464)) | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1477,plain,
% 1.92/1.50 ((hskp31 | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c0_1(a464)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474))) <=> (hskp31 | (~c0_1(a464)) | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1478,plain,
% 1.92/1.50 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c0_1(a464)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~c0_1(a464)) | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.92/1.50 inference(monotonicity,[status(thm)],[1477])).
% 1.92/1.50 tff(1479,plain,
% 1.92/1.50 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c0_1(a464)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~c0_1(a464)) | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.92/1.50 inference(transitivity,[status(thm)],[1478, 1476])).
% 1.92/1.50 tff(1480,plain,
% 1.92/1.50 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c0_1(a464)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))),
% 1.92/1.50 inference(quant_inst,[status(thm)],[])).
% 1.92/1.50 tff(1481,plain,
% 1.92/1.50 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~c0_1(a464)) | (~ndr1_0) | (~c1_1(a464)) | (~c3_1(a464)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 1.92/1.50 tff(1482,plain,
% 1.92/1.50 (~c3_1(a464)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1481, 236, 81, 1475, 1474, 1473, 1358, 1290, 1465])).
% 1.92/1.50 tff(1483,plain,
% 1.92/1.50 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a464) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a464) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1484,plain,
% 1.92/1.50 (((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a464) | c2_1(a464) | (~c0_1(a464))) <=> (c3_1(a464) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1485,plain,
% 1.92/1.50 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a464) | c2_1(a464) | (~c0_1(a464)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a464) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.92/1.50 inference(monotonicity,[status(thm)],[1484])).
% 1.92/1.50 tff(1486,plain,
% 1.92/1.50 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a464) | c2_1(a464) | (~c0_1(a464)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a464) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.92/1.50 inference(transitivity,[status(thm)],[1485, 1483])).
% 1.92/1.50 tff(1487,plain,
% 1.92/1.50 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a464) | c2_1(a464) | (~c0_1(a464)))),
% 1.92/1.50 inference(quant_inst,[status(thm)],[])).
% 1.92/1.50 tff(1488,plain,
% 1.92/1.50 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a464) | (~c0_1(a464)) | c2_1(a464) | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1487, 1486])).
% 1.92/1.50 tff(1489,plain,
% 1.92/1.50 ($false),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1488, 81, 1475, 1474, 1473, 1482, 1358, 237, 109])).
% 1.92/1.50 tff(1490,plain,(c2_1(a464) | hskp31 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.92/1.50 tff(1491,plain,
% 1.92/1.50 (c2_1(a464)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1490, 236, 235])).
% 1.92/1.50 tff(1492,plain,
% 1.92/1.50 (((~hskp2) | (~c2_1(a464))) <=> ((~hskp2) | (~c2_1(a464)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1493,plain,
% 1.92/1.50 (((~c2_1(a464)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a464)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1494,axiom,((~c2_1(a464)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 1.92/1.50 tff(1495,plain,
% 1.92/1.50 ((~hskp2) | (~c2_1(a464))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1494, 1493])).
% 1.92/1.50 tff(1496,plain,
% 1.92/1.50 ((~hskp2) | (~c2_1(a464))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1495, 1492])).
% 1.92/1.50 tff(1497,plain,
% 1.92/1.50 (~hskp2),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1496, 1491])).
% 1.92/1.50 tff(1498,plain,
% 1.92/1.50 (hskp12),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1453, 1497, 236, 235])).
% 1.92/1.50 tff(1499,plain,
% 1.92/1.50 (~c3_1(a481)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[463, 1498])).
% 1.92/1.50 tff(1500,plain,
% 1.92/1.50 (~c0_1(a481)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[469, 1498])).
% 1.92/1.50 tff(1501,plain,
% 1.92/1.50 (c1_1(a481)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[480, 1498])).
% 1.92/1.50 tff(1502,plain,
% 1.92/1.50 (c2_1(a481)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[487, 81, 1501, 1500, 1499, 10])).
% 1.92/1.50 tff(1503,assumption,(c1_1(a481)), introduced(assumption)).
% 1.92/1.50 tff(1504,plain,
% 1.92/1.50 (c2_1(a481)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[487, 81, 1503, 1017, 1016, 10])).
% 1.92/1.50 tff(1505,assumption,(hskp7), introduced(assumption)).
% 1.92/1.50 tff(1506,plain,
% 1.92/1.50 (~c2_1(a471)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[528, 1505])).
% 1.92/1.50 tff(1507,plain,
% 1.92/1.50 (c0_1(a471)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[550, 1505])).
% 1.92/1.50 tff(1508,plain,
% 1.92/1.50 (c1_1(a471)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1009, 81, 1503, 1507, 1017, 1506, 405, 1504])).
% 1.92/1.50 tff(1509,plain,
% 1.92/1.50 (c3_1(a471)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[539, 1505])).
% 1.92/1.50 tff(1510,plain,
% 1.92/1.50 (hskp29 | (~c1_1(a471))),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1051, 81, 1503, 1507, 1016, 1506, 1045, 1504])).
% 1.92/1.50 tff(1511,plain,
% 1.92/1.50 (hskp29),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1510, 1508])).
% 1.92/1.50 tff(1512,plain,
% 1.92/1.50 (c2_1(a474)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[340, 1511])).
% 1.92/1.50 tff(1513,plain,
% 1.92/1.50 (c1_1(a474)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[351, 1511])).
% 1.92/1.50 tff(1514,plain,
% 1.92/1.50 (c0_1(a474)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[362, 1511])).
% 1.92/1.50 tff(1515,plain,
% 1.92/1.50 ($false),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1300, 236, 81, 1514, 1513, 1512, 1507, 1509, 1290, 1508])).
% 1.92/1.50 tff(1516,plain,((~hskp7) | hskp31 | (~c1_1(a481)) | c3_1(a481) | c0_1(a481)), inference(lemma,lemma(discharge,[]))).
% 1.92/1.50 tff(1517,plain,
% 1.92/1.50 (~hskp7),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1516, 236, 1501, 1499, 1500])).
% 1.92/1.50 tff(1518,plain,
% 1.92/1.50 (hskp16),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1246, 1517])).
% 1.92/1.50 tff(1519,plain,
% 1.92/1.50 (~c2_1(a487)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[284, 1518])).
% 1.92/1.50 tff(1520,plain,
% 1.92/1.50 (~c1_1(a487)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[27, 1518])).
% 1.92/1.50 tff(1521,plain,
% 1.92/1.50 (c0_1(a487)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[295, 1518])).
% 1.92/1.50 tff(1522,plain,
% 1.92/1.50 ($false),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1242, 81, 1521, 1501, 1520, 1519, 1500, 405, 1502])).
% 1.92/1.50 tff(1523,plain,(hskp31 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.92/1.50 tff(1524,plain,
% 1.92/1.50 (hskp31),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1523, 234])).
% 1.92/1.50 tff(1525,plain,
% 1.92/1.50 (((~hskp31) | c0_1(a529)) <=> ((~hskp31) | c0_1(a529))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1526,axiom,((~hskp31) | c0_1(a529)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 1.92/1.50 tff(1527,plain,
% 1.92/1.50 ((~hskp31) | c0_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1526, 1525])).
% 1.92/1.50 tff(1528,plain,
% 1.92/1.50 ((~hskp31) | c0_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1527, 1525])).
% 1.92/1.50 tff(1529,plain,
% 1.92/1.50 ((~hskp31) | c0_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1528, 1525])).
% 1.92/1.50 tff(1530,plain,
% 1.92/1.50 ((~hskp31) | c0_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1529, 1525])).
% 1.92/1.50 tff(1531,plain,
% 1.92/1.50 ((~hskp31) | c0_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1530, 1525])).
% 1.92/1.50 tff(1532,plain,
% 1.92/1.50 ((~hskp31) | c0_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1531, 1525])).
% 1.92/1.50 tff(1533,plain,
% 1.92/1.50 ((~hskp31) | c0_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1532, 1525])).
% 1.92/1.50 tff(1534,plain,
% 1.92/1.50 ((~hskp31) | c0_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1533, 1525])).
% 1.92/1.50 tff(1535,plain,
% 1.92/1.50 (c0_1(a529)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1534, 1524])).
% 1.92/1.50 tff(1536,plain,
% 1.92/1.50 (((~hskp31) | c3_1(a529)) <=> ((~hskp31) | c3_1(a529))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1537,axiom,((~hskp31) | c3_1(a529)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.92/1.50 tff(1538,plain,
% 1.92/1.50 ((~hskp31) | c3_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 1.92/1.50 tff(1539,plain,
% 1.92/1.50 ((~hskp31) | c3_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1538, 1536])).
% 1.92/1.50 tff(1540,plain,
% 1.92/1.50 ((~hskp31) | c3_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1539, 1536])).
% 1.92/1.50 tff(1541,plain,
% 1.92/1.50 ((~hskp31) | c3_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1540, 1536])).
% 1.92/1.50 tff(1542,plain,
% 1.92/1.50 ((~hskp31) | c3_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1541, 1536])).
% 1.92/1.50 tff(1543,plain,
% 1.92/1.50 ((~hskp31) | c3_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1542, 1536])).
% 1.92/1.50 tff(1544,plain,
% 1.92/1.50 ((~hskp31) | c3_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1543, 1536])).
% 1.92/1.50 tff(1545,plain,
% 1.92/1.50 ((~hskp31) | c3_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1544, 1536])).
% 1.92/1.50 tff(1546,plain,
% 1.92/1.50 (c3_1(a529)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1545, 1524])).
% 1.92/1.50 tff(1547,plain,
% 1.92/1.50 (((~hskp31) | c1_1(a529)) <=> ((~hskp31) | c1_1(a529))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1548,axiom,((~hskp31) | c1_1(a529)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 1.92/1.50 tff(1549,plain,
% 1.92/1.50 ((~hskp31) | c1_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1548, 1547])).
% 1.92/1.50 tff(1550,plain,
% 1.92/1.50 ((~hskp31) | c1_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1549, 1547])).
% 1.92/1.50 tff(1551,plain,
% 1.92/1.50 ((~hskp31) | c1_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1550, 1547])).
% 1.92/1.50 tff(1552,plain,
% 1.92/1.50 ((~hskp31) | c1_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1551, 1547])).
% 1.92/1.50 tff(1553,plain,
% 1.92/1.50 ((~hskp31) | c1_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1552, 1547])).
% 1.92/1.50 tff(1554,plain,
% 1.92/1.50 ((~hskp31) | c1_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1553, 1547])).
% 1.92/1.50 tff(1555,plain,
% 1.92/1.50 ((~hskp31) | c1_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1554, 1547])).
% 1.92/1.50 tff(1556,plain,
% 1.92/1.50 ((~hskp31) | c1_1(a529)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1555, 1547])).
% 1.92/1.50 tff(1557,plain,
% 1.92/1.50 (c1_1(a529)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1556, 1524])).
% 1.92/1.50 tff(1558,plain,
% 1.92/1.50 (^[U: $i] : refl((hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 1.92/1.50 inference(bind,[status(th)],[])).
% 1.92/1.50 tff(1559,plain,
% 1.92/1.50 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.92/1.50 inference(quant_intro,[status(thm)],[1558])).
% 1.92/1.50 tff(1560,plain,
% 1.92/1.50 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1561,plain,
% 1.92/1.50 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp14) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp14) | hskp10) <=> ((hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp14) | hskp10) <=> (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.92/1.50 inference(bind,[status(th)],[])).
% 1.92/1.50 tff(1562,plain,
% 1.92/1.50 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp14) | hskp10) <=> ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.92/1.50 inference(quant_intro,[status(thm)],[1561])).
% 1.92/1.50 tff(1563,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp14) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 1.92/1.50 tff(1564,plain,
% 1.92/1.50 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1563, 1562])).
% 1.92/1.50 tff(1565,plain,
% 1.92/1.50 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1564, 1560])).
% 1.92/1.50 tff(1566,plain,(
% 1.92/1.50 ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.92/1.50 inference(skolemize,[status(sab)],[1565])).
% 1.92/1.50 tff(1567,plain,
% 1.92/1.50 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1566, 1559])).
% 1.92/1.50 tff(1568,plain,
% 1.92/1.50 (hskp31),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1523, 235])).
% 1.92/1.50 tff(1569,plain,
% 1.92/1.50 (c3_1(a529)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1545, 1568])).
% 1.92/1.50 tff(1570,plain,
% 1.92/1.50 (c1_1(a529)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1556, 1568])).
% 1.92/1.50 tff(1571,plain,
% 1.92/1.50 (c0_1(a529)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1534, 1568])).
% 1.92/1.50 tff(1572,assumption,(~hskp10), introduced(assumption)).
% 1.92/1.50 tff(1573,plain,
% 1.92/1.50 (hskp29),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[457, 1269, 21])).
% 1.92/1.50 tff(1574,plain,
% 1.92/1.50 (c2_1(a474)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[340, 1573])).
% 1.92/1.50 tff(1575,plain,
% 1.92/1.50 (c1_1(a474)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[351, 1573])).
% 1.92/1.50 tff(1576,plain,
% 1.92/1.50 (c0_1(a474)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[362, 1573])).
% 1.92/1.50 tff(1577,plain,
% 1.92/1.50 (((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | hskp10 | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1578,plain,
% 1.92/1.50 ((hskp14 | hskp10 | (~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474))) <=> (hskp14 | hskp10 | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1579,plain,
% 1.92/1.50 (((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.92/1.50 inference(monotonicity,[status(thm)],[1578])).
% 1.92/1.50 tff(1580,plain,
% 1.92/1.50 (((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | hskp10 | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.92/1.50 inference(transitivity,[status(thm)],[1579, 1577])).
% 1.92/1.50 tff(1581,plain,
% 1.92/1.50 ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))),
% 1.92/1.50 inference(quant_inst,[status(thm)],[])).
% 1.92/1.50 tff(1582,plain,
% 1.92/1.50 ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp14 | hskp10 | (~ndr1_0) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1581, 1580])).
% 1.92/1.50 tff(1583,plain,
% 1.92/1.50 (hskp14),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1582, 81, 1572, 1576, 1575, 1574, 1567])).
% 1.92/1.50 tff(1584,plain,
% 1.92/1.50 (((~hskp14) | (~c0_1(a483))) <=> ((~hskp14) | (~c0_1(a483)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1585,plain,
% 1.92/1.50 (((~c0_1(a483)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a483)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1586,axiom,((~c0_1(a483)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 1.92/1.50 tff(1587,plain,
% 1.92/1.50 ((~hskp14) | (~c0_1(a483))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1586, 1585])).
% 1.92/1.50 tff(1588,plain,
% 1.92/1.50 ((~hskp14) | (~c0_1(a483))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1587, 1584])).
% 1.92/1.50 tff(1589,plain,
% 1.92/1.50 (~c0_1(a483)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1588, 1583])).
% 1.92/1.50 tff(1590,plain,
% 1.92/1.50 (((~hskp14) | c2_1(a483)) <=> ((~hskp14) | c2_1(a483))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1591,axiom,((~hskp14) | c2_1(a483)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 1.92/1.50 tff(1592,plain,
% 1.92/1.50 ((~hskp14) | c2_1(a483)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 1.92/1.50 tff(1593,plain,
% 1.92/1.50 ((~hskp14) | c2_1(a483)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1592, 1590])).
% 1.92/1.50 tff(1594,plain,
% 1.92/1.50 ((~hskp14) | c2_1(a483)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1593, 1590])).
% 1.92/1.50 tff(1595,plain,
% 1.92/1.50 ((~hskp14) | c2_1(a483)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1594, 1590])).
% 1.92/1.50 tff(1596,plain,
% 1.92/1.50 ((~hskp14) | c2_1(a483)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1595, 1590])).
% 1.92/1.50 tff(1597,plain,
% 1.92/1.50 ((~hskp14) | c2_1(a483)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1596, 1590])).
% 1.92/1.50 tff(1598,plain,
% 1.92/1.50 ((~hskp14) | c2_1(a483)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1597, 1590])).
% 1.92/1.50 tff(1599,plain,
% 1.92/1.50 ((~hskp14) | c2_1(a483)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1598, 1590])).
% 1.92/1.50 tff(1600,plain,
% 1.92/1.50 (c2_1(a483)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1599, 1583])).
% 1.92/1.50 tff(1601,plain,
% 1.92/1.50 (((~hskp14) | c1_1(a483)) <=> ((~hskp14) | c1_1(a483))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1602,axiom,((~hskp14) | c1_1(a483)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.92/1.50 tff(1603,plain,
% 1.92/1.50 ((~hskp14) | c1_1(a483)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1602, 1601])).
% 1.92/1.50 tff(1604,plain,
% 1.92/1.50 ((~hskp14) | c1_1(a483)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1603, 1601])).
% 1.92/1.50 tff(1605,plain,
% 1.92/1.50 ((~hskp14) | c1_1(a483)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1604, 1601])).
% 1.92/1.50 tff(1606,plain,
% 1.92/1.50 ((~hskp14) | c1_1(a483)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1605, 1601])).
% 1.92/1.50 tff(1607,plain,
% 1.92/1.50 ((~hskp14) | c1_1(a483)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1606, 1601])).
% 1.92/1.50 tff(1608,plain,
% 1.92/1.50 ((~hskp14) | c1_1(a483)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1607, 1601])).
% 1.92/1.50 tff(1609,plain,
% 1.92/1.50 ((~hskp14) | c1_1(a483)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1608, 1601])).
% 1.92/1.50 tff(1610,plain,
% 1.92/1.50 ((~hskp14) | c1_1(a483)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1609, 1601])).
% 1.92/1.50 tff(1611,plain,
% 1.92/1.50 (c1_1(a483)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1610, 1583])).
% 1.92/1.50 tff(1612,plain,
% 1.92/1.50 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a483) | (~ndr1_0) | (~c3_1(a483)) | (~c1_1(a483)) | (~c2_1(a483)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a483) | (~ndr1_0) | (~c3_1(a483)) | (~c1_1(a483)) | (~c2_1(a483)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1613,plain,
% 1.92/1.50 ((hskp16 | (~ndr1_0) | (~c1_1(a483)) | (~c3_1(a483)) | (~c2_1(a483)) | c0_1(a483) | (~c3_1(a483)) | (~c1_1(a483))) <=> (hskp16 | c0_1(a483) | (~ndr1_0) | (~c3_1(a483)) | (~c1_1(a483)) | (~c2_1(a483)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(1614,plain,
% 1.92/1.50 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c1_1(a483)) | (~c3_1(a483)) | (~c2_1(a483)) | c0_1(a483) | (~c3_1(a483)) | (~c1_1(a483)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a483) | (~ndr1_0) | (~c3_1(a483)) | (~c1_1(a483)) | (~c2_1(a483))))),
% 1.92/1.50 inference(monotonicity,[status(thm)],[1613])).
% 1.92/1.50 tff(1615,plain,
% 1.92/1.50 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c1_1(a483)) | (~c3_1(a483)) | (~c2_1(a483)) | c0_1(a483) | (~c3_1(a483)) | (~c1_1(a483)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a483) | (~ndr1_0) | (~c3_1(a483)) | (~c1_1(a483)) | (~c2_1(a483)))),
% 1.92/1.50 inference(transitivity,[status(thm)],[1614, 1612])).
% 1.92/1.50 tff(1616,plain,
% 1.92/1.50 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c1_1(a483)) | (~c3_1(a483)) | (~c2_1(a483)) | c0_1(a483) | (~c3_1(a483)) | (~c1_1(a483)))),
% 1.92/1.50 inference(quant_inst,[status(thm)],[])).
% 1.92/1.50 tff(1617,plain,
% 1.92/1.50 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a483) | (~ndr1_0) | (~c3_1(a483)) | (~c1_1(a483)) | (~c2_1(a483))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[1616, 1615])).
% 1.92/1.50 tff(1618,plain,
% 1.92/1.50 (~c3_1(a483)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[1617, 81, 110, 1611, 1600, 1589, 225])).
% 1.92/1.50 tff(1619,plain,
% 1.92/1.50 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a483) | (~ndr1_0) | c3_1(a483) | (~c2_1(a483)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a483) | (~ndr1_0) | c3_1(a483) | (~c2_1(a483)))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1620,plain,
% 1.92/1.51 ((hskp16 | hskp7 | (~ndr1_0) | c0_1(a483) | c3_1(a483) | (~c2_1(a483))) <=> (hskp16 | hskp7 | c0_1(a483) | (~ndr1_0) | c3_1(a483) | (~c2_1(a483)))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1621,plain,
% 1.92/1.51 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a483) | c3_1(a483) | (~c2_1(a483)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a483) | (~ndr1_0) | c3_1(a483) | (~c2_1(a483))))),
% 1.92/1.51 inference(monotonicity,[status(thm)],[1620])).
% 1.92/1.51 tff(1622,plain,
% 1.92/1.51 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a483) | c3_1(a483) | (~c2_1(a483)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a483) | (~ndr1_0) | c3_1(a483) | (~c2_1(a483)))),
% 1.92/1.51 inference(transitivity,[status(thm)],[1621, 1619])).
% 1.92/1.51 tff(1623,plain,
% 1.92/1.51 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a483) | c3_1(a483) | (~c2_1(a483)))),
% 1.92/1.51 inference(quant_inst,[status(thm)],[])).
% 1.92/1.51 tff(1624,plain,
% 1.92/1.51 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a483) | (~ndr1_0) | c3_1(a483) | (~c2_1(a483))),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1623, 1622])).
% 1.92/1.51 tff(1625,plain,
% 1.92/1.51 (hskp7),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[1624, 81, 110, 1600, 1589, 20, 1618])).
% 1.92/1.51 tff(1626,plain,
% 1.92/1.51 (c0_1(a471)),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[550, 1625])).
% 1.92/1.51 tff(1627,plain,
% 1.92/1.51 (c3_1(a471)),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[539, 1625])).
% 1.92/1.51 tff(1628,plain,
% 1.92/1.51 ($false),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[1274, 1627, 1626, 235, 21, 263, 1251, 29])).
% 1.92/1.51 tff(1629,plain,((~c0_1(a465)) | hskp19 | hskp12 | c1_1(a465) | c2_1(a471) | hskp16 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.92/1.51 tff(1630,plain,
% 1.92/1.51 (~c0_1(a465)),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[1629, 1572, 21, 263, 29, 110, 235])).
% 1.92/1.51 tff(1631,assumption,(c1_1(a529)), introduced(assumption)).
% 1.92/1.51 tff(1632,assumption,(c3_1(a529)), introduced(assumption)).
% 1.92/1.51 tff(1633,assumption,(c0_1(a529)), introduced(assumption)).
% 1.92/1.51 tff(1634,plain,
% 1.92/1.51 (hskp2),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[1444, 31, 264, 263, 373, 21])).
% 1.92/1.51 tff(1635,plain,
% 1.92/1.51 (hskp5 | c0_1(a464) | (~c3_1(a464))),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[627, 81, 21, 237, 41])).
% 1.92/1.51 tff(1636,plain,
% 1.92/1.51 (~c3_1(a464)),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[1635, 31, 238])).
% 1.92/1.51 tff(1637,plain,
% 1.92/1.51 ($false),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[659, 1636, 1634])).
% 1.92/1.51 tff(1638,plain,(hskp5 | c0_1(a464) | hskp12 | c2_1(a464) | c0_1(a465) | c1_1(a465) | (~c3_1(a465))), inference(lemma,lemma(discharge,[]))).
% 1.92/1.51 tff(1639,plain,
% 1.92/1.51 (hskp5),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[1638, 373, 21, 237, 264, 263, 238])).
% 1.92/1.51 tff(1640,plain,
% 1.92/1.51 (~c3_1(a467)),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[1169, 1639])).
% 1.92/1.51 tff(1641,plain,
% 1.92/1.51 (~c1_1(a467)),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[1064, 1639])).
% 1.92/1.51 tff(1642,plain,
% 1.92/1.51 (c0_1(a467)),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[602, 1639])).
% 1.92/1.51 tff(1643,plain,
% 1.92/1.51 (c2_1(a467)),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[570, 81, 110, 1642, 1641, 1640, 564])).
% 1.92/1.51 tff(1644,plain,
% 1.92/1.51 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.92/1.51 inference(bind,[status(th)],[])).
% 1.92/1.51 tff(1645,plain,
% 1.92/1.51 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.92/1.51 inference(quant_intro,[status(thm)],[1644])).
% 1.92/1.51 tff(1646,plain,
% 1.92/1.51 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1647,plain,
% 1.92/1.51 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp7) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp7))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.92/1.51 inference(bind,[status(th)],[])).
% 1.92/1.51 tff(1648,plain,
% 1.92/1.51 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.92/1.51 inference(quant_intro,[status(thm)],[1647])).
% 1.92/1.51 tff(1649,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 1.92/1.51 tff(1650,plain,
% 1.92/1.51 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1649, 1648])).
% 1.92/1.51 tff(1651,plain,
% 1.92/1.51 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1650, 1646])).
% 1.92/1.51 tff(1652,plain,(
% 1.92/1.51 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.92/1.51 inference(skolemize,[status(sab)],[1651])).
% 1.92/1.51 tff(1653,plain,
% 1.92/1.51 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1652, 1645])).
% 1.92/1.51 tff(1654,plain,
% 1.92/1.51 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 1.92/1.51 inference(bind,[status(th)],[])).
% 1.92/1.51 tff(1655,plain,
% 1.92/1.51 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.92/1.51 inference(quant_intro,[status(thm)],[1654])).
% 1.92/1.51 tff(1656,plain,
% 1.92/1.51 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1657,plain,
% 1.92/1.51 (^[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) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 1.92/1.51 inference(bind,[status(th)],[])).
% 1.92/1.51 tff(1658,plain,
% 1.92/1.51 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.92/1.51 inference(quant_intro,[status(thm)],[1657])).
% 1.92/1.51 tff(1659,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 1.92/1.51 tff(1660,plain,
% 1.92/1.51 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1659, 1658])).
% 1.92/1.51 tff(1661,plain,
% 1.92/1.51 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1660, 1656])).
% 1.92/1.51 tff(1662,plain,(
% 1.92/1.51 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.92/1.51 inference(skolemize,[status(sab)],[1661])).
% 1.92/1.51 tff(1663,plain,
% 1.92/1.51 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1662, 1655])).
% 1.92/1.51 tff(1664,plain,
% 1.92/1.51 (~hskp7),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[550, 30])).
% 1.92/1.51 tff(1665,assumption,(~c3_1(a471)), introduced(assumption)).
% 1.92/1.51 tff(1666,plain,
% 1.92/1.51 (^[U: $i] : refl((hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 1.92/1.51 inference(bind,[status(th)],[])).
% 1.92/1.51 tff(1667,plain,
% 1.92/1.51 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.92/1.51 inference(quant_intro,[status(thm)],[1666])).
% 1.92/1.51 tff(1668,plain,
% 1.92/1.51 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1669,plain,
% 1.92/1.51 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp8) <=> ((hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp8))), rewrite(((hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 1.92/1.51 inference(bind,[status(th)],[])).
% 1.92/1.51 tff(1670,plain,
% 1.92/1.51 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp8) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.92/1.51 inference(quant_intro,[status(thm)],[1669])).
% 1.92/1.51 tff(1671,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 1.92/1.51 tff(1672,plain,
% 1.92/1.51 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1671, 1670])).
% 1.92/1.51 tff(1673,plain,
% 1.92/1.51 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1672, 1668])).
% 1.92/1.51 tff(1674,plain,(
% 1.92/1.51 ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.92/1.51 inference(skolemize,[status(sab)],[1673])).
% 1.92/1.51 tff(1675,plain,
% 1.92/1.51 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1674, 1667])).
% 1.92/1.51 tff(1676,plain,
% 1.92/1.51 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1677,plain,
% 1.92/1.51 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a471) | c0_1(a471) | c3_1(a471)) <=> (hskp8 | hskp7 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1678,plain,
% 1.92/1.51 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a471) | c0_1(a471) | c3_1(a471))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0)))),
% 1.92/1.51 inference(monotonicity,[status(thm)],[1677])).
% 1.92/1.51 tff(1679,plain,
% 1.92/1.51 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a471) | c0_1(a471) | c3_1(a471))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0))),
% 1.92/1.51 inference(transitivity,[status(thm)],[1678, 1676])).
% 1.92/1.51 tff(1680,plain,
% 1.92/1.51 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a471) | c0_1(a471) | c3_1(a471))),
% 1.92/1.51 inference(quant_inst,[status(thm)],[])).
% 1.92/1.51 tff(1681,plain,
% 1.92/1.51 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0)),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1680, 1679])).
% 1.92/1.51 tff(1682,plain,
% 1.92/1.51 (hskp8 | hskp7 | c0_1(a471) | c3_1(a471)),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[1681, 81, 29, 1675])).
% 1.92/1.51 tff(1683,plain,
% 1.92/1.51 (hskp8),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[1682, 1665, 30, 1664])).
% 1.92/1.51 tff(1684,plain,
% 1.92/1.51 (((~hskp8) | (~c2_1(a472))) <=> ((~hskp8) | (~c2_1(a472)))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1685,plain,
% 1.92/1.51 (((~c2_1(a472)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a472)))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1686,axiom,((~c2_1(a472)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 1.92/1.51 tff(1687,plain,
% 1.92/1.51 ((~hskp8) | (~c2_1(a472))),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1686, 1685])).
% 1.92/1.51 tff(1688,plain,
% 1.92/1.51 ((~hskp8) | (~c2_1(a472))),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1687, 1684])).
% 1.92/1.51 tff(1689,plain,
% 1.92/1.51 (~c2_1(a472)),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[1688, 1683])).
% 1.92/1.51 tff(1690,plain,
% 1.92/1.51 (((~hskp8) | c3_1(a472)) <=> ((~hskp8) | c3_1(a472))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1691,axiom,((~hskp8) | c3_1(a472)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.92/1.51 tff(1692,plain,
% 1.92/1.51 ((~hskp8) | c3_1(a472)),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1691, 1690])).
% 1.92/1.51 tff(1693,plain,
% 1.92/1.51 ((~hskp8) | c3_1(a472)),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1692, 1690])).
% 1.92/1.51 tff(1694,plain,
% 1.92/1.51 ((~hskp8) | c3_1(a472)),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1693, 1690])).
% 1.92/1.51 tff(1695,plain,
% 1.92/1.51 ((~hskp8) | c3_1(a472)),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1694, 1690])).
% 1.92/1.51 tff(1696,plain,
% 1.92/1.51 ((~hskp8) | c3_1(a472)),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1695, 1690])).
% 1.92/1.51 tff(1697,plain,
% 1.92/1.51 ((~hskp8) | c3_1(a472)),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1696, 1690])).
% 1.92/1.51 tff(1698,plain,
% 1.92/1.51 ((~hskp8) | c3_1(a472)),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1697, 1690])).
% 1.92/1.51 tff(1699,plain,
% 1.92/1.51 ((~hskp8) | c3_1(a472)),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1698, 1690])).
% 1.92/1.51 tff(1700,plain,
% 1.92/1.51 (c3_1(a472)),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[1699, 1683])).
% 1.92/1.51 tff(1701,plain,
% 1.92/1.51 (((~hskp8) | c1_1(a472)) <=> ((~hskp8) | c1_1(a472))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1702,axiom,((~hskp8) | c1_1(a472)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 1.92/1.51 tff(1703,plain,
% 1.92/1.51 ((~hskp8) | c1_1(a472)),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1702, 1701])).
% 1.92/1.51 tff(1704,plain,
% 1.92/1.51 ((~hskp8) | c1_1(a472)),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1703, 1701])).
% 1.92/1.51 tff(1705,plain,
% 1.92/1.51 ((~hskp8) | c1_1(a472)),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1704, 1701])).
% 1.92/1.51 tff(1706,plain,
% 1.92/1.51 ((~hskp8) | c1_1(a472)),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1705, 1701])).
% 1.92/1.51 tff(1707,plain,
% 1.92/1.51 ((~hskp8) | c1_1(a472)),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1706, 1701])).
% 1.92/1.51 tff(1708,plain,
% 1.92/1.51 ((~hskp8) | c1_1(a472)),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1707, 1701])).
% 1.92/1.51 tff(1709,plain,
% 1.92/1.51 ((~hskp8) | c1_1(a472)),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1708, 1701])).
% 1.92/1.51 tff(1710,plain,
% 1.92/1.51 ((~hskp8) | c1_1(a472)),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1709, 1701])).
% 1.92/1.51 tff(1711,plain,
% 1.92/1.51 (c1_1(a472)),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[1710, 1683])).
% 1.92/1.51 tff(1712,plain,
% 1.92/1.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a472) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a472)) | (~c3_1(a472)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a472) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a472)) | (~c3_1(a472)))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1713,plain,
% 1.92/1.51 ((hskp10 | (~ndr1_0) | c2_1(a472) | (~c1_1(a472)) | (~c3_1(a472)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464))) <=> (hskp10 | c2_1(a472) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a472)) | (~c3_1(a472)))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1714,plain,
% 1.92/1.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a472) | (~c1_1(a472)) | (~c3_1(a472)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a472) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a472)) | (~c3_1(a472))))),
% 1.92/1.51 inference(monotonicity,[status(thm)],[1713])).
% 1.92/1.51 tff(1715,plain,
% 1.92/1.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a472) | (~c1_1(a472)) | (~c3_1(a472)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a472) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a472)) | (~c3_1(a472)))),
% 1.92/1.51 inference(transitivity,[status(thm)],[1714, 1712])).
% 1.92/1.51 tff(1716,plain,
% 1.92/1.51 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a472) | (~c1_1(a472)) | (~c3_1(a472)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464)))),
% 1.92/1.51 inference(quant_inst,[status(thm)],[])).
% 1.92/1.51 tff(1717,plain,
% 1.92/1.51 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a472) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a472)) | (~c3_1(a472))),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1716, 1715])).
% 1.92/1.51 tff(1718,plain,
% 1.92/1.51 (~c3_1(a464)),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[1717, 81, 1572, 1711, 1700, 1689, 238, 237, 1663])).
% 1.92/1.51 tff(1719,plain,
% 1.92/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1720,plain,
% 1.92/1.51 (((~ndr1_0) | c0_1(a471) | c3_1(a471) | (~c1_1(a471)) | c0_1(a471) | c2_1(a471) | (~c1_1(a471)) | c3_1(a471) | c0_1(a471) | c2_1(a471)) <=> (c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1721,plain,
% 1.92/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a471) | c3_1(a471) | (~c1_1(a471)) | c0_1(a471) | c2_1(a471) | (~c1_1(a471)) | c3_1(a471) | c0_1(a471) | c2_1(a471))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471))))),
% 1.92/1.51 inference(monotonicity,[status(thm)],[1720])).
% 1.92/1.51 tff(1722,plain,
% 1.92/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a471) | c3_1(a471) | (~c1_1(a471)) | c0_1(a471) | c2_1(a471) | (~c1_1(a471)) | c3_1(a471) | c0_1(a471) | c2_1(a471))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471)))),
% 1.92/1.51 inference(transitivity,[status(thm)],[1721, 1719])).
% 1.92/1.51 tff(1723,plain,
% 1.92/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a471) | c3_1(a471) | (~c1_1(a471)) | c0_1(a471) | c2_1(a471) | (~c1_1(a471)) | c3_1(a471) | c0_1(a471) | c2_1(a471))),
% 1.92/1.51 inference(quant_inst,[status(thm)],[])).
% 1.92/1.51 tff(1724,plain,
% 1.92/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a471))),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1723, 1722])).
% 1.92/1.51 tff(1725,plain,
% 1.92/1.51 (~c1_1(a471)),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[1724, 81, 30, 1665, 29, 10])).
% 1.92/1.51 tff(1726,plain,
% 1.92/1.51 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c1_1(a471))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c1_1(a471))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1727,plain,
% 1.92/1.51 ((hskp16 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c0_1(a467)) | c3_1(a471) | c1_1(a471) | c2_1(a471)) <=> (hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c1_1(a471))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1728,plain,
% 1.92/1.51 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c0_1(a467)) | c3_1(a471) | c1_1(a471) | c2_1(a471))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c1_1(a471)))),
% 1.92/1.51 inference(monotonicity,[status(thm)],[1727])).
% 1.92/1.51 tff(1729,plain,
% 1.92/1.51 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c0_1(a467)) | c3_1(a471) | c1_1(a471) | c2_1(a471))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c1_1(a471))),
% 1.92/1.51 inference(transitivity,[status(thm)],[1728, 1726])).
% 1.92/1.51 tff(1730,plain,
% 1.92/1.51 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c0_1(a467)) | c3_1(a471) | c1_1(a471) | c2_1(a471))),
% 1.92/1.51 inference(quant_inst,[status(thm)],[])).
% 1.92/1.51 tff(1731,plain,
% 1.92/1.51 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c1_1(a471)),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1730, 1729])).
% 1.92/1.51 tff(1732,plain,
% 1.92/1.51 (~c0_1(a467)),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[1731, 81, 110, 1665, 29, 269, 268, 564, 1725])).
% 1.92/1.51 tff(1733,plain,
% 1.92/1.51 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1734,plain,
% 1.92/1.51 ((hskp16 | hskp7 | (~ndr1_0) | c0_1(a467) | c3_1(a467) | (~c2_1(a467))) <=> (hskp16 | hskp7 | c0_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1735,plain,
% 1.92/1.51 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a467) | c3_1(a467) | (~c2_1(a467)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467))))),
% 1.92/1.51 inference(monotonicity,[status(thm)],[1734])).
% 1.92/1.51 tff(1736,plain,
% 1.92/1.51 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a467) | c3_1(a467) | (~c2_1(a467)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)))),
% 1.92/1.51 inference(transitivity,[status(thm)],[1735, 1733])).
% 1.92/1.51 tff(1737,plain,
% 1.92/1.51 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a467) | c3_1(a467) | (~c2_1(a467)))),
% 1.92/1.51 inference(quant_inst,[status(thm)],[])).
% 1.92/1.51 tff(1738,plain,
% 1.92/1.51 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467))),
% 1.92/1.51 inference(modus_ponens,[status(thm)],[1737, 1736])).
% 1.92/1.51 tff(1739,plain,
% 1.92/1.51 (c0_1(a467) | (~c2_1(a467))),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[1738, 81, 110, 1664, 268, 20])).
% 1.92/1.51 tff(1740,plain,
% 1.92/1.51 (~c2_1(a467)),
% 1.92/1.51 inference(unit_resolution,[status(thm)],[1739, 1732])).
% 1.92/1.51 tff(1741,plain,
% 1.92/1.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a472) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c1_1(a472)) | (~c3_1(a472)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a472) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c1_1(a472)) | (~c3_1(a472)))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1742,plain,
% 1.92/1.51 ((hskp10 | (~ndr1_0) | c2_1(a472) | (~c1_1(a472)) | (~c3_1(a472)) | c0_1(a465) | c2_1(a465) | (~c3_1(a465))) <=> (hskp10 | c2_1(a472) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c1_1(a472)) | (~c3_1(a472)))),
% 1.92/1.51 inference(rewrite,[status(thm)],[])).
% 1.92/1.51 tff(1743,plain,
% 1.92/1.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a472) | (~c1_1(a472)) | (~c3_1(a472)) | c0_1(a465) | c2_1(a465) | (~c3_1(a465)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a472) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c1_1(a472)) | (~c3_1(a472))))),
% 1.92/1.51 inference(monotonicity,[status(thm)],[1742])).
% 1.92/1.51 tff(1744,plain,
% 1.92/1.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a472) | (~c1_1(a472)) | (~c3_1(a472)) | c0_1(a465) | c2_1(a465) | (~c3_1(a465)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a472) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c1_1(a472)) | (~c3_1(a472)))),
% 1.92/1.52 inference(transitivity,[status(thm)],[1743, 1741])).
% 1.92/1.52 tff(1745,plain,
% 1.92/1.52 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a472) | (~c1_1(a472)) | (~c3_1(a472)) | c0_1(a465) | c2_1(a465) | (~c3_1(a465)))),
% 1.92/1.52 inference(quant_inst,[status(thm)],[])).
% 1.92/1.52 tff(1746,plain,
% 1.92/1.52 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a472) | c0_1(a465) | (~ndr1_0) | (~c3_1(a465)) | c2_1(a465) | (~c1_1(a472)) | (~c3_1(a472))),
% 1.92/1.52 inference(modus_ponens,[status(thm)],[1745, 1744])).
% 1.92/1.52 tff(1747,plain,
% 1.92/1.52 (c2_1(a465)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[1746, 81, 1572, 1711, 1700, 373, 1689, 264, 1663])).
% 1.92/1.52 tff(1748,plain,
% 1.92/1.52 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c1_1(a467) | c3_1(a467) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c2_1(a467))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c1_1(a467) | c3_1(a467) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c2_1(a467))),
% 1.92/1.52 inference(rewrite,[status(thm)],[])).
% 1.92/1.52 tff(1749,plain,
% 1.92/1.52 ((hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a467) | c1_1(a467) | c2_1(a467)) <=> (hskp2 | c1_1(a467) | c3_1(a467) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c2_1(a467))),
% 1.92/1.52 inference(rewrite,[status(thm)],[])).
% 1.92/1.52 tff(1750,plain,
% 1.92/1.52 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a467) | c1_1(a467) | c2_1(a467))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c1_1(a467) | c3_1(a467) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c2_1(a467)))),
% 1.92/1.52 inference(monotonicity,[status(thm)],[1749])).
% 1.92/1.52 tff(1751,plain,
% 1.92/1.52 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a467) | c1_1(a467) | c2_1(a467))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c1_1(a467) | c3_1(a467) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c2_1(a467))),
% 1.92/1.52 inference(transitivity,[status(thm)],[1750, 1748])).
% 1.92/1.52 tff(1752,plain,
% 1.92/1.52 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a467) | c1_1(a467) | c2_1(a467))),
% 1.92/1.52 inference(quant_inst,[status(thm)],[])).
% 1.92/1.52 tff(1753,plain,
% 1.92/1.52 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c1_1(a467) | c3_1(a467) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c2_1(a467)),
% 1.92/1.52 inference(modus_ponens,[status(thm)],[1752, 1751])).
% 1.92/1.52 tff(1754,plain,
% 1.92/1.52 (hskp2 | c1_1(a467) | (~c2_1(a465)) | c2_1(a467)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[1753, 81, 373, 268, 263, 648])).
% 1.92/1.52 tff(1755,plain,
% 1.92/1.52 (hskp2),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[1754, 1747, 269, 1740])).
% 1.92/1.52 tff(1756,plain,
% 1.92/1.52 ($false),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[659, 1755, 1718])).
% 1.92/1.52 tff(1757,plain,(c3_1(a471) | c1_1(a467) | (~c3_1(a465)) | c3_1(a467) | c1_1(a465) | hskp16 | hskp10 | c0_1(a464) | c2_1(a464) | c0_1(a465) | c2_1(a471) | c0_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.92/1.52 tff(1758,plain,
% 1.92/1.52 (c3_1(a471)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[1757, 269, 373, 268, 263, 110, 1572, 238, 237, 264, 29, 30])).
% 1.92/1.52 tff(1759,plain,
% 1.92/1.52 (hskp5),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[88, 1758, 30])).
% 1.92/1.52 tff(1760,plain,
% 1.92/1.52 (c0_1(a467)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[602, 1759])).
% 1.92/1.52 tff(1761,plain,
% 1.92/1.52 ((~c0_1(a467)) | c2_1(a467)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[570, 81, 110, 269, 268, 564])).
% 1.92/1.52 tff(1762,plain,
% 1.92/1.52 (c2_1(a467)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[1761, 1760])).
% 1.92/1.52 tff(1763,plain,
% 1.92/1.52 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)) | (~c2_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)) | (~c2_1(a467)))),
% 1.92/1.52 inference(rewrite,[status(thm)],[])).
% 1.92/1.52 tff(1764,plain,
% 1.92/1.52 ((hskp7 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c2_1(a529)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467))) <=> (hskp7 | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)) | (~c2_1(a467)))),
% 1.92/1.52 inference(rewrite,[status(thm)],[])).
% 1.92/1.52 tff(1765,plain,
% 1.92/1.52 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c2_1(a529)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)) | (~c2_1(a467))))),
% 1.92/1.52 inference(monotonicity,[status(thm)],[1764])).
% 1.92/1.52 tff(1766,plain,
% 1.92/1.52 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c2_1(a529)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)) | (~c2_1(a467)))),
% 1.92/1.52 inference(transitivity,[status(thm)],[1765, 1763])).
% 1.92/1.52 tff(1767,plain,
% 1.92/1.52 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c2_1(a529)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))),
% 1.92/1.52 inference(quant_inst,[status(thm)],[])).
% 1.92/1.52 tff(1768,plain,
% 1.92/1.52 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)) | (~c2_1(a467))),
% 1.92/1.52 inference(modus_ponens,[status(thm)],[1767, 1766])).
% 1.92/1.52 tff(1769,plain,
% 1.92/1.52 ((~c2_1(a529)) | (~c0_1(a467)) | (~c2_1(a467))),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[1768, 81, 1664, 1631, 1632, 268, 1653])).
% 1.92/1.52 tff(1770,plain,
% 1.92/1.52 (~c2_1(a529)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[1769, 1762, 1760])).
% 1.92/1.52 tff(1771,plain,
% 1.92/1.52 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c1_1(a467) | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)) | (~c0_1(a467)) | (~c2_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c1_1(a467) | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)) | (~c0_1(a467)) | (~c2_1(a467)))),
% 1.92/1.52 inference(rewrite,[status(thm)],[])).
% 1.92/1.52 tff(1772,plain,
% 1.92/1.52 ((hskp12 | (~ndr1_0) | c2_1(a529) | (~c3_1(a529)) | (~c0_1(a529)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467))) <=> (hskp12 | c1_1(a467) | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)) | (~c0_1(a467)) | (~c2_1(a467)))),
% 1.92/1.52 inference(rewrite,[status(thm)],[])).
% 1.92/1.52 tff(1773,plain,
% 1.92/1.52 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a529) | (~c3_1(a529)) | (~c0_1(a529)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c1_1(a467) | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)) | (~c0_1(a467)) | (~c2_1(a467))))),
% 1.92/1.52 inference(monotonicity,[status(thm)],[1772])).
% 1.92/1.52 tff(1774,plain,
% 1.92/1.52 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a529) | (~c3_1(a529)) | (~c0_1(a529)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c1_1(a467) | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)) | (~c0_1(a467)) | (~c2_1(a467)))),
% 1.92/1.52 inference(transitivity,[status(thm)],[1773, 1771])).
% 1.92/1.52 tff(1775,plain,
% 1.92/1.52 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a529) | (~c3_1(a529)) | (~c0_1(a529)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))),
% 1.92/1.52 inference(quant_inst,[status(thm)],[])).
% 1.92/1.52 tff(1776,plain,
% 1.92/1.52 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c1_1(a467) | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)) | (~c0_1(a467)) | (~c2_1(a467))),
% 1.92/1.52 inference(modus_ponens,[status(thm)],[1775, 1774])).
% 1.92/1.52 tff(1777,plain,
% 1.92/1.52 ($false),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[1776, 81, 21, 1633, 1632, 1760, 269, 582, 1770, 1762])).
% 1.92/1.52 tff(1778,plain,(c1_1(a467) | hskp12 | (~c0_1(a529)) | (~c3_1(a529)) | (~c1_1(a529)) | c3_1(a467) | hskp16 | c0_1(a471) | c2_1(a471) | (~c3_1(a465)) | c1_1(a465) | hskp10 | c0_1(a464) | c2_1(a464) | c0_1(a465)), inference(lemma,lemma(discharge,[]))).
% 1.92/1.52 tff(1779,plain,
% 1.92/1.52 (c0_1(a471)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[1778, 1640, 1633, 1632, 1631, 21, 110, 1641, 29, 373, 263, 1572, 238, 237, 264])).
% 1.92/1.52 tff(1780,plain,
% 1.92/1.52 (~c3_1(a471)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[591, 1779, 21, 1641, 29, 1640, 110, 1642])).
% 1.92/1.52 tff(1781,plain,
% 1.92/1.52 (~hskp7),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[539, 1780])).
% 1.92/1.52 tff(1782,plain,
% 1.92/1.52 (~c2_1(a529)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[1768, 81, 1781, 1631, 1632, 1642, 1640, 1653, 1643])).
% 1.92/1.52 tff(1783,plain,
% 1.92/1.52 ($false),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[1776, 81, 21, 1633, 1632, 1642, 1641, 582, 1782, 1643])).
% 1.92/1.52 tff(1784,plain,((~c3_1(a465)) | hskp12 | (~c0_1(a529)) | (~c3_1(a529)) | (~c1_1(a529)) | hskp16 | c2_1(a471) | c1_1(a465) | hskp10 | c0_1(a464) | c2_1(a464) | c0_1(a465)), inference(lemma,lemma(discharge,[]))).
% 1.92/1.52 tff(1785,plain,
% 1.92/1.52 (~c3_1(a465)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[1784, 238, 1633, 1632, 1631, 110, 29, 263, 1572, 21, 237, 264])).
% 1.92/1.52 tff(1786,plain,
% 1.92/1.52 (~hskp3),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[442, 1785])).
% 1.92/1.52 tff(1787,plain,
% 1.92/1.52 (hskp29),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[457, 1786, 21])).
% 1.92/1.52 tff(1788,plain,
% 1.92/1.52 (c2_1(a474)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[340, 1787])).
% 1.92/1.52 tff(1789,plain,
% 1.92/1.52 (c1_1(a474)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[351, 1787])).
% 1.92/1.52 tff(1790,plain,
% 1.92/1.52 (c0_1(a474)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[362, 1787])).
% 1.92/1.52 tff(1791,plain,
% 1.92/1.52 (hskp14),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[1582, 81, 1572, 1790, 1789, 1788, 1567])).
% 1.92/1.52 tff(1792,plain,
% 1.92/1.52 (~c0_1(a483)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[1588, 1791])).
% 1.92/1.52 tff(1793,plain,
% 1.92/1.52 (c2_1(a483)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[1599, 1791])).
% 1.92/1.52 tff(1794,plain,
% 1.92/1.52 (c1_1(a483)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[1610, 1791])).
% 1.92/1.52 tff(1795,plain,
% 1.92/1.52 (~c3_1(a483)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[1617, 81, 110, 1794, 1793, 1792, 225])).
% 1.92/1.52 tff(1796,plain,
% 1.92/1.52 (hskp7),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[1624, 81, 110, 1793, 1792, 20, 1795])).
% 1.92/1.52 tff(1797,plain,
% 1.92/1.52 (c0_1(a471)),
% 1.92/1.52 inference(unit_resolution,[status(thm)],[550, 1796])).
% 1.92/1.52 tff(1798,plain,
% 1.92/1.52 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c0_1(a483) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a483)) | (~c2_1(a483)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a483) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a483)) | (~c2_1(a483)))),
% 1.95/1.52 inference(rewrite,[status(thm)],[])).
% 1.95/1.52 tff(1799,plain,
% 1.95/1.52 (((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a483) | (~c1_1(a483)) | (~c2_1(a483))) <=> (c0_1(a483) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a483)) | (~c2_1(a483)))),
% 1.95/1.52 inference(rewrite,[status(thm)],[])).
% 1.95/1.52 tff(1800,plain,
% 1.95/1.52 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a483) | (~c1_1(a483)) | (~c2_1(a483)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (c0_1(a483) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a483)) | (~c2_1(a483))))),
% 1.95/1.52 inference(monotonicity,[status(thm)],[1799])).
% 1.95/1.52 tff(1801,plain,
% 1.95/1.52 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a483) | (~c1_1(a483)) | (~c2_1(a483)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a483) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a483)) | (~c2_1(a483)))),
% 1.95/1.52 inference(transitivity,[status(thm)],[1800, 1798])).
% 1.95/1.52 tff(1802,plain,
% 1.95/1.52 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | c2_1(a471) | c1_1(a471) | (~c0_1(a471)) | c0_1(a483) | (~c1_1(a483)) | (~c2_1(a483)))),
% 1.95/1.52 inference(quant_inst,[status(thm)],[])).
% 1.95/1.52 tff(1803,plain,
% 1.95/1.52 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | c0_1(a483) | c2_1(a471) | (~ndr1_0) | c1_1(a471) | (~c0_1(a471)) | (~c1_1(a483)) | (~c2_1(a483))),
% 1.95/1.52 inference(modus_ponens,[status(thm)],[1802, 1801])).
% 1.95/1.52 tff(1804,plain,
% 1.95/1.52 (c1_1(a471) | (~c0_1(a471))),
% 1.95/1.52 inference(unit_resolution,[status(thm)],[1803, 81, 1794, 1793, 1792, 29, 405])).
% 1.95/1.52 tff(1805,plain,
% 1.95/1.52 (c1_1(a471)),
% 1.95/1.52 inference(unit_resolution,[status(thm)],[1804, 1797])).
% 1.95/1.52 tff(1806,plain,
% 1.95/1.52 (c3_1(a471)),
% 1.95/1.52 inference(unit_resolution,[status(thm)],[539, 1796])).
% 1.95/1.52 tff(1807,plain,
% 1.95/1.52 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a471) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a471)) | (~c3_1(a471)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a471) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a471)) | (~c3_1(a471)))),
% 1.95/1.52 inference(rewrite,[status(thm)],[])).
% 1.95/1.52 tff(1808,plain,
% 1.95/1.52 ((hskp10 | (~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c3_1(a471)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464))) <=> (hskp10 | c2_1(a471) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a471)) | (~c3_1(a471)))),
% 1.95/1.52 inference(rewrite,[status(thm)],[])).
% 1.95/1.52 tff(1809,plain,
% 1.95/1.52 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c3_1(a471)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a471) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a471)) | (~c3_1(a471))))),
% 1.95/1.52 inference(monotonicity,[status(thm)],[1808])).
% 1.95/1.52 tff(1810,plain,
% 1.95/1.52 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c3_1(a471)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a471) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a471)) | (~c3_1(a471)))),
% 1.95/1.52 inference(transitivity,[status(thm)],[1809, 1807])).
% 1.95/1.52 tff(1811,plain,
% 1.95/1.52 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c3_1(a471)) | c0_1(a464) | c2_1(a464) | (~c3_1(a464)))),
% 1.95/1.52 inference(quant_inst,[status(thm)],[])).
% 1.95/1.52 tff(1812,plain,
% 1.95/1.52 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a471) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c3_1(a464)) | (~c1_1(a471)) | (~c3_1(a471))),
% 1.95/1.52 inference(modus_ponens,[status(thm)],[1811, 1810])).
% 1.95/1.52 tff(1813,plain,
% 1.95/1.52 ((~c3_1(a464)) | (~c1_1(a471)) | (~c3_1(a471))),
% 1.95/1.52 inference(unit_resolution,[status(thm)],[1812, 81, 1572, 29, 238, 237, 1663])).
% 1.95/1.52 tff(1814,plain,
% 1.95/1.52 (~c3_1(a464)),
% 1.95/1.52 inference(unit_resolution,[status(thm)],[1813, 1806, 1805])).
% 1.95/1.52 tff(1815,plain,
% 1.95/1.52 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.95/1.52 inference(bind,[status(th)],[])).
% 1.95/1.52 tff(1816,plain,
% 1.95/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.95/1.52 inference(quant_intro,[status(thm)],[1815])).
% 1.95/1.52 tff(1817,plain,
% 1.95/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.95/1.52 inference(rewrite,[status(thm)],[])).
% 1.95/1.52 tff(1818,plain,
% 1.95/1.52 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.95/1.52 inference(bind,[status(th)],[])).
% 1.95/1.52 tff(1819,plain,
% 1.95/1.52 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.95/1.52 inference(quant_intro,[status(thm)],[1818])).
% 1.95/1.52 tff(1820,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 1.95/1.52 tff(1821,plain,
% 1.95/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.95/1.52 inference(modus_ponens,[status(thm)],[1820, 1819])).
% 1.95/1.52 tff(1822,plain,
% 1.95/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.95/1.52 inference(modus_ponens,[status(thm)],[1821, 1817])).
% 1.95/1.52 tff(1823,plain,(
% 1.95/1.52 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.95/1.52 inference(skolemize,[status(sab)],[1822])).
% 1.95/1.52 tff(1824,plain,
% 1.95/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.95/1.52 inference(modus_ponens,[status(thm)],[1823, 1816])).
% 1.95/1.52 tff(1825,plain,
% 1.95/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a465) | c3_1(a464) | c0_1(a465) | c1_1(a465) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a465) | c3_1(a464) | c0_1(a465) | c1_1(a465) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.95/1.52 inference(rewrite,[status(thm)],[])).
% 1.95/1.52 tff(1826,plain,
% 1.95/1.52 (((~ndr1_0) | c2_1(a464) | c3_1(a464) | (~c1_1(a464)) | c0_1(a464) | c2_1(a464) | (~c1_1(a464)) | c3_1(a465) | c1_1(a465) | c0_1(a465)) <=> (c3_1(a465) | c3_1(a464) | c0_1(a465) | c1_1(a465) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.95/1.52 inference(rewrite,[status(thm)],[])).
% 1.95/1.52 tff(1827,plain,
% 1.95/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a464) | c3_1(a464) | (~c1_1(a464)) | c0_1(a464) | c2_1(a464) | (~c1_1(a464)) | c3_1(a465) | c1_1(a465) | c0_1(a465))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a465) | c3_1(a464) | c0_1(a465) | c1_1(a465) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464))))),
% 1.95/1.52 inference(monotonicity,[status(thm)],[1826])).
% 1.95/1.52 tff(1828,plain,
% 1.95/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a464) | c3_1(a464) | (~c1_1(a464)) | c0_1(a464) | c2_1(a464) | (~c1_1(a464)) | c3_1(a465) | c1_1(a465) | c0_1(a465))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a465) | c3_1(a464) | c0_1(a465) | c1_1(a465) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464)))),
% 1.95/1.52 inference(transitivity,[status(thm)],[1827, 1825])).
% 1.95/1.52 tff(1829,plain,
% 1.95/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a464) | c3_1(a464) | (~c1_1(a464)) | c0_1(a464) | c2_1(a464) | (~c1_1(a464)) | c3_1(a465) | c1_1(a465) | c0_1(a465))),
% 1.95/1.52 inference(quant_inst,[status(thm)],[])).
% 1.95/1.52 tff(1830,plain,
% 1.95/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a465) | c3_1(a464) | c0_1(a465) | c1_1(a465) | c0_1(a464) | c2_1(a464) | (~ndr1_0) | (~c1_1(a464))),
% 1.95/1.52 inference(modus_ponens,[status(thm)],[1829, 1828])).
% 1.95/1.52 tff(1831,plain,
% 1.95/1.52 (c3_1(a464) | (~c1_1(a464))),
% 1.95/1.52 inference(unit_resolution,[status(thm)],[1830, 81, 1785, 264, 263, 238, 237, 1824])).
% 1.95/1.52 tff(1832,plain,
% 1.95/1.52 (~c1_1(a464)),
% 1.95/1.52 inference(unit_resolution,[status(thm)],[1831, 1814])).
% 1.95/1.52 tff(1833,plain,
% 1.95/1.52 (~hskp2),
% 1.95/1.52 inference(unit_resolution,[status(thm)],[659, 1814])).
% 1.95/1.52 tff(1834,plain,
% 1.95/1.52 (hskp1),
% 1.95/1.52 inference(unit_resolution,[status(thm)],[1117, 1833, 238, 1832])).
% 1.95/1.52 tff(1835,plain,
% 1.95/1.52 (~c3_1(a463)),
% 1.95/1.52 inference(unit_resolution,[status(thm)],[1123, 1834])).
% 1.95/1.52 tff(1836,plain,
% 1.95/1.52 (~c1_1(a463)),
% 1.95/1.52 inference(unit_resolution,[status(thm)],[1129, 1834])).
% 1.95/1.52 tff(1837,plain,
% 1.95/1.52 (c2_1(a463)),
% 1.95/1.52 inference(unit_resolution,[status(thm)],[1140, 1834])).
% 1.95/1.52 tff(1838,plain,
% 1.95/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a483) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a483) | (~c1_1(a483)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a483) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a483) | (~c1_1(a483)))),
% 1.95/1.52 inference(rewrite,[status(thm)],[])).
% 1.95/1.52 tff(1839,plain,
% 1.95/1.52 (((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c3_1(a483) | c0_1(a483) | (~c1_1(a483))) <=> (c0_1(a483) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a483) | (~c1_1(a483)))),
% 1.95/1.52 inference(rewrite,[status(thm)],[])).
% 1.95/1.52 tff(1840,plain,
% 1.95/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c3_1(a483) | c0_1(a483) | (~c1_1(a483)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a483) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a483) | (~c1_1(a483))))),
% 1.95/1.52 inference(monotonicity,[status(thm)],[1839])).
% 1.95/1.52 tff(1841,plain,
% 1.95/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c3_1(a483) | c0_1(a483) | (~c1_1(a483)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a483) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a483) | (~c1_1(a483)))),
% 1.95/1.52 inference(transitivity,[status(thm)],[1840, 1838])).
% 1.95/1.52 tff(1842,plain,
% 1.95/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a471) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a463) | c1_1(a463) | (~c2_1(a463)) | c3_1(a483) | c0_1(a483) | (~c1_1(a483)))),
% 1.95/1.52 inference(quant_inst,[status(thm)],[])).
% 1.95/1.52 tff(1843,plain,
% 1.95/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a483) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c2_1(a463)) | (~c1_1(a471)) | (~c0_1(a471)) | c3_1(a483) | (~c1_1(a483))),
% 1.95/1.52 inference(modus_ponens,[status(thm)],[1842, 1841])).
% 1.95/1.52 tff(1844,plain,
% 1.95/1.52 ($false),
% 1.95/1.52 inference(unit_resolution,[status(thm)],[1843, 81, 1794, 1797, 1837, 1792, 29, 1836, 1835, 499, 1805, 1795])).
% 1.95/1.52 tff(1845,plain,(c0_1(a464) | c2_1(a471) | c2_1(a464) | c0_1(a465) | c1_1(a465) | hskp10 | hskp16 | hskp12 | (~c0_1(a529)) | (~c3_1(a529)) | (~c1_1(a529))), inference(lemma,lemma(discharge,[]))).
% 1.95/1.52 tff(1846,plain,
% 1.95/1.52 (c0_1(a464)),
% 1.95/1.52 inference(unit_resolution,[status(thm)],[1845, 264, 237, 29, 263, 1572, 110, 21, 1633, 1632, 1631])).
% 1.95/1.52 tff(1847,plain,
% 1.95/1.52 (~hskp2),
% 1.95/1.52 inference(unit_resolution,[status(thm)],[1363, 1846])).
% 1.95/1.52 tff(1848,plain,
% 1.95/1.52 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.95/1.52 inference(bind,[status(th)],[])).
% 1.95/1.52 tff(1849,plain,
% 1.95/1.52 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.95/1.52 inference(quant_intro,[status(thm)],[1848])).
% 1.95/1.52 tff(1850,plain,
% 1.95/1.52 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.95/1.52 inference(rewrite,[status(thm)],[])).
% 1.95/1.52 tff(1851,plain,
% 1.95/1.52 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_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)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp2))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.95/1.53 inference(bind,[status(th)],[])).
% 1.95/1.53 tff(1852,plain,
% 1.95/1.53 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.95/1.53 inference(quant_intro,[status(thm)],[1851])).
% 1.95/1.53 tff(1853,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 1.95/1.53 tff(1854,plain,
% 1.95/1.53 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.95/1.53 inference(modus_ponens,[status(thm)],[1853, 1852])).
% 1.95/1.53 tff(1855,plain,
% 1.95/1.53 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.95/1.53 inference(modus_ponens,[status(thm)],[1854, 1850])).
% 1.95/1.53 tff(1856,plain,(
% 1.95/1.53 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.95/1.53 inference(skolemize,[status(sab)],[1855])).
% 1.95/1.53 tff(1857,plain,
% 1.95/1.53 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.95/1.53 inference(modus_ponens,[status(thm)],[1856, 1849])).
% 1.95/1.53 tff(1858,assumption,(hskp5), introduced(assumption)).
% 1.95/1.53 tff(1859,plain,
% 1.95/1.53 (~c3_1(a467)),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[1169, 1858])).
% 1.95/1.53 tff(1860,plain,
% 1.95/1.53 (~c1_1(a467)),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[1064, 1858])).
% 1.95/1.53 tff(1861,plain,
% 1.95/1.53 (c0_1(a467)),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[602, 1858])).
% 1.95/1.53 tff(1862,plain,
% 1.95/1.53 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)))),
% 1.95/1.53 inference(rewrite,[status(thm)],[])).
% 1.95/1.53 tff(1863,plain,
% 1.95/1.53 ((hskp2 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467))) <=> (hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)))),
% 1.95/1.53 inference(rewrite,[status(thm)],[])).
% 1.95/1.53 tff(1864,plain,
% 1.95/1.53 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c0_1(a467))))),
% 1.95/1.53 inference(monotonicity,[status(thm)],[1863])).
% 1.95/1.53 tff(1865,plain,
% 1.95/1.53 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c0_1(a467)))),
% 1.95/1.53 inference(transitivity,[status(thm)],[1864, 1862])).
% 1.95/1.53 tff(1866,plain,
% 1.95/1.53 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467)))),
% 1.95/1.53 inference(quant_inst,[status(thm)],[])).
% 1.95/1.53 tff(1867,plain,
% 1.95/1.53 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c0_1(a467))),
% 1.95/1.53 inference(modus_ponens,[status(thm)],[1866, 1865])).
% 1.95/1.53 tff(1868,plain,
% 1.95/1.53 ($false),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[1867, 81, 1373, 1633, 1631, 1632, 1861, 1860, 1859, 1857])).
% 1.95/1.53 tff(1869,plain,((~hskp5) | hskp2 | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a529))), inference(lemma,lemma(discharge,[]))).
% 1.95/1.53 tff(1870,plain,
% 1.95/1.53 (~hskp5),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[1869, 1847, 1633, 1631, 1632])).
% 1.95/1.53 tff(1871,plain,
% 1.95/1.53 (~c3_1(a465)),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[1444, 1870, 264, 263, 1847, 21])).
% 1.95/1.53 tff(1872,plain,
% 1.95/1.53 (~hskp3),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[442, 1871])).
% 1.95/1.53 tff(1873,plain,
% 1.95/1.53 (hskp29),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[457, 1872, 21])).
% 1.95/1.53 tff(1874,plain,
% 1.95/1.53 (c2_1(a474)),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[340, 1873])).
% 1.95/1.53 tff(1875,plain,
% 1.95/1.53 (c1_1(a474)),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[351, 1873])).
% 1.95/1.53 tff(1876,plain,
% 1.95/1.53 (c0_1(a474)),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[362, 1873])).
% 1.95/1.53 tff(1877,plain,
% 1.95/1.53 (hskp14),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[1582, 81, 1572, 1876, 1875, 1874, 1567])).
% 1.95/1.53 tff(1878,plain,
% 1.95/1.53 (~c0_1(a483)),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[1588, 1877])).
% 1.95/1.53 tff(1879,plain,
% 1.95/1.53 (c2_1(a483)),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[1599, 1877])).
% 1.95/1.53 tff(1880,plain,
% 1.95/1.53 (c1_1(a483)),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[1610, 1877])).
% 1.95/1.53 tff(1881,plain,
% 1.95/1.53 (~c3_1(a483)),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[1617, 81, 110, 1880, 1879, 1878, 225])).
% 1.95/1.53 tff(1882,plain,
% 1.95/1.53 (hskp7),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[1624, 81, 110, 1879, 1878, 20, 1881])).
% 1.95/1.53 tff(1883,plain,
% 1.95/1.53 (c0_1(a471)),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[550, 1882])).
% 1.95/1.53 tff(1884,plain,
% 1.95/1.53 (c1_1(a471) | (~c0_1(a471))),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[1803, 81, 1880, 1879, 1878, 29, 405])).
% 1.95/1.53 tff(1885,plain,
% 1.95/1.53 (c1_1(a471)),
% 1.95/1.53 inference(unit_resolution,[status(thm)],[1884, 1883])).
% 1.95/1.53 tff(1886,plain,
% 1.95/1.53 ((hskp23 | hskp5 | hskp3) <=> (hskp23 | hskp5 | hskp3)),
% 1.95/1.53 inference(rewrite,[status(thm)],[])).
% 1.95/1.53 tff(1887,plain,
% 1.95/1.53 (((hskp5 | hskp3) | hskp23) <=> (hskp23 | hskp5 | hskp3)),
% 1.95/1.53 inference(rewrite,[status(thm)],[])).
% 1.95/1.53 tff(1888,plain,
% 1.96/1.53 ((hskp5 | hskp3) <=> (hskp5 | hskp3)),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(1889,plain,
% 1.96/1.53 (((hskp5 | hskp3) | hskp23) <=> ((hskp5 | hskp3) | hskp23)),
% 1.96/1.53 inference(monotonicity,[status(thm)],[1888])).
% 1.96/1.53 tff(1890,plain,
% 1.96/1.53 (((hskp5 | hskp3) | hskp23) <=> (hskp23 | hskp5 | hskp3)),
% 1.96/1.53 inference(transitivity,[status(thm)],[1889, 1887])).
% 1.96/1.53 tff(1891,axiom,((hskp5 | hskp3) | hskp23), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 1.96/1.53 tff(1892,plain,
% 1.96/1.53 (hskp23 | hskp5 | hskp3),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[1891, 1890])).
% 1.96/1.53 tff(1893,plain,
% 1.96/1.53 (hskp23 | hskp5 | hskp3),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[1892, 1886])).
% 1.96/1.53 tff(1894,plain,
% 1.96/1.53 (hskp23 | hskp5 | hskp3),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[1893, 1886])).
% 1.96/1.53 tff(1895,plain,
% 1.96/1.53 (hskp23 | hskp5 | hskp3),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[1894, 1886])).
% 1.96/1.53 tff(1896,plain,
% 1.96/1.53 (hskp23 | hskp5 | hskp3),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[1895, 1886])).
% 1.96/1.53 tff(1897,plain,
% 1.96/1.53 (hskp23 | hskp5 | hskp3),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[1896, 1886])).
% 1.96/1.53 tff(1898,plain,
% 1.96/1.53 (hskp23 | hskp5 | hskp3),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[1897, 1886])).
% 1.96/1.53 tff(1899,plain,
% 1.96/1.53 (hskp23 | hskp5 | hskp3),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[1898, 1886])).
% 1.96/1.53 tff(1900,plain,
% 1.96/1.53 (hskp23),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1899, 1872, 1870])).
% 1.96/1.53 tff(1901,plain,
% 1.96/1.53 (((~hskp23) | (~c3_1(a521))) <=> ((~hskp23) | (~c3_1(a521)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(1902,plain,
% 1.96/1.53 (((~c3_1(a521)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a521)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(1903,axiom,((~c3_1(a521)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 1.96/1.53 tff(1904,plain,
% 1.96/1.53 ((~hskp23) | (~c3_1(a521))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[1903, 1902])).
% 1.96/1.53 tff(1905,plain,
% 1.96/1.53 ((~hskp23) | (~c3_1(a521))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[1904, 1901])).
% 1.96/1.53 tff(1906,plain,
% 1.96/1.53 (~c3_1(a521)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1905, 1900])).
% 1.96/1.53 tff(1907,plain,
% 1.96/1.53 (((~hskp23) | (~c2_1(a521))) <=> ((~hskp23) | (~c2_1(a521)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(1908,plain,
% 1.96/1.53 (((~c2_1(a521)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a521)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(1909,axiom,((~c2_1(a521)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 1.96/1.53 tff(1910,plain,
% 1.96/1.53 ((~hskp23) | (~c2_1(a521))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[1909, 1908])).
% 1.96/1.53 tff(1911,plain,
% 1.96/1.53 ((~hskp23) | (~c2_1(a521))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[1910, 1907])).
% 1.96/1.53 tff(1912,plain,
% 1.96/1.53 (~c2_1(a521)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1911, 1900])).
% 1.96/1.53 tff(1913,plain,
% 1.96/1.53 (((~hskp23) | (~c0_1(a521))) <=> ((~hskp23) | (~c0_1(a521)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(1914,plain,
% 1.96/1.53 (((~c0_1(a521)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a521)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(1915,axiom,((~c0_1(a521)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 1.96/1.53 tff(1916,plain,
% 1.96/1.53 ((~hskp23) | (~c0_1(a521))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[1915, 1914])).
% 1.96/1.53 tff(1917,plain,
% 1.96/1.53 ((~hskp23) | (~c0_1(a521))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[1916, 1913])).
% 1.96/1.53 tff(1918,plain,
% 1.96/1.53 (~c0_1(a521)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1917, 1900])).
% 1.96/1.53 tff(1919,plain,
% 1.96/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0) | (~c1_1(a521)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0) | (~c1_1(a521)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(1920,plain,
% 1.96/1.53 (((~ndr1_0) | c0_1(a521) | c3_1(a521) | (~c1_1(a521)) | c0_1(a521) | c2_1(a521) | (~c1_1(a521)) | c3_1(a521) | c0_1(a521) | c2_1(a521)) <=> (c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0) | (~c1_1(a521)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(1921,plain,
% 1.96/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a521) | c3_1(a521) | (~c1_1(a521)) | c0_1(a521) | c2_1(a521) | (~c1_1(a521)) | c3_1(a521) | c0_1(a521) | c2_1(a521))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0) | (~c1_1(a521))))),
% 1.96/1.53 inference(monotonicity,[status(thm)],[1920])).
% 1.96/1.53 tff(1922,plain,
% 1.96/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a521) | c3_1(a521) | (~c1_1(a521)) | c0_1(a521) | c2_1(a521) | (~c1_1(a521)) | c3_1(a521) | c0_1(a521) | c2_1(a521))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0) | (~c1_1(a521)))),
% 1.96/1.53 inference(transitivity,[status(thm)],[1921, 1919])).
% 1.96/1.53 tff(1923,plain,
% 1.96/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c0_1(a521) | c3_1(a521) | (~c1_1(a521)) | c0_1(a521) | c2_1(a521) | (~c1_1(a521)) | c3_1(a521) | c0_1(a521) | c2_1(a521))),
% 1.96/1.53 inference(quant_inst,[status(thm)],[])).
% 1.96/1.53 tff(1924,plain,
% 1.96/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0) | (~c1_1(a521))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[1923, 1922])).
% 1.96/1.53 tff(1925,plain,
% 1.96/1.53 (~c1_1(a521)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1924, 81, 1918, 1912, 1906, 10])).
% 1.96/1.53 tff(1926,plain,
% 1.96/1.53 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a521) | c2_1(a521) | (~ndr1_0) | c1_1(a521))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a521) | c2_1(a521) | (~ndr1_0) | c1_1(a521))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(1927,plain,
% 1.96/1.53 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a521) | c1_1(a521) | c0_1(a521)) <=> (hskp2 | hskp1 | c0_1(a521) | c2_1(a521) | (~ndr1_0) | c1_1(a521))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(1928,plain,
% 1.96/1.53 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a521) | c1_1(a521) | c0_1(a521))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a521) | c2_1(a521) | (~ndr1_0) | c1_1(a521)))),
% 1.96/1.53 inference(monotonicity,[status(thm)],[1927])).
% 1.96/1.53 tff(1929,plain,
% 1.96/1.53 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a521) | c1_1(a521) | c0_1(a521))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a521) | c2_1(a521) | (~ndr1_0) | c1_1(a521))),
% 1.96/1.53 inference(transitivity,[status(thm)],[1928, 1926])).
% 1.96/1.53 tff(1930,plain,
% 1.96/1.53 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a521) | c1_1(a521) | c0_1(a521))),
% 1.96/1.53 inference(quant_inst,[status(thm)],[])).
% 1.96/1.53 tff(1931,plain,
% 1.96/1.53 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a521) | c2_1(a521) | (~ndr1_0) | c1_1(a521)),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[1930, 1929])).
% 1.96/1.53 tff(1932,plain,
% 1.96/1.53 (hskp1),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1931, 81, 1847, 1918, 1912, 1110, 1925])).
% 1.96/1.53 tff(1933,plain,
% 1.96/1.53 (~c3_1(a463)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1123, 1932])).
% 1.96/1.53 tff(1934,plain,
% 1.96/1.53 (~c1_1(a463)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1129, 1932])).
% 1.96/1.53 tff(1935,plain,
% 1.96/1.53 (c2_1(a463)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1140, 1932])).
% 1.96/1.53 tff(1936,plain,
% 1.96/1.53 ($false),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1843, 81, 1880, 1883, 1935, 1878, 29, 1934, 1933, 499, 1885, 1881])).
% 1.96/1.53 tff(1937,plain,(c0_1(a465) | c2_1(a471) | hskp16 | hskp10 | hskp12 | c1_1(a465) | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a529)) | c2_1(a464)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.53 tff(1938,plain,
% 1.96/1.53 (c2_1(a464)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1937, 1630, 110, 1572, 21, 263, 1571, 1570, 1569, 29])).
% 1.96/1.53 tff(1939,plain,
% 1.96/1.53 (~hskp2),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1496, 1938])).
% 1.96/1.53 tff(1940,plain,
% 1.96/1.53 (~hskp5),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1869, 1939, 1571, 1570, 1569])).
% 1.96/1.53 tff(1941,plain,
% 1.96/1.53 (~c3_1(a465)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1444, 1940, 1630, 263, 1939, 21])).
% 1.96/1.53 tff(1942,plain,
% 1.96/1.53 (~hskp3),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[442, 1941])).
% 1.96/1.53 tff(1943,plain,
% 1.96/1.53 (hskp29),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[457, 1942, 21])).
% 1.96/1.53 tff(1944,plain,
% 1.96/1.53 (c2_1(a474)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[340, 1943])).
% 1.96/1.53 tff(1945,plain,
% 1.96/1.53 (c1_1(a474)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[351, 1943])).
% 1.96/1.53 tff(1946,plain,
% 1.96/1.53 (c0_1(a474)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[362, 1943])).
% 1.96/1.53 tff(1947,plain,
% 1.96/1.53 (hskp14),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1582, 81, 1572, 1946, 1945, 1944, 1567])).
% 1.96/1.53 tff(1948,plain,
% 1.96/1.53 (~c0_1(a483)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1588, 1947])).
% 1.96/1.53 tff(1949,plain,
% 1.96/1.53 (c2_1(a483)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1599, 1947])).
% 1.96/1.53 tff(1950,plain,
% 1.96/1.53 (c1_1(a483)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1610, 1947])).
% 1.96/1.53 tff(1951,plain,
% 1.96/1.53 (~c3_1(a483)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1617, 81, 110, 1950, 1949, 1948, 225])).
% 1.96/1.53 tff(1952,plain,
% 1.96/1.53 (hskp7),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1624, 81, 110, 1949, 1948, 20, 1951])).
% 1.96/1.53 tff(1953,plain,
% 1.96/1.53 (c0_1(a471)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[550, 1952])).
% 1.96/1.53 tff(1954,plain,
% 1.96/1.53 (c1_1(a471) | (~c0_1(a471))),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1803, 81, 1950, 1949, 1948, 29, 405])).
% 1.96/1.53 tff(1955,plain,
% 1.96/1.53 (c1_1(a471)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1954, 1953])).
% 1.96/1.53 tff(1956,plain,
% 1.96/1.53 (hskp23),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1899, 1942, 1940])).
% 1.96/1.53 tff(1957,plain,
% 1.96/1.53 (~c3_1(a521)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1905, 1956])).
% 1.96/1.53 tff(1958,plain,
% 1.96/1.53 (~c2_1(a521)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1911, 1956])).
% 1.96/1.53 tff(1959,plain,
% 1.96/1.53 (~c0_1(a521)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1917, 1956])).
% 1.96/1.53 tff(1960,plain,
% 1.96/1.53 (~c1_1(a521)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1924, 81, 1959, 1958, 1957, 10])).
% 1.96/1.53 tff(1961,plain,
% 1.96/1.53 (hskp1),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1931, 81, 1939, 1959, 1958, 1110, 1960])).
% 1.96/1.53 tff(1962,plain,
% 1.96/1.53 (~c3_1(a463)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1123, 1961])).
% 1.96/1.53 tff(1963,plain,
% 1.96/1.53 (~c1_1(a463)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1129, 1961])).
% 1.96/1.53 tff(1964,plain,
% 1.96/1.53 (c2_1(a463)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1140, 1961])).
% 1.96/1.53 tff(1965,plain,
% 1.96/1.53 ($false),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1843, 81, 1950, 1953, 1964, 1948, 29, 1963, 1962, 499, 1955, 1951])).
% 1.96/1.53 tff(1966,plain,(hskp10 | c2_1(a471) | hskp16 | hskp12 | c1_1(a465) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.96/1.53 tff(1967,plain,
% 1.96/1.53 (hskp10),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1966, 263, 110, 21, 29, 235])).
% 1.96/1.53 tff(1968,plain,
% 1.96/1.53 (~c3_1(a478)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[244, 1967])).
% 1.96/1.53 tff(1969,plain,
% 1.96/1.53 (~c0_1(a478)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[250, 1967])).
% 1.96/1.53 tff(1970,plain,
% 1.96/1.53 (c2_1(a478)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[261, 1967])).
% 1.96/1.53 tff(1971,plain,
% 1.96/1.53 (hskp7),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[521, 81, 110, 1970, 1969, 1968, 20])).
% 1.96/1.53 tff(1972,plain,
% 1.96/1.53 (c0_1(a471)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[550, 1971])).
% 1.96/1.53 tff(1973,plain,
% 1.96/1.53 (c3_1(a471)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[539, 1971])).
% 1.96/1.53 tff(1974,plain,
% 1.96/1.53 (~c0_1(a465)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1274, 1973, 235, 21, 263, 1972, 29])).
% 1.96/1.53 tff(1975,plain,
% 1.96/1.53 (~hskp5),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1869, 1373, 1633, 1631, 1632])).
% 1.96/1.53 tff(1976,plain,
% 1.96/1.53 (hskp17),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[740, 1975, 552, 553])).
% 1.96/1.53 tff(1977,plain,
% 1.96/1.53 (~c0_1(a493)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[757, 1976])).
% 1.96/1.53 tff(1978,plain,
% 1.96/1.53 (c3_1(a493)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[768, 1976])).
% 1.96/1.53 tff(1979,plain,
% 1.96/1.53 (c2_1(a493)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[751, 1976])).
% 1.96/1.53 tff(1980,plain,
% 1.96/1.53 (~c3_1(a465)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1444, 1975, 264, 263, 1373, 21])).
% 1.96/1.53 tff(1981,plain,
% 1.96/1.53 (~hskp3),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[442, 1980])).
% 1.96/1.53 tff(1982,plain,
% 1.96/1.53 (hskp29),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[457, 1981, 21])).
% 1.96/1.53 tff(1983,plain,
% 1.96/1.53 (c2_1(a474)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[340, 1982])).
% 1.96/1.53 tff(1984,plain,
% 1.96/1.53 (c1_1(a474)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[351, 1982])).
% 1.96/1.53 tff(1985,plain,
% 1.96/1.53 (c0_1(a474)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[362, 1982])).
% 1.96/1.53 tff(1986,plain,
% 1.96/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a493) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a493) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(1987,plain,
% 1.96/1.53 (((~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493))) <=> (c0_1(a493) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(1988,plain,
% 1.96/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a493) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.96/1.53 inference(monotonicity,[status(thm)],[1987])).
% 1.96/1.53 tff(1989,plain,
% 1.96/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a493) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.53 inference(transitivity,[status(thm)],[1988, 1986])).
% 1.96/1.53 tff(1990,plain,
% 1.96/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)))),
% 1.96/1.53 inference(quant_inst,[status(thm)],[])).
% 1.96/1.53 tff(1991,plain,
% 1.96/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a493) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a493)) | (~c2_1(a493)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[1990, 1989])).
% 1.96/1.53 tff(1992,plain,
% 1.96/1.53 ($false),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1991, 81, 1633, 1631, 1632, 1985, 1984, 1983, 1979, 1978, 1977, 919])).
% 1.96/1.53 tff(1993,plain,(hskp2 | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a529)) | hskp12 | (~c0_1(a471)) | (~c3_1(a471)) | c2_1(a471) | c0_1(a465) | c1_1(a465)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.53 tff(1994,plain,
% 1.96/1.53 (hskp2),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1993, 1972, 1570, 1569, 21, 1571, 1973, 29, 1974, 263])).
% 1.96/1.53 tff(1995,plain,
% 1.96/1.53 (~c0_1(a464)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1363, 1994])).
% 1.96/1.53 tff(1996,plain,
% 1.96/1.53 (~c2_1(a464)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1496, 1994])).
% 1.96/1.53 tff(1997,plain,
% 1.96/1.53 ($false),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1208, 1996, 1995, 263, 1970, 1974, 1969, 1968, 235])).
% 1.96/1.53 tff(1998,plain,(c1_1(a465) | hskp19 | hskp12 | c2_1(a471) | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.96/1.53 tff(1999,plain,
% 1.96/1.53 (c1_1(a465)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1998, 234, 21, 29, 110])).
% 1.96/1.53 tff(2000,plain,
% 1.96/1.53 (~hskp3),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1308, 1999])).
% 1.96/1.53 tff(2001,plain,
% 1.96/1.53 (hskp29),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[457, 2000, 21])).
% 1.96/1.53 tff(2002,plain,
% 1.96/1.53 (c2_1(a474)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[340, 2001])).
% 1.96/1.53 tff(2003,plain,
% 1.96/1.53 (c1_1(a474)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[351, 2001])).
% 1.96/1.53 tff(2004,plain,
% 1.96/1.53 (c0_1(a474)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[362, 2001])).
% 1.96/1.53 tff(2005,assumption,(hskp17), introduced(assumption)).
% 1.96/1.53 tff(2006,plain,
% 1.96/1.53 (~c0_1(a493)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[757, 2005])).
% 1.96/1.53 tff(2007,plain,
% 1.96/1.53 (c3_1(a493)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[768, 2005])).
% 1.96/1.53 tff(2008,plain,
% 1.96/1.53 (c2_1(a493)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[751, 2005])).
% 1.96/1.53 tff(2009,assumption,(c2_1(a474)), introduced(assumption)).
% 1.96/1.53 tff(2010,assumption,(c1_1(a474)), introduced(assumption)).
% 1.96/1.53 tff(2011,assumption,(c0_1(a474)), introduced(assumption)).
% 1.96/1.53 tff(2012,plain,
% 1.96/1.53 ($false),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[1991, 81, 1633, 1631, 1632, 2011, 2010, 2009, 2008, 2007, 2006, 919])).
% 1.96/1.53 tff(2013,plain,((~hskp17) | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474))), inference(lemma,lemma(discharge,[]))).
% 1.96/1.53 tff(2014,plain,
% 1.96/1.53 (~hskp17),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[2013, 1535, 1557, 1546, 2004, 2003, 2002])).
% 1.96/1.53 tff(2015,plain,
% 1.96/1.53 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(2016,plain,
% 1.96/1.53 ((hskp17 | hskp5 | (~ndr1_0) | c2_1(a529) | (~c3_1(a529)) | (~c0_1(a529))) <=> (hskp17 | hskp5 | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(2017,plain,
% 1.96/1.53 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a529) | (~c3_1(a529)) | (~c0_1(a529)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529))))),
% 1.96/1.53 inference(monotonicity,[status(thm)],[2016])).
% 1.96/1.53 tff(2018,plain,
% 1.96/1.53 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a529) | (~c3_1(a529)) | (~c0_1(a529)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529)))),
% 1.96/1.53 inference(transitivity,[status(thm)],[2017, 2015])).
% 1.96/1.53 tff(2019,plain,
% 1.96/1.53 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a529) | (~c3_1(a529)) | (~c0_1(a529)))),
% 1.96/1.53 inference(quant_inst,[status(thm)],[])).
% 1.96/1.53 tff(2020,plain,
% 1.96/1.53 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | (~ndr1_0) | (~c3_1(a529)) | c2_1(a529) | (~c0_1(a529))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[2019, 2018])).
% 1.96/1.53 tff(2021,plain,
% 1.96/1.53 (hskp17 | hskp5 | c2_1(a529)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[2020, 81, 1633, 1632, 733])).
% 1.96/1.53 tff(2022,plain,
% 1.96/1.53 (c2_1(a529)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[2021, 31, 1011])).
% 1.96/1.53 tff(2023,plain,
% 1.96/1.53 (^[U: $i] : refl((hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))),
% 1.96/1.53 inference(bind,[status(th)],[])).
% 1.96/1.53 tff(2024,plain,
% 1.96/1.53 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.96/1.53 inference(quant_intro,[status(thm)],[2023])).
% 1.96/1.53 tff(2025,plain,
% 1.96/1.53 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(2026,plain,
% 1.96/1.53 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp8))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) | hskp17) <=> ((hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp17))), rewrite(((hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp17) <=> (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) | hskp17) <=> (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.96/1.53 inference(bind,[status(th)],[])).
% 1.96/1.53 tff(2027,plain,
% 1.96/1.53 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) | hskp17) <=> ![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.96/1.53 inference(quant_intro,[status(thm)],[2026])).
% 1.96/1.53 tff(2028,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 1.96/1.53 tff(2029,plain,
% 1.96/1.53 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[2028, 2027])).
% 1.96/1.53 tff(2030,plain,
% 1.96/1.53 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[2029, 2025])).
% 1.96/1.53 tff(2031,plain,(
% 1.96/1.53 ![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.96/1.53 inference(skolemize,[status(sab)],[2030])).
% 1.96/1.53 tff(2032,plain,
% 1.96/1.53 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[2031, 2024])).
% 1.96/1.53 tff(2033,plain,
% 1.96/1.53 (((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)))) <=> ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp17 | hskp8 | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2034,plain,
% 1.96/1.54 ((hskp17 | hskp8 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c2_1(a529))) <=> (hskp17 | hskp8 | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2035,plain,
% 1.96/1.54 (((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c2_1(a529)))) <=> ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529))))),
% 1.96/1.54 inference(monotonicity,[status(thm)],[2034])).
% 1.96/1.54 tff(2036,plain,
% 1.96/1.54 (((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c2_1(a529)))) <=> ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp17 | hskp8 | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)))),
% 1.96/1.54 inference(transitivity,[status(thm)],[2035, 2033])).
% 1.96/1.54 tff(2037,plain,
% 1.96/1.54 ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c2_1(a529)))),
% 1.96/1.54 inference(quant_inst,[status(thm)],[])).
% 1.96/1.54 tff(2038,plain,
% 1.96/1.54 ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp17 | hskp8 | (~ndr1_0) | (~c3_1(a529)) | (~c2_1(a529)) | (~c1_1(a529))),
% 1.96/1.54 inference(modus_ponens,[status(thm)],[2037, 2036])).
% 1.96/1.54 tff(2039,plain,
% 1.96/1.54 (hskp17 | hskp8 | (~c2_1(a529))),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2038, 81, 1631, 1632, 2032])).
% 1.96/1.54 tff(2040,plain,
% 1.96/1.54 (hskp8),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2039, 2022, 1011])).
% 1.96/1.54 tff(2041,plain,
% 1.96/1.54 (~c2_1(a472)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[1688, 2040])).
% 1.96/1.54 tff(2042,plain,
% 1.96/1.54 (c3_1(a472)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[1699, 2040])).
% 1.96/1.54 tff(2043,plain,
% 1.96/1.54 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | c2_1(a472) | (~ndr1_0) | (~c0_1(a472)) | (~c3_1(a472)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a472) | (~ndr1_0) | (~c0_1(a472)) | (~c3_1(a472)))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2044,plain,
% 1.96/1.54 ((hskp17 | hskp5 | (~ndr1_0) | c2_1(a472) | (~c3_1(a472)) | (~c0_1(a472))) <=> (hskp17 | hskp5 | c2_1(a472) | (~ndr1_0) | (~c0_1(a472)) | (~c3_1(a472)))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2045,plain,
% 1.96/1.54 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a472) | (~c3_1(a472)) | (~c0_1(a472)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | c2_1(a472) | (~ndr1_0) | (~c0_1(a472)) | (~c3_1(a472))))),
% 1.96/1.54 inference(monotonicity,[status(thm)],[2044])).
% 1.96/1.54 tff(2046,plain,
% 1.96/1.54 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a472) | (~c3_1(a472)) | (~c0_1(a472)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a472) | (~ndr1_0) | (~c0_1(a472)) | (~c3_1(a472)))),
% 1.96/1.54 inference(transitivity,[status(thm)],[2045, 2043])).
% 1.96/1.54 tff(2047,plain,
% 1.96/1.54 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c2_1(a472) | (~c3_1(a472)) | (~c0_1(a472)))),
% 1.96/1.54 inference(quant_inst,[status(thm)],[])).
% 1.96/1.54 tff(2048,plain,
% 1.96/1.54 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp17 | hskp5 | c2_1(a472) | (~ndr1_0) | (~c0_1(a472)) | (~c3_1(a472))),
% 1.96/1.54 inference(modus_ponens,[status(thm)],[2047, 2046])).
% 1.96/1.54 tff(2049,plain,
% 1.96/1.54 (~c0_1(a472)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2048, 81, 1011, 31, 2042, 2041, 733])).
% 1.96/1.54 tff(2050,plain,
% 1.96/1.54 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2051,plain,
% 1.96/1.54 ((hskp12 | hskp5 | (~ndr1_0) | c2_1(a472) | c0_1(a472) | (~c3_1(a472))) <=> (hskp12 | hskp5 | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2052,plain,
% 1.96/1.54 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a472) | c0_1(a472) | (~c3_1(a472)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472))))),
% 1.96/1.54 inference(monotonicity,[status(thm)],[2051])).
% 1.96/1.54 tff(2053,plain,
% 1.96/1.54 (((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a472) | c0_1(a472) | (~c3_1(a472)))) <=> ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)))),
% 1.96/1.54 inference(transitivity,[status(thm)],[2052, 2050])).
% 1.96/1.54 tff(2054,plain,
% 1.96/1.54 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | hskp5 | (~ndr1_0) | c2_1(a472) | c0_1(a472) | (~c3_1(a472)))),
% 1.96/1.54 inference(quant_inst,[status(thm)],[])).
% 1.96/1.54 tff(2055,plain,
% 1.96/1.54 ((~![U: $i] : (hskp12 | hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | hskp5 | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472))),
% 1.96/1.54 inference(modus_ponens,[status(thm)],[2054, 2053])).
% 1.96/1.54 tff(2056,plain,
% 1.96/1.54 ($false),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2055, 81, 21, 31, 2042, 2041, 41, 2049])).
% 1.96/1.54 tff(2057,plain,(hskp5 | hskp12 | hskp17 | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529))), inference(lemma,lemma(discharge,[]))).
% 1.96/1.54 tff(2058,plain,
% 1.96/1.54 (hskp5),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2057, 2014, 21, 1557, 1546, 1535])).
% 1.96/1.54 tff(2059,plain,
% 1.96/1.54 (c0_1(a467)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[602, 2058])).
% 1.96/1.54 tff(2060,plain,
% 1.96/1.54 (~c1_1(a467)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[1064, 2058])).
% 1.96/1.54 tff(2061,assumption,(hskp31), introduced(assumption)).
% 1.96/1.54 tff(2062,plain,
% 1.96/1.54 (c3_1(a529)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[1545, 2061])).
% 1.96/1.54 tff(2063,plain,
% 1.96/1.54 (c0_1(a529)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[1534, 2061])).
% 1.96/1.54 tff(2064,plain,
% 1.96/1.54 (c1_1(a529)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[1556, 2061])).
% 1.96/1.54 tff(2065,plain,
% 1.96/1.54 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | c1_1(a471))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | c1_1(a471))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2066,plain,
% 1.96/1.54 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a471) | c1_1(a471) | c0_1(a471)) <=> (hskp2 | hskp1 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | c1_1(a471))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2067,plain,
% 1.96/1.54 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a471) | c1_1(a471) | c0_1(a471))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | c1_1(a471)))),
% 1.96/1.54 inference(monotonicity,[status(thm)],[2066])).
% 1.96/1.54 tff(2068,plain,
% 1.96/1.54 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a471) | c1_1(a471) | c0_1(a471))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | c1_1(a471))),
% 1.96/1.54 inference(transitivity,[status(thm)],[2067, 2065])).
% 1.96/1.54 tff(2069,plain,
% 1.96/1.54 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a471) | c1_1(a471) | c0_1(a471))),
% 1.96/1.54 inference(quant_inst,[status(thm)],[])).
% 1.96/1.54 tff(2070,plain,
% 1.96/1.54 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a471) | c2_1(a471) | (~ndr1_0) | c1_1(a471)),
% 1.96/1.54 inference(modus_ponens,[status(thm)],[2069, 2068])).
% 1.96/1.54 tff(2071,plain,
% 1.96/1.54 (hskp2 | hskp1 | c0_1(a471) | c1_1(a471)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2070, 81, 29, 1110])).
% 1.96/1.54 tff(2072,plain,
% 1.96/1.54 (hskp1),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2071, 1725, 1373, 30])).
% 1.96/1.54 tff(2073,plain,
% 1.96/1.54 (~c3_1(a463)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[1123, 2072])).
% 1.96/1.54 tff(2074,plain,
% 1.96/1.54 (~c1_1(a463)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[1129, 2072])).
% 1.96/1.54 tff(2075,plain,
% 1.96/1.54 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c0_1(a463)) | c1_1(a471))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c0_1(a463)) | c1_1(a471))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2076,plain,
% 1.96/1.54 ((hskp16 | (~ndr1_0) | c1_1(a463) | c3_1(a463) | (~c0_1(a463)) | c3_1(a471) | c1_1(a471) | c2_1(a471)) <=> (hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c0_1(a463)) | c1_1(a471))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2077,plain,
% 1.96/1.54 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a463) | c3_1(a463) | (~c0_1(a463)) | c3_1(a471) | c1_1(a471) | c2_1(a471))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c0_1(a463)) | c1_1(a471)))),
% 1.96/1.54 inference(monotonicity,[status(thm)],[2076])).
% 1.96/1.54 tff(2078,plain,
% 1.96/1.54 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a463) | c3_1(a463) | (~c0_1(a463)) | c3_1(a471) | c1_1(a471) | c2_1(a471))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c0_1(a463)) | c1_1(a471))),
% 1.96/1.54 inference(transitivity,[status(thm)],[2077, 2075])).
% 1.96/1.54 tff(2079,plain,
% 1.96/1.54 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp16 | (~ndr1_0) | c1_1(a463) | c3_1(a463) | (~c0_1(a463)) | c3_1(a471) | c1_1(a471) | c2_1(a471))),
% 1.96/1.54 inference(quant_inst,[status(thm)],[])).
% 1.96/1.54 tff(2080,plain,
% 1.96/1.54 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp16 | c3_1(a471) | c2_1(a471) | c1_1(a463) | c3_1(a463) | (~ndr1_0) | (~c0_1(a463)) | c1_1(a471)),
% 1.96/1.54 inference(modus_ponens,[status(thm)],[2079, 2078])).
% 1.96/1.54 tff(2081,plain,
% 1.96/1.54 (~c0_1(a463)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2080, 81, 110, 1665, 29, 2074, 2073, 564, 1725])).
% 1.96/1.54 tff(2082,plain,
% 1.96/1.54 (c2_1(a463)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[1140, 2072])).
% 1.96/1.54 tff(2083,plain,
% 1.96/1.54 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c3_1(a463) | (~ndr1_0) | c0_1(a463) | (~c2_1(a463)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c3_1(a463) | (~ndr1_0) | c0_1(a463) | (~c2_1(a463)))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2084,plain,
% 1.96/1.54 ((hskp16 | hskp7 | (~ndr1_0) | c0_1(a463) | c3_1(a463) | (~c2_1(a463))) <=> (hskp16 | hskp7 | c3_1(a463) | (~ndr1_0) | c0_1(a463) | (~c2_1(a463)))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2085,plain,
% 1.96/1.54 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a463) | c3_1(a463) | (~c2_1(a463)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c3_1(a463) | (~ndr1_0) | c0_1(a463) | (~c2_1(a463))))),
% 1.96/1.54 inference(monotonicity,[status(thm)],[2084])).
% 1.96/1.54 tff(2086,plain,
% 1.96/1.54 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a463) | c3_1(a463) | (~c2_1(a463)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c3_1(a463) | (~ndr1_0) | c0_1(a463) | (~c2_1(a463)))),
% 1.96/1.54 inference(transitivity,[status(thm)],[2085, 2083])).
% 1.96/1.54 tff(2087,plain,
% 1.96/1.54 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a463) | c3_1(a463) | (~c2_1(a463)))),
% 1.96/1.54 inference(quant_inst,[status(thm)],[])).
% 1.96/1.54 tff(2088,plain,
% 1.96/1.54 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c3_1(a463) | (~ndr1_0) | c0_1(a463) | (~c2_1(a463))),
% 1.96/1.54 inference(modus_ponens,[status(thm)],[2087, 2086])).
% 1.96/1.54 tff(2089,plain,
% 1.96/1.54 ($false),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2088, 81, 110, 1664, 2082, 2073, 20, 2081])).
% 1.96/1.54 tff(2090,plain,(c3_1(a471) | hskp16 | c2_1(a471) | hskp2 | c0_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.54 tff(2091,plain,
% 1.96/1.54 (c3_1(a471)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2090, 1373, 29, 30, 110])).
% 1.96/1.54 tff(2092,plain,
% 1.96/1.54 ($false),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[88, 2091, 1975, 30])).
% 1.96/1.54 tff(2093,plain,(hskp2 | c0_1(a471) | hskp12 | c2_1(a471) | hskp16 | (~c0_1(a529)) | (~c1_1(a529)) | (~c3_1(a529))), inference(lemma,lemma(discharge,[]))).
% 1.96/1.54 tff(2094,plain,
% 1.96/1.54 ($false),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2093, 2064, 2063, 21, 29, 110, 30, 1373, 2062])).
% 1.96/1.54 tff(2095,plain,((~hskp31) | hskp12 | c2_1(a471) | hskp16 | c0_1(a471) | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.96/1.54 tff(2096,plain,
% 1.96/1.54 (hskp2),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2095, 30, 29, 110, 1524, 21])).
% 1.96/1.54 tff(2097,plain,
% 1.96/1.54 (~c2_1(a464)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[1496, 2096])).
% 1.96/1.54 tff(2098,plain,
% 1.96/1.54 (~c0_1(a464)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[1363, 2096])).
% 1.96/1.54 tff(2099,plain,
% 1.96/1.54 (c3_1(a464)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[659, 2096])).
% 1.96/1.54 tff(2100,plain,
% 1.96/1.54 (hskp5),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[627, 81, 21, 2099, 2098, 2097, 41])).
% 1.96/1.54 tff(2101,plain,
% 1.96/1.54 (~c3_1(a467)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[1169, 2100])).
% 1.96/1.54 tff(2102,plain,
% 1.96/1.54 (~c1_1(a467)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[1064, 2100])).
% 1.96/1.54 tff(2103,plain,
% 1.96/1.54 (c0_1(a467)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[602, 2100])).
% 1.96/1.54 tff(2104,plain,
% 1.96/1.54 (c2_1(a467)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[570, 81, 110, 2103, 2102, 2101, 564])).
% 1.96/1.54 tff(2105,plain,
% 1.96/1.54 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c1_1(a474)))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2106,plain,
% 1.96/1.54 ((hskp7 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c2_1(a474)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467))) <=> (hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c1_1(a474)))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2107,plain,
% 1.96/1.54 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c2_1(a474)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c1_1(a474))))),
% 1.96/1.54 inference(monotonicity,[status(thm)],[2106])).
% 1.96/1.54 tff(2108,plain,
% 1.96/1.54 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c2_1(a474)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c1_1(a474)))),
% 1.96/1.54 inference(transitivity,[status(thm)],[2107, 2105])).
% 1.96/1.54 tff(2109,plain,
% 1.96/1.54 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c2_1(a474)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))),
% 1.96/1.54 inference(quant_inst,[status(thm)],[])).
% 1.96/1.54 tff(2110,plain,
% 1.96/1.54 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c3_1(a474)) | (~c2_1(a474)) | (~c1_1(a474))),
% 1.96/1.54 inference(modus_ponens,[status(thm)],[2109, 2108])).
% 1.96/1.54 tff(2111,plain,
% 1.96/1.54 (~c3_1(a474)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2110, 81, 1664, 2003, 2002, 2103, 2101, 1653, 2104])).
% 1.96/1.54 tff(2112,assumption,(c2_1(a467)), introduced(assumption)).
% 1.96/1.54 tff(2113,assumption,(hskp30), introduced(assumption)).
% 1.96/1.54 tff(2114,plain,
% 1.96/1.54 (c3_1(a488)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[185, 2113])).
% 1.96/1.54 tff(2115,plain,
% 1.96/1.54 (c2_1(a488)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[196, 2113])).
% 1.96/1.54 tff(2116,plain,
% 1.96/1.54 (c1_1(a488)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[207, 2113])).
% 1.96/1.54 tff(2117,assumption,(~hskp7), introduced(assumption)).
% 1.96/1.54 tff(2118,plain,
% 1.96/1.54 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2119,plain,
% 1.96/1.54 ((hskp7 | (~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467))) <=> (hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2120,plain,
% 1.96/1.54 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488))))),
% 1.96/1.54 inference(monotonicity,[status(thm)],[2119])).
% 1.96/1.54 tff(2121,plain,
% 1.96/1.54 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488)))),
% 1.96/1.54 inference(transitivity,[status(thm)],[2120, 2118])).
% 1.96/1.54 tff(2122,plain,
% 1.96/1.54 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a488)) | (~c3_1(a488)) | (~c2_1(a488)) | c3_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))),
% 1.96/1.54 inference(quant_inst,[status(thm)],[])).
% 1.96/1.54 tff(2123,plain,
% 1.96/1.54 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c2_1(a488)) | (~c3_1(a488)) | (~c1_1(a488))),
% 1.96/1.54 inference(modus_ponens,[status(thm)],[2122, 2121])).
% 1.96/1.54 tff(2124,plain,
% 1.96/1.54 ($false),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2123, 81, 2117, 2116, 2115, 2114, 554, 268, 1653, 2112])).
% 1.96/1.54 tff(2125,plain,((~hskp30) | hskp7 | (~c0_1(a467)) | c3_1(a467) | (~c2_1(a467))), inference(lemma,lemma(discharge,[]))).
% 1.96/1.54 tff(2126,plain,
% 1.96/1.54 (~hskp30),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2125, 2104, 2103, 2101, 1664])).
% 1.96/1.54 tff(2127,plain,
% 1.96/1.54 (hskp30 | c3_1(a474)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[1327, 81, 21, 2004, 2003, 167])).
% 1.96/1.54 tff(2128,plain,
% 1.96/1.54 ($false),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2127, 2126, 2111])).
% 1.96/1.54 tff(2129,plain,(c0_1(a471) | hskp12 | hskp16 | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.54 tff(2130,plain,
% 1.96/1.54 (c0_1(a471)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2129, 110, 21, 29])).
% 1.96/1.54 tff(2131,plain,
% 1.96/1.54 (~c3_1(a467)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[1169, 2058])).
% 1.96/1.54 tff(2132,plain,
% 1.96/1.54 (~c3_1(a471)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[591, 2131, 21, 2130, 29, 2060, 110, 2059])).
% 1.96/1.54 tff(2133,plain,
% 1.96/1.54 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2134,plain,
% 1.96/1.54 (((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a471) | c2_1(a471) | (~c0_1(a471))) <=> (c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2135,plain,
% 1.96/1.54 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a471) | c2_1(a471) | (~c0_1(a471)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.96/1.54 inference(monotonicity,[status(thm)],[2134])).
% 1.96/1.54 tff(2136,plain,
% 1.96/1.54 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a471) | c2_1(a471) | (~c0_1(a471)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.54 inference(transitivity,[status(thm)],[2135, 2133])).
% 1.96/1.54 tff(2137,plain,
% 1.96/1.54 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a471) | c2_1(a471) | (~c0_1(a471)))),
% 1.96/1.54 inference(quant_inst,[status(thm)],[])).
% 1.96/1.54 tff(2138,plain,
% 1.96/1.54 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c0_1(a471)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.96/1.54 inference(modus_ponens,[status(thm)],[2137, 2136])).
% 1.96/1.54 tff(2139,plain,
% 1.96/1.54 ($false),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2138, 81, 2004, 2003, 2002, 2130, 2132, 29, 109])).
% 1.96/1.54 tff(2140,plain,(hskp16 | c2_1(a471) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.96/1.54 tff(2141,plain,
% 1.96/1.54 (hskp16),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2140, 29, 21])).
% 1.96/1.54 tff(2142,plain,
% 1.96/1.54 (~c2_1(a487)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[284, 2141])).
% 1.96/1.54 tff(2143,plain,
% 1.96/1.54 (~c1_1(a487)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[27, 2141])).
% 1.96/1.54 tff(2144,plain,
% 1.96/1.54 (hskp5 | c0_1(a472)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2055, 81, 21, 1700, 1689, 41])).
% 1.96/1.54 tff(2145,plain,
% 1.96/1.54 (c0_1(a472)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2144, 31])).
% 1.96/1.54 tff(2146,plain,
% 1.96/1.54 (hskp17 | hskp5 | (~c0_1(a472))),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2048, 81, 1700, 1689, 733])).
% 1.96/1.54 tff(2147,plain,
% 1.96/1.54 (hskp17),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2146, 2145, 31])).
% 1.96/1.54 tff(2148,plain,
% 1.96/1.54 (~c0_1(a493)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[757, 2147])).
% 1.96/1.54 tff(2149,plain,
% 1.96/1.54 (c0_1(a487)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[295, 2141])).
% 1.96/1.54 tff(2150,plain,
% 1.96/1.54 (c3_1(a493)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[768, 2147])).
% 1.96/1.54 tff(2151,plain,
% 1.96/1.54 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp5 | c0_1(a493) | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)) | (~c3_1(a493)) | (~c1_1(a493)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a493) | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)) | (~c3_1(a493)) | (~c1_1(a493)))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2152,plain,
% 1.96/1.54 ((hskp5 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a493) | (~c3_1(a493)) | (~c1_1(a493))) <=> (hskp5 | c0_1(a493) | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)) | (~c3_1(a493)) | (~c1_1(a493)))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2153,plain,
% 1.96/1.54 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a493) | (~c3_1(a493)) | (~c1_1(a493)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp5 | c0_1(a493) | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)) | (~c3_1(a493)) | (~c1_1(a493))))),
% 1.96/1.54 inference(monotonicity,[status(thm)],[2152])).
% 1.96/1.54 tff(2154,plain,
% 1.96/1.54 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a493) | (~c3_1(a493)) | (~c1_1(a493)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a493) | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)) | (~c3_1(a493)) | (~c1_1(a493)))),
% 1.96/1.54 inference(transitivity,[status(thm)],[2153, 2151])).
% 1.96/1.54 tff(2155,plain,
% 1.96/1.54 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a493) | (~c3_1(a493)) | (~c1_1(a493)))),
% 1.96/1.54 inference(quant_inst,[status(thm)],[])).
% 1.96/1.54 tff(2156,plain,
% 1.96/1.54 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a493) | c1_1(a487) | c2_1(a487) | (~ndr1_0) | (~c0_1(a487)) | (~c3_1(a493)) | (~c1_1(a493))),
% 1.96/1.54 inference(modus_ponens,[status(thm)],[2155, 2154])).
% 1.96/1.54 tff(2157,plain,
% 1.96/1.54 (~c1_1(a493)),
% 1.96/1.54 inference(unit_resolution,[status(thm)],[2156, 81, 31, 2150, 2149, 2148, 2143, 2142, 99])).
% 1.96/1.54 tff(2158,plain,
% 1.96/1.54 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 1.96/1.54 inference(bind,[status(th)],[])).
% 1.96/1.54 tff(2159,plain,
% 1.96/1.54 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.96/1.54 inference(quant_intro,[status(thm)],[2158])).
% 1.96/1.54 tff(2160,plain,
% 1.96/1.54 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.54 tff(2161,plain,
% 1.96/1.54 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp6))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 1.96/1.54 inference(bind,[status(th)],[])).
% 1.96/1.54 tff(2162,plain,
% 1.96/1.54 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.96/1.54 inference(quant_intro,[status(thm)],[2161])).
% 1.96/1.54 tff(2163,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 1.96/1.54 tff(2164,plain,
% 1.96/1.54 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.96/1.54 inference(modus_ponens,[status(thm)],[2163, 2162])).
% 1.96/1.54 tff(2165,plain,
% 1.96/1.54 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.96/1.54 inference(modus_ponens,[status(thm)],[2164, 2160])).
% 1.96/1.54 tff(2166,plain,(
% 1.96/1.54 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.96/1.54 inference(skolemize,[status(sab)],[2165])).
% 1.96/1.54 tff(2167,plain,
% 1.96/1.54 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.96/1.54 inference(modus_ponens,[status(thm)],[2166, 2159])).
% 1.96/1.54 tff(2168,plain,
% 1.96/1.54 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)))),
% 1.96/1.54 inference(rewrite,[status(thm)],[])).
% 1.96/1.55 tff(2169,plain,
% 1.96/1.55 ((hskp6 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | c3_1(a471) | c0_1(a471) | c2_1(a471)) <=> (hskp6 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)))),
% 1.96/1.55 inference(rewrite,[status(thm)],[])).
% 1.96/1.55 tff(2170,plain,
% 1.96/1.55 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | c3_1(a471) | c0_1(a471) | c2_1(a471))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472))))),
% 1.96/1.55 inference(monotonicity,[status(thm)],[2169])).
% 1.96/1.55 tff(2171,plain,
% 1.96/1.55 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | c3_1(a471) | c0_1(a471) | c2_1(a471))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)))),
% 1.96/1.55 inference(transitivity,[status(thm)],[2170, 2168])).
% 1.96/1.55 tff(2172,plain,
% 1.96/1.55 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | c3_1(a471) | c0_1(a471) | c2_1(a471))),
% 1.96/1.55 inference(quant_inst,[status(thm)],[])).
% 1.96/1.55 tff(2173,plain,
% 1.96/1.55 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a471) | c3_1(a471) | c2_1(a471) | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472))),
% 1.96/1.55 inference(modus_ponens,[status(thm)],[2172, 2171])).
% 1.96/1.55 tff(2174,plain,
% 1.96/1.55 (hskp6 | (~c0_1(a472))),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[2173, 81, 1711, 1700, 30, 1665, 29, 2167])).
% 1.96/1.55 tff(2175,plain,
% 1.96/1.55 (hskp6),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[2174, 2145])).
% 1.96/1.55 tff(2176,plain,
% 1.96/1.55 (~c2_1(a470)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[1385, 2175])).
% 1.96/1.55 tff(2177,plain,
% 1.96/1.55 (~c0_1(a470)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[1391, 2175])).
% 1.96/1.55 tff(2178,plain,
% 1.96/1.55 (~c3_1(a470)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[1398, 81, 21, 31, 2177, 2176, 41])).
% 1.96/1.55 tff(2179,plain,
% 1.96/1.55 (~c1_1(a470)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[1405, 2175])).
% 1.96/1.55 tff(2180,plain,
% 1.96/1.55 (c2_1(a493)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[751, 2147])).
% 1.96/1.55 tff(2181,plain,
% 1.96/1.55 (hskp8),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[1682, 89, 30, 1664])).
% 1.96/1.55 tff(2182,plain,
% 1.96/1.55 (~c2_1(a472)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[1688, 2181])).
% 1.96/1.55 tff(2183,plain,
% 1.96/1.55 (c3_1(a472)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[1699, 2181])).
% 1.96/1.55 tff(2184,plain,
% 1.96/1.55 (c0_1(a472)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[2055, 81, 21, 31, 2183, 2182, 41])).
% 1.96/1.55 tff(2185,plain,
% 1.96/1.55 (hskp17 | (~c0_1(a472))),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[2048, 81, 31, 2183, 2182, 733])).
% 1.96/1.55 tff(2186,plain,
% 1.96/1.55 (hskp17),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[2185, 2184])).
% 1.96/1.55 tff(2187,plain,
% 1.96/1.55 (~c0_1(a493)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[757, 2186])).
% 1.96/1.55 tff(2188,plain,
% 1.96/1.55 (c3_1(a493)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[768, 2186])).
% 1.96/1.55 tff(2189,plain,
% 1.96/1.55 (~c1_1(a493)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[2156, 81, 31, 2188, 2149, 2187, 2143, 2142, 99])).
% 1.96/1.55 tff(2190,plain,
% 1.96/1.55 (c1_1(a472)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[1710, 2181])).
% 1.96/1.55 tff(2191,plain,
% 1.96/1.55 (hskp6 | (~c0_1(a472))),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[2173, 81, 2190, 2183, 30, 89, 29, 2167])).
% 1.96/1.55 tff(2192,plain,
% 1.96/1.55 (hskp6),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[2191, 2184])).
% 1.96/1.55 tff(2193,plain,
% 1.96/1.55 (~c2_1(a470)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[1385, 2192])).
% 1.96/1.55 tff(2194,plain,
% 1.96/1.55 (~c0_1(a470)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[1391, 2192])).
% 1.96/1.55 tff(2195,plain,
% 1.96/1.55 (~c3_1(a470)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[1398, 81, 21, 31, 2194, 2193, 41])).
% 1.96/1.55 tff(2196,plain,
% 1.96/1.55 (~c1_1(a470)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[1405, 2192])).
% 1.96/1.55 tff(2197,plain,
% 1.96/1.55 (c2_1(a493)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[751, 2186])).
% 1.96/1.55 tff(2198,plain,
% 1.96/1.55 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c1_1(a470) | c2_1(a470) | (~ndr1_0) | c3_1(a470) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a493))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c1_1(a470) | c2_1(a470) | (~ndr1_0) | c3_1(a470) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a493))),
% 1.96/1.55 inference(rewrite,[status(thm)],[])).
% 1.96/1.55 tff(2199,plain,
% 1.96/1.55 ((hskp2 | (~ndr1_0) | c1_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a470) | c1_1(a470) | c2_1(a470)) <=> (hskp2 | c1_1(a470) | c2_1(a470) | (~ndr1_0) | c3_1(a470) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a493))),
% 1.96/1.55 inference(rewrite,[status(thm)],[])).
% 1.96/1.55 tff(2200,plain,
% 1.96/1.55 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a470) | c1_1(a470) | c2_1(a470))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | c1_1(a470) | c2_1(a470) | (~ndr1_0) | c3_1(a470) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a493)))),
% 1.96/1.55 inference(monotonicity,[status(thm)],[2199])).
% 1.96/1.55 tff(2201,plain,
% 1.96/1.55 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a470) | c1_1(a470) | c2_1(a470))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c1_1(a470) | c2_1(a470) | (~ndr1_0) | c3_1(a470) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a493))),
% 1.96/1.55 inference(transitivity,[status(thm)],[2200, 2198])).
% 1.96/1.55 tff(2202,plain,
% 1.96/1.55 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a470) | c1_1(a470) | c2_1(a470))),
% 1.96/1.55 inference(quant_inst,[status(thm)],[])).
% 1.96/1.55 tff(2203,plain,
% 1.96/1.55 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp2 | c1_1(a470) | c2_1(a470) | (~ndr1_0) | c3_1(a470) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a493)),
% 1.96/1.55 inference(modus_ponens,[status(thm)],[2202, 2201])).
% 1.96/1.55 tff(2204,plain,
% 1.96/1.55 (hskp2),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[2203, 81, 2197, 2188, 2196, 2193, 648, 2195, 2189])).
% 1.96/1.55 tff(2205,plain,
% 1.96/1.55 (c3_1(a464)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[659, 2204])).
% 1.96/1.55 tff(2206,plain,
% 1.96/1.55 (~c0_1(a464)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[1363, 2204])).
% 1.96/1.55 tff(2207,plain,
% 1.96/1.55 ($false),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[1635, 2206, 2205, 31])).
% 1.96/1.55 tff(2208,plain,(hskp5 | hskp12 | c2_1(a464) | c0_1(a471) | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.55 tff(2209,plain,
% 1.96/1.55 (hskp5),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[2208, 237, 21, 30, 29])).
% 1.96/1.55 tff(2210,plain,
% 1.96/1.55 (~c3_1(a467)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[1169, 2209])).
% 1.96/1.55 tff(2211,plain,
% 1.96/1.55 (c0_1(a467)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[602, 2209])).
% 1.96/1.55 tff(2212,plain,
% 1.96/1.55 (~c1_1(a467)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[1064, 2209])).
% 1.96/1.55 tff(2213,plain,
% 1.96/1.55 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)))),
% 1.96/1.55 inference(rewrite,[status(thm)],[])).
% 1.96/1.55 tff(2214,plain,
% 1.96/1.55 ((hskp2 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467))) <=> (hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)))),
% 1.96/1.55 inference(rewrite,[status(thm)],[])).
% 1.96/1.55 tff(2215,plain,
% 1.96/1.55 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472))))),
% 1.96/1.55 inference(monotonicity,[status(thm)],[2214])).
% 1.96/1.55 tff(2216,plain,
% 1.96/1.55 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)))),
% 1.96/1.55 inference(transitivity,[status(thm)],[2215, 2213])).
% 1.96/1.55 tff(2217,plain,
% 1.96/1.55 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467)))),
% 1.96/1.55 inference(quant_inst,[status(thm)],[])).
% 1.96/1.55 tff(2218,plain,
% 1.96/1.55 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472))),
% 1.96/1.55 inference(modus_ponens,[status(thm)],[2217, 2216])).
% 1.96/1.55 tff(2219,plain,
% 1.96/1.55 (~c0_1(a472)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[2218, 81, 1373, 1711, 1700, 554, 269, 268, 1857])).
% 1.96/1.55 tff(2220,plain,
% 1.96/1.55 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.96/1.55 inference(bind,[status(th)],[])).
% 1.96/1.55 tff(2221,plain,
% 1.96/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_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)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.96/1.55 inference(quant_intro,[status(thm)],[2220])).
% 1.96/1.55 tff(2222,plain,
% 1.96/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_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)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.96/1.55 inference(rewrite,[status(thm)],[])).
% 1.96/1.55 tff(2223,plain,
% 1.96/1.55 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.96/1.55 inference(bind,[status(th)],[])).
% 1.96/1.55 tff(2224,plain,
% 1.96/1.55 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.96/1.55 inference(quant_intro,[status(thm)],[2223])).
% 1.96/1.55 tff(2225,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause202')).
% 1.96/1.55 tff(2226,plain,
% 1.96/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.96/1.55 inference(modus_ponens,[status(thm)],[2225, 2224])).
% 1.96/1.55 tff(2227,plain,
% 1.96/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.96/1.55 inference(modus_ponens,[status(thm)],[2226, 2222])).
% 1.96/1.55 tff(2228,plain,(
% 1.96/1.55 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.96/1.55 inference(skolemize,[status(sab)],[2227])).
% 1.96/1.55 tff(2229,plain,
% 1.96/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.96/1.55 inference(modus_ponens,[status(thm)],[2228, 2221])).
% 1.96/1.55 tff(2230,plain,
% 1.96/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a471) | c3_1(a471) | c1_1(a487) | (~ndr1_0) | c1_1(a471) | (~c1_1(a472)) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)) | (~c3_1(a487)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a471) | c3_1(a471) | c1_1(a487) | (~ndr1_0) | c1_1(a471) | (~c1_1(a472)) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)) | (~c3_1(a487)))),
% 1.96/1.55 inference(rewrite,[status(thm)],[])).
% 1.96/1.55 tff(2231,plain,
% 1.96/1.55 (((~ndr1_0) | c1_1(a487) | (~c3_1(a487)) | (~c0_1(a487)) | c0_1(a472) | (~c3_1(a472)) | (~c1_1(a472)) | c3_1(a471) | c1_1(a471) | c0_1(a471)) <=> (c0_1(a471) | c3_1(a471) | c1_1(a487) | (~ndr1_0) | c1_1(a471) | (~c1_1(a472)) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)) | (~c3_1(a487)))),
% 1.96/1.55 inference(rewrite,[status(thm)],[])).
% 1.96/1.55 tff(2232,plain,
% 1.96/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a487) | (~c3_1(a487)) | (~c0_1(a487)) | c0_1(a472) | (~c3_1(a472)) | (~c1_1(a472)) | c3_1(a471) | c1_1(a471) | c0_1(a471))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a471) | c3_1(a471) | c1_1(a487) | (~ndr1_0) | c1_1(a471) | (~c1_1(a472)) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)) | (~c3_1(a487))))),
% 1.96/1.55 inference(monotonicity,[status(thm)],[2231])).
% 1.96/1.55 tff(2233,plain,
% 1.96/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a487) | (~c3_1(a487)) | (~c0_1(a487)) | c0_1(a472) | (~c3_1(a472)) | (~c1_1(a472)) | c3_1(a471) | c1_1(a471) | c0_1(a471))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a471) | c3_1(a471) | c1_1(a487) | (~ndr1_0) | c1_1(a471) | (~c1_1(a472)) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)) | (~c3_1(a487)))),
% 1.96/1.55 inference(transitivity,[status(thm)],[2232, 2230])).
% 1.96/1.55 tff(2234,plain,
% 1.96/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a487) | (~c3_1(a487)) | (~c0_1(a487)) | c0_1(a472) | (~c3_1(a472)) | (~c1_1(a472)) | c3_1(a471) | c1_1(a471) | c0_1(a471))),
% 1.96/1.55 inference(quant_inst,[status(thm)],[])).
% 1.96/1.55 tff(2235,plain,
% 1.96/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a471) | c3_1(a471) | c1_1(a487) | (~ndr1_0) | c1_1(a471) | (~c1_1(a472)) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)) | (~c3_1(a487))),
% 1.96/1.55 inference(modus_ponens,[status(thm)],[2234, 2233])).
% 1.96/1.55 tff(2236,plain,
% 1.96/1.55 (~c3_1(a487)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[2235, 81, 387, 1711, 1700, 30, 1665, 386, 2229, 1725, 2219])).
% 1.96/1.55 tff(2237,plain,
% 1.96/1.55 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a487) | c2_1(a487) | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a487) | c2_1(a487) | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)))),
% 1.96/1.55 inference(rewrite,[status(thm)],[])).
% 1.96/1.55 tff(2238,plain,
% 1.96/1.55 ((hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a472) | c2_1(a472) | (~c3_1(a472))) <=> (hskp29 | c1_1(a487) | c2_1(a487) | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)))),
% 1.96/1.55 inference(rewrite,[status(thm)],[])).
% 1.96/1.55 tff(2239,plain,
% 1.96/1.55 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a472) | c2_1(a472) | (~c3_1(a472)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c1_1(a487) | c2_1(a487) | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487))))),
% 1.96/1.55 inference(monotonicity,[status(thm)],[2238])).
% 1.96/1.55 tff(2240,plain,
% 1.96/1.55 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a472) | c2_1(a472) | (~c3_1(a472)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a487) | c2_1(a487) | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487)))),
% 1.96/1.55 inference(transitivity,[status(thm)],[2239, 2237])).
% 1.96/1.55 tff(2241,plain,
% 1.96/1.55 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a472) | c2_1(a472) | (~c3_1(a472)))),
% 1.96/1.55 inference(quant_inst,[status(thm)],[])).
% 1.96/1.55 tff(2242,plain,
% 1.96/1.55 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c1_1(a487) | c2_1(a487) | c2_1(a472) | (~ndr1_0) | c0_1(a472) | (~c3_1(a472)) | (~c0_1(a487))),
% 1.96/1.55 inference(modus_ponens,[status(thm)],[2241, 2240])).
% 1.96/1.55 tff(2243,plain,
% 1.96/1.55 (hskp29),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[2242, 81, 387, 1700, 386, 385, 1689, 384, 2219])).
% 1.96/1.55 tff(2244,plain,
% 1.96/1.55 (c2_1(a474)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[340, 2243])).
% 1.96/1.55 tff(2245,plain,
% 1.96/1.55 (c1_1(a474)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[351, 2243])).
% 1.96/1.55 tff(2246,plain,
% 1.96/1.55 (c0_1(a474)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[362, 2243])).
% 1.96/1.55 tff(2247,plain,
% 1.96/1.55 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a487) | (~ndr1_0) | c3_1(a487) | (~c0_1(a487)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a487) | (~ndr1_0) | c3_1(a487) | (~c0_1(a487)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.55 inference(rewrite,[status(thm)],[])).
% 1.96/1.55 tff(2248,plain,
% 1.96/1.55 (((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a487) | c2_1(a487) | (~c0_1(a487))) <=> (c2_1(a487) | (~ndr1_0) | c3_1(a487) | (~c0_1(a487)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.55 inference(rewrite,[status(thm)],[])).
% 1.96/1.55 tff(2249,plain,
% 1.96/1.55 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a487) | c2_1(a487) | (~c0_1(a487)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a487) | (~ndr1_0) | c3_1(a487) | (~c0_1(a487)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.96/1.55 inference(monotonicity,[status(thm)],[2248])).
% 1.96/1.55 tff(2250,plain,
% 1.96/1.55 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a487) | c2_1(a487) | (~c0_1(a487)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a487) | (~ndr1_0) | c3_1(a487) | (~c0_1(a487)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.55 inference(transitivity,[status(thm)],[2249, 2247])).
% 1.96/1.55 tff(2251,plain,
% 1.96/1.55 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a487) | c2_1(a487) | (~c0_1(a487)))),
% 1.96/1.55 inference(quant_inst,[status(thm)],[])).
% 1.96/1.55 tff(2252,plain,
% 1.96/1.55 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a487) | (~ndr1_0) | c3_1(a487) | (~c0_1(a487)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.96/1.55 inference(modus_ponens,[status(thm)],[2251, 2250])).
% 1.96/1.55 tff(2253,plain,
% 1.96/1.55 ($false),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[2252, 81, 2246, 2245, 2244, 387, 385, 109, 2236])).
% 1.96/1.55 tff(2254,plain,(c3_1(a471) | (~c0_1(a487)) | c2_1(a487) | c1_1(a487) | c0_1(a471) | c2_1(a471) | hskp2 | (~c0_1(a467)) | c1_1(a467) | c3_1(a467)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.55 tff(2255,plain,
% 1.96/1.55 (c3_1(a471)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[2254, 1373, 2142, 2143, 30, 29, 2149, 554, 269, 268])).
% 1.96/1.55 tff(2256,plain,
% 1.96/1.55 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a471) | c1_1(a487) | c2_1(a487) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)) | (~c0_1(a487)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a471) | c1_1(a487) | c2_1(a487) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)) | (~c0_1(a487)))),
% 1.96/1.55 inference(rewrite,[status(thm)],[])).
% 1.96/1.55 tff(2257,plain,
% 1.96/1.55 ((hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a471) | c2_1(a471) | (~c3_1(a471))) <=> (hskp29 | c0_1(a471) | c1_1(a487) | c2_1(a487) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)) | (~c0_1(a487)))),
% 1.96/1.55 inference(rewrite,[status(thm)],[])).
% 1.96/1.55 tff(2258,plain,
% 1.96/1.55 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a471) | c2_1(a471) | (~c3_1(a471)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | c0_1(a471) | c1_1(a487) | c2_1(a487) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)) | (~c0_1(a487))))),
% 1.96/1.55 inference(monotonicity,[status(thm)],[2257])).
% 1.96/1.55 tff(2259,plain,
% 1.96/1.55 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a471) | c2_1(a471) | (~c3_1(a471)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a471) | c1_1(a487) | c2_1(a487) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)) | (~c0_1(a487)))),
% 1.96/1.55 inference(transitivity,[status(thm)],[2258, 2256])).
% 1.96/1.55 tff(2260,plain,
% 1.96/1.55 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a487) | c1_1(a487) | (~c0_1(a487)) | c0_1(a471) | c2_1(a471) | (~c3_1(a471)))),
% 1.96/1.55 inference(quant_inst,[status(thm)],[])).
% 1.96/1.55 tff(2261,plain,
% 1.96/1.55 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp29 | c0_1(a471) | c1_1(a487) | c2_1(a487) | c2_1(a471) | (~ndr1_0) | (~c3_1(a471)) | (~c0_1(a487))),
% 1.96/1.55 inference(modus_ponens,[status(thm)],[2260, 2259])).
% 1.96/1.55 tff(2262,plain,
% 1.96/1.55 (hskp29 | (~c3_1(a471))),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[2261, 81, 2149, 30, 2143, 2142, 29, 384])).
% 1.96/1.55 tff(2263,plain,
% 1.96/1.55 (hskp29),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[2262, 2255])).
% 1.96/1.55 tff(2264,plain,
% 1.96/1.55 (c2_1(a474)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[340, 2263])).
% 1.96/1.55 tff(2265,plain,
% 1.96/1.55 (c1_1(a474)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[351, 2263])).
% 1.96/1.55 tff(2266,plain,
% 1.96/1.55 (c0_1(a474)),
% 1.96/1.55 inference(unit_resolution,[status(thm)],[362, 2263])).
% 1.96/1.55 tff(2267,plain,
% 1.96/1.55 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.56 inference(rewrite,[status(thm)],[])).
% 1.96/1.56 tff(2268,plain,
% 1.96/1.56 (((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a467) | c2_1(a467) | (~c0_1(a467))) <=> (c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.56 inference(rewrite,[status(thm)],[])).
% 1.96/1.56 tff(2269,plain,
% 1.96/1.56 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a467) | c2_1(a467) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.96/1.56 inference(monotonicity,[status(thm)],[2268])).
% 1.96/1.56 tff(2270,plain,
% 1.96/1.56 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a467) | c2_1(a467) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.56 inference(transitivity,[status(thm)],[2269, 2267])).
% 1.96/1.56 tff(2271,plain,
% 1.96/1.56 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)) | c3_1(a467) | c2_1(a467) | (~c0_1(a467)))),
% 1.96/1.56 inference(quant_inst,[status(thm)],[])).
% 1.96/1.56 tff(2272,plain,
% 1.96/1.56 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | c2_1(a467) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.96/1.56 inference(modus_ponens,[status(thm)],[2271, 2270])).
% 1.96/1.56 tff(2273,plain,
% 1.96/1.56 (c2_1(a467)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2272, 81, 2266, 2265, 2264, 554, 268, 109])).
% 1.96/1.56 tff(2274,plain,
% 1.96/1.56 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.56 inference(rewrite,[status(thm)],[])).
% 1.96/1.56 tff(2275,plain,
% 1.96/1.56 ((hskp2 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467))) <=> (hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.56 inference(rewrite,[status(thm)],[])).
% 1.96/1.56 tff(2276,plain,
% 1.96/1.56 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.96/1.56 inference(monotonicity,[status(thm)],[2275])).
% 1.96/1.56 tff(2277,plain,
% 1.96/1.56 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.56 inference(transitivity,[status(thm)],[2276, 2274])).
% 1.96/1.56 tff(2278,plain,
% 1.96/1.56 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c1_1(a474)) | (~c3_1(a474)) | (~c0_1(a474)) | c3_1(a467) | c1_1(a467) | (~c0_1(a467)))),
% 1.96/1.56 inference(quant_inst,[status(thm)],[])).
% 1.96/1.56 tff(2279,plain,
% 1.96/1.56 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c3_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.96/1.56 inference(modus_ponens,[status(thm)],[2278, 2277])).
% 1.96/1.56 tff(2280,plain,
% 1.96/1.56 (~c3_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2279, 81, 1373, 2266, 2265, 554, 269, 268, 1857])).
% 1.96/1.56 tff(2281,plain,
% 1.96/1.56 (hskp30 | c3_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1327, 81, 21, 2266, 2265, 167])).
% 1.96/1.56 tff(2282,plain,
% 1.96/1.56 (hskp30),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2281, 2280])).
% 1.96/1.56 tff(2283,plain,
% 1.96/1.56 ($false),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2125, 2282, 2273, 554, 268, 1664])).
% 1.96/1.56 tff(2284,plain,(hskp2 | (~c0_1(a467)) | c3_1(a467) | hskp12 | c1_1(a467) | c0_1(a471) | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.56 tff(2285,plain,
% 1.96/1.56 (hskp2),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2284, 2211, 2210, 21, 2212, 30, 29])).
% 1.96/1.56 tff(2286,plain,
% 1.96/1.56 (~c0_1(a464)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1363, 2285])).
% 1.96/1.56 tff(2287,plain,
% 1.96/1.56 (c3_1(a464)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[659, 2285])).
% 1.96/1.56 tff(2288,plain,
% 1.96/1.56 (hskp29),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1226, 81, 2149, 2287, 2143, 2142, 2286, 237, 384])).
% 1.96/1.56 tff(2289,plain,
% 1.96/1.56 (c2_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[340, 2288])).
% 1.96/1.56 tff(2290,plain,
% 1.96/1.56 (c1_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[351, 2288])).
% 1.96/1.56 tff(2291,plain,
% 1.96/1.56 (c0_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[362, 2288])).
% 1.96/1.56 tff(2292,plain,
% 1.96/1.56 (c2_1(a467)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2272, 81, 2291, 2290, 2289, 2211, 2210, 109])).
% 1.96/1.56 tff(2293,plain,
% 1.96/1.56 (~hskp30),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2125, 2292, 2211, 2210, 1664])).
% 1.96/1.56 tff(2294,plain,
% 1.96/1.56 ((~c2_1(a467)) | (~c3_1(a474))),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2110, 81, 1664, 2290, 2289, 2211, 2210, 1653])).
% 1.96/1.56 tff(2295,plain,
% 1.96/1.56 (~c3_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2294, 2292])).
% 1.96/1.56 tff(2296,plain,
% 1.96/1.56 (hskp30 | c3_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1327, 81, 21, 2291, 2290, 167])).
% 1.96/1.56 tff(2297,plain,
% 1.96/1.56 ($false),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2296, 2295, 2293])).
% 1.96/1.56 tff(2298,plain,(c2_1(a464) | hskp12 | c0_1(a471) | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.56 tff(2299,plain,
% 1.96/1.56 (c2_1(a464)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2298, 30, 21, 29])).
% 1.96/1.56 tff(2300,plain,
% 1.96/1.56 (~hskp2),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1496, 2299])).
% 1.96/1.56 tff(2301,plain,
% 1.96/1.56 ($false),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2203, 81, 2300, 2180, 2150, 2179, 2176, 648, 2178, 2157])).
% 1.96/1.56 tff(2302,plain,(hskp5 | hskp12 | c0_1(a471) | c3_1(a471) | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.56 tff(2303,plain,
% 1.96/1.56 ($false),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2302, 89, 31, 30, 21, 29])).
% 1.96/1.56 tff(2304,plain,(hskp5 | c0_1(a471) | hskp12 | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.56 tff(2305,plain,
% 1.96/1.56 (hskp5),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2304, 30, 21, 29])).
% 1.96/1.56 tff(2306,plain,
% 1.96/1.56 (~c3_1(a467)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1169, 2305])).
% 1.96/1.56 tff(2307,plain,
% 1.96/1.56 ($false),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2284, 1860, 1861, 2300, 21, 268, 30, 29])).
% 1.96/1.56 tff(2308,plain,((~hskp5) | hskp12 | c3_1(a467) | c0_1(a471) | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.56 tff(2309,plain,
% 1.96/1.56 ($false),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2308, 2306, 2305, 21, 30, 29])).
% 1.96/1.56 tff(2310,plain,(c0_1(a471) | hskp12 | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.56 tff(2311,plain,
% 1.96/1.56 (c0_1(a471)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2310, 29, 21])).
% 1.96/1.56 tff(2312,assumption,(~hskp29), introduced(assumption)).
% 1.96/1.56 tff(2313,plain,
% 1.96/1.56 (hskp3),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[457, 2312, 21])).
% 1.96/1.56 tff(2314,plain,
% 1.96/1.56 (~c0_1(a465)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1214, 2313])).
% 1.96/1.56 tff(2315,plain,
% 1.96/1.56 (c3_1(a465)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[442, 2313])).
% 1.96/1.56 tff(2316,plain,
% 1.96/1.56 (c2_1(a465)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[393, 81, 2312, 2149, 2315, 2143, 2142, 2314, 384])).
% 1.96/1.56 tff(2317,plain,
% 1.96/1.56 (~c1_1(a465)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1308, 2313])).
% 1.96/1.56 tff(2318,plain,
% 1.96/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a471) | c2_1(a471) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a471)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a471) | c2_1(a471) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a471)))),
% 1.96/1.56 inference(rewrite,[status(thm)],[])).
% 1.96/1.56 tff(2319,plain,
% 1.96/1.56 (((~ndr1_0) | c2_1(a471) | c3_1(a471) | (~c0_1(a471)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465))) <=> (c3_1(a471) | c2_1(a471) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a471)))),
% 1.96/1.56 inference(rewrite,[status(thm)],[])).
% 1.96/1.56 tff(2320,plain,
% 1.96/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a471) | c3_1(a471) | (~c0_1(a471)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a471) | c2_1(a471) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a471))))),
% 1.96/1.56 inference(monotonicity,[status(thm)],[2319])).
% 1.96/1.56 tff(2321,plain,
% 1.96/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a471) | c3_1(a471) | (~c0_1(a471)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a471) | c2_1(a471) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a471)))),
% 1.96/1.56 inference(transitivity,[status(thm)],[2320, 2318])).
% 1.96/1.56 tff(2322,plain,
% 1.96/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a471) | c3_1(a471) | (~c0_1(a471)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))),
% 1.96/1.56 inference(quant_inst,[status(thm)],[])).
% 1.96/1.56 tff(2323,plain,
% 1.96/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a471) | c2_1(a471) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a471))),
% 1.96/1.56 inference(modus_ponens,[status(thm)],[2322, 2321])).
% 1.96/1.56 tff(2324,plain,
% 1.96/1.56 ($false),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2323, 81, 2311, 1665, 2315, 29, 2314, 2317, 422, 2316])).
% 1.96/1.56 tff(2325,plain,(hskp29 | c3_1(a471) | c2_1(a471) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.96/1.56 tff(2326,plain,
% 1.96/1.56 (hskp29),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2325, 1665, 29, 21])).
% 1.96/1.56 tff(2327,plain,
% 1.96/1.56 (c2_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[340, 2326])).
% 1.96/1.56 tff(2328,plain,
% 1.96/1.56 (c0_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[362, 2326])).
% 1.96/1.56 tff(2329,plain,
% 1.96/1.56 (c1_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[351, 2326])).
% 1.96/1.56 tff(2330,plain,
% 1.96/1.56 ($false),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2138, 81, 2011, 2010, 2009, 552, 1665, 29, 109])).
% 1.96/1.56 tff(2331,plain,(c3_1(a471) | (~c0_1(a474)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a471)) | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.56 tff(2332,plain,
% 1.96/1.56 ($false),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2331, 2329, 2328, 1665, 2327, 2311, 29])).
% 1.96/1.56 tff(2333,plain,(c3_1(a471) | c2_1(a471) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.96/1.56 tff(2334,plain,
% 1.96/1.56 (c3_1(a471)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2333, 29, 21])).
% 1.96/1.56 tff(2335,plain,
% 1.96/1.56 (hskp29),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[457, 1216, 21])).
% 1.96/1.56 tff(2336,plain,
% 1.96/1.56 (c2_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[340, 2335])).
% 1.96/1.56 tff(2337,plain,
% 1.96/1.56 (c1_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[351, 2335])).
% 1.96/1.56 tff(2338,plain,
% 1.96/1.56 (c0_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[362, 2335])).
% 1.96/1.56 tff(2339,plain,
% 1.96/1.56 (c3_1(a471)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2331, 2338, 2337, 2336, 2311, 29])).
% 1.96/1.56 tff(2340,plain,
% 1.96/1.56 (hskp17),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[740, 2339, 2311, 31])).
% 1.96/1.56 tff(2341,plain,
% 1.96/1.56 (~c0_1(a493)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[757, 2340])).
% 1.96/1.56 tff(2342,plain,
% 1.96/1.56 (c3_1(a493)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[768, 2340])).
% 1.96/1.56 tff(2343,plain,
% 1.96/1.56 (c2_1(a493)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[751, 2340])).
% 1.96/1.56 tff(2344,plain,
% 1.96/1.56 (~c3_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1187, 81, 2338, 2337, 2336, 2343, 2342, 2341, 919])).
% 1.96/1.56 tff(2345,plain,
% 1.96/1.56 (hskp23),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1899, 1216, 31])).
% 1.96/1.56 tff(2346,plain,
% 1.96/1.56 (~c3_1(a521)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1905, 2345])).
% 1.96/1.56 tff(2347,plain,
% 1.96/1.56 (~c2_1(a521)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1911, 2345])).
% 1.96/1.56 tff(2348,plain,
% 1.96/1.56 (~c0_1(a521)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1917, 2345])).
% 1.96/1.56 tff(2349,plain,
% 1.96/1.56 (~c1_1(a521)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1924, 81, 2348, 2347, 2346, 10])).
% 1.96/1.56 tff(2350,plain,
% 1.96/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a521) | c3_1(a521) | c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a521) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a521) | c3_1(a521) | c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a521) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.56 inference(rewrite,[status(thm)],[])).
% 1.96/1.56 tff(2351,plain,
% 1.96/1.56 (((~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a521) | c1_1(a521) | c2_1(a521)) <=> (c2_1(a521) | c3_1(a521) | c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a521) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.56 inference(rewrite,[status(thm)],[])).
% 1.96/1.56 tff(2352,plain,
% 1.96/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a521) | c1_1(a521) | c2_1(a521))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a521) | c3_1(a521) | c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a521) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.96/1.56 inference(monotonicity,[status(thm)],[2351])).
% 1.96/1.56 tff(2353,plain,
% 1.96/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a521) | c1_1(a521) | c2_1(a521))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a521) | c3_1(a521) | c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a521) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.56 inference(transitivity,[status(thm)],[2352, 2350])).
% 1.96/1.56 tff(2354,plain,
% 1.96/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a474) | (~c1_1(a474)) | (~c0_1(a474)) | c0_1(a493) | (~c3_1(a493)) | (~c2_1(a493)) | c3_1(a521) | c1_1(a521) | c2_1(a521))),
% 1.96/1.56 inference(quant_inst,[status(thm)],[])).
% 1.96/1.56 tff(2355,plain,
% 1.96/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a521) | c3_1(a521) | c0_1(a493) | (~ndr1_0) | (~c3_1(a493)) | (~c2_1(a493)) | c1_1(a521) | c3_1(a474) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.96/1.56 inference(modus_ponens,[status(thm)],[2354, 2353])).
% 1.96/1.56 tff(2356,plain,
% 1.96/1.56 ($false),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2355, 81, 2338, 2337, 2343, 2342, 2347, 2346, 2341, 817, 2349, 2344])).
% 1.96/1.56 tff(2357,plain,(hskp3 | hskp5 | c2_1(a471) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.96/1.56 tff(2358,plain,
% 1.96/1.56 (hskp3),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2357, 31, 29, 21])).
% 1.96/1.56 tff(2359,plain,
% 1.96/1.56 (c3_1(a465)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[442, 2358])).
% 1.96/1.56 tff(2360,plain,
% 1.96/1.56 (~c0_1(a465)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1214, 2358])).
% 1.96/1.56 tff(2361,plain,
% 1.96/1.56 (~c1_1(a465)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1308, 2358])).
% 1.96/1.56 tff(2362,assumption,(hskp3), introduced(assumption)).
% 1.96/1.56 tff(2363,plain,
% 1.96/1.56 (~c1_1(a465)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1308, 2362])).
% 1.96/1.56 tff(2364,plain,
% 1.96/1.56 (c3_1(a465)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[442, 2362])).
% 1.96/1.56 tff(2365,plain,
% 1.96/1.56 (~c0_1(a465)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1214, 2362])).
% 1.96/1.56 tff(2366,plain,
% 1.96/1.56 ($false),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1444, 2365, 2364, 2363, 31, 1373, 21])).
% 1.96/1.56 tff(2367,plain,((~hskp3) | hskp5 | hskp2 | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.96/1.56 tff(2368,plain,
% 1.96/1.56 (hskp2),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2367, 2358, 31, 21])).
% 1.96/1.56 tff(2369,plain,
% 1.96/1.56 (~c0_1(a464)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1363, 2368])).
% 1.96/1.56 tff(2370,plain,
% 1.96/1.56 (~c2_1(a464)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1496, 2368])).
% 1.96/1.56 tff(2371,plain,
% 1.96/1.56 ($false),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1638, 2370, 2369, 21, 2361, 31, 2360, 2359])).
% 1.96/1.56 tff(2372,plain,(hskp5 | hskp12 | c2_1(a471)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.56 tff(2373,plain,
% 1.96/1.56 (hskp5),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2372, 29, 21])).
% 1.96/1.56 tff(2374,plain,
% 1.96/1.56 (~c1_1(a467)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1064, 2373])).
% 1.96/1.56 tff(2375,plain,
% 1.96/1.56 (c0_1(a467)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[602, 2373])).
% 1.96/1.56 tff(2376,plain,
% 1.96/1.56 ((~c2_1(a467)) | (~c3_1(a471))),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[588, 81, 21, 2311, 2375, 29, 2374, 582])).
% 1.96/1.56 tff(2377,plain,
% 1.96/1.56 (~c2_1(a467)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2376, 2334])).
% 1.96/1.56 tff(2378,plain,
% 1.96/1.56 (~c3_1(a467)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1169, 2373])).
% 1.96/1.56 tff(2379,assumption,(~c2_1(a467)), introduced(assumption)).
% 1.96/1.56 tff(2380,plain,
% 1.96/1.56 (c2_1(a465)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[393, 81, 2312, 387, 2315, 386, 385, 2314, 384])).
% 1.96/1.56 tff(2381,plain,
% 1.96/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a467) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a467)) | c2_1(a467))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a467) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a467)) | c2_1(a467))),
% 1.96/1.56 inference(rewrite,[status(thm)],[])).
% 1.96/1.56 tff(2382,plain,
% 1.96/1.56 (((~ndr1_0) | c2_1(a467) | c3_1(a467) | (~c0_1(a467)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465))) <=> (c3_1(a467) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a467)) | c2_1(a467))),
% 1.96/1.56 inference(rewrite,[status(thm)],[])).
% 1.96/1.56 tff(2383,plain,
% 1.96/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a467) | c3_1(a467) | (~c0_1(a467)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a467) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a467)) | c2_1(a467)))),
% 1.96/1.56 inference(monotonicity,[status(thm)],[2382])).
% 1.96/1.56 tff(2384,plain,
% 1.96/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a467) | c3_1(a467) | (~c0_1(a467)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a467) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a467)) | c2_1(a467))),
% 1.96/1.56 inference(transitivity,[status(thm)],[2383, 2381])).
% 1.96/1.56 tff(2385,plain,
% 1.96/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a467) | c3_1(a467) | (~c0_1(a467)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))),
% 1.96/1.56 inference(quant_inst,[status(thm)],[])).
% 1.96/1.56 tff(2386,plain,
% 1.96/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a467) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | (~c0_1(a467)) | c2_1(a467)),
% 1.96/1.56 inference(modus_ponens,[status(thm)],[2385, 2384])).
% 1.96/1.56 tff(2387,plain,
% 1.96/1.56 ($false),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2386, 81, 554, 2315, 268, 2314, 2317, 422, 2380, 2379])).
% 1.96/1.56 tff(2388,plain,(hskp29 | (~c0_1(a467)) | c3_1(a467) | c2_1(a467) | (~c0_1(a487)) | c1_1(a487) | c2_1(a487) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.96/1.56 tff(2389,plain,
% 1.96/1.56 (hskp29),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2388, 2375, 2378, 2377, 2149, 2143, 2142, 21])).
% 1.96/1.56 tff(2390,plain,
% 1.96/1.56 (c2_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[340, 2389])).
% 1.96/1.56 tff(2391,plain,
% 1.96/1.56 (c1_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[351, 2389])).
% 1.96/1.56 tff(2392,plain,
% 1.96/1.56 (c0_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[362, 2389])).
% 1.96/1.56 tff(2393,plain,
% 1.96/1.56 ($false),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2272, 81, 2392, 2391, 2390, 2375, 2378, 109, 2377])).
% 1.96/1.56 tff(2394,plain,(c2_1(a471) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.96/1.56 tff(2395,plain,
% 1.96/1.56 (c2_1(a471)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2394, 21])).
% 1.96/1.56 tff(2396,plain,
% 1.96/1.56 (~hskp7),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[528, 2395])).
% 1.96/1.56 tff(2397,plain,
% 1.96/1.56 (hskp2),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2367, 2362, 31, 21])).
% 1.96/1.56 tff(2398,plain,
% 1.96/1.56 (~c0_1(a464)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1363, 2397])).
% 1.96/1.56 tff(2399,plain,
% 1.96/1.56 (~c2_1(a464)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1496, 2397])).
% 1.96/1.56 tff(2400,plain,
% 1.96/1.56 ($false),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1638, 2399, 2398, 21, 2363, 31, 2365, 2364])).
% 1.96/1.56 tff(2401,plain,((~hskp3) | hskp12 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.96/1.56 tff(2402,plain,
% 1.96/1.56 (~hskp3),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2401, 31, 21])).
% 1.96/1.56 tff(2403,plain,
% 1.96/1.56 (hskp29),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[457, 2402, 21])).
% 1.96/1.56 tff(2404,plain,
% 1.96/1.56 (c2_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[340, 2403])).
% 1.96/1.56 tff(2405,plain,
% 1.96/1.56 (c1_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[351, 2403])).
% 1.96/1.56 tff(2406,plain,
% 1.96/1.56 (c0_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[362, 2403])).
% 1.96/1.56 tff(2407,plain,
% 1.96/1.56 (hskp23),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1899, 2402, 31])).
% 1.96/1.56 tff(2408,plain,
% 1.96/1.56 (~c3_1(a521)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1905, 2407])).
% 1.96/1.56 tff(2409,plain,
% 1.96/1.56 (~c2_1(a521)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1911, 2407])).
% 1.96/1.56 tff(2410,plain,
% 1.96/1.56 (~c0_1(a521)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1917, 2407])).
% 1.96/1.56 tff(2411,plain,
% 1.96/1.56 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0))),
% 1.96/1.56 inference(rewrite,[status(thm)],[])).
% 1.96/1.56 tff(2412,plain,
% 1.96/1.56 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a521) | c0_1(a521) | c3_1(a521)) <=> (hskp8 | hskp7 | c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0))),
% 1.96/1.56 inference(rewrite,[status(thm)],[])).
% 1.96/1.56 tff(2413,plain,
% 1.96/1.56 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a521) | c0_1(a521) | c3_1(a521))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0)))),
% 1.96/1.56 inference(monotonicity,[status(thm)],[2412])).
% 1.96/1.56 tff(2414,plain,
% 1.96/1.56 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a521) | c0_1(a521) | c3_1(a521))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0))),
% 1.96/1.56 inference(transitivity,[status(thm)],[2413, 2411])).
% 1.96/1.56 tff(2415,plain,
% 1.96/1.56 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a521) | c0_1(a521) | c3_1(a521))),
% 1.96/1.56 inference(quant_inst,[status(thm)],[])).
% 1.96/1.56 tff(2416,plain,
% 1.96/1.56 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp8 | hskp7 | c0_1(a521) | c2_1(a521) | c3_1(a521) | (~ndr1_0)),
% 1.96/1.56 inference(modus_ponens,[status(thm)],[2415, 2414])).
% 1.96/1.56 tff(2417,plain,
% 1.96/1.56 (hskp8),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2416, 81, 2396, 2410, 2409, 2408, 1675])).
% 1.96/1.56 tff(2418,plain,
% 1.96/1.56 (~c2_1(a472)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1688, 2417])).
% 1.96/1.56 tff(2419,plain,
% 1.96/1.56 (c3_1(a472)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1699, 2417])).
% 1.96/1.56 tff(2420,plain,
% 1.96/1.56 (c0_1(a472)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2055, 81, 21, 31, 2419, 2418, 41])).
% 1.96/1.56 tff(2421,plain,
% 1.96/1.56 (c1_1(a472)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1710, 2417])).
% 1.96/1.56 tff(2422,plain,
% 1.96/1.56 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.56 inference(rewrite,[status(thm)],[])).
% 1.96/1.56 tff(2423,plain,
% 1.96/1.56 ((hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474))) <=> (hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.56 inference(rewrite,[status(thm)],[])).
% 1.96/1.56 tff(2424,plain,
% 1.96/1.56 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))))),
% 1.96/1.56 inference(monotonicity,[status(thm)],[2423])).
% 1.96/1.56 tff(2425,plain,
% 1.96/1.56 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474)))),
% 1.96/1.56 inference(transitivity,[status(thm)],[2424, 2422])).
% 1.96/1.56 tff(2426,plain,
% 1.96/1.56 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c3_1(a472)) | (~c0_1(a472)) | (~c1_1(a474)) | (~c2_1(a474)) | (~c0_1(a474)))),
% 1.96/1.56 inference(quant_inst,[status(thm)],[])).
% 1.96/1.56 tff(2427,plain,
% 1.96/1.56 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp31 | (~ndr1_0) | (~c1_1(a472)) | (~c0_1(a472)) | (~c3_1(a472)) | (~c2_1(a474)) | (~c0_1(a474)) | (~c1_1(a474))),
% 1.96/1.56 inference(modus_ponens,[status(thm)],[2426, 2425])).
% 1.96/1.56 tff(2428,plain,
% 1.96/1.56 (hskp31 | (~c0_1(a472))),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2427, 81, 2406, 2405, 2404, 2421, 2419, 1290])).
% 1.96/1.56 tff(2429,plain,
% 1.96/1.56 (hskp31),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2428, 2420])).
% 1.96/1.56 tff(2430,plain,
% 1.96/1.56 (c3_1(a529)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1545, 2429])).
% 1.96/1.56 tff(2431,plain,
% 1.96/1.56 (hskp17 | (~c0_1(a472))),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2048, 81, 31, 2419, 2418, 733])).
% 1.96/1.56 tff(2432,plain,
% 1.96/1.56 (hskp17),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2431, 2420])).
% 1.96/1.56 tff(2433,plain,
% 1.96/1.56 (c0_1(a529)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1534, 2429])).
% 1.96/1.56 tff(2434,plain,
% 1.96/1.56 (c1_1(a529)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1556, 2429])).
% 1.96/1.56 tff(2435,plain,
% 1.96/1.56 ($false),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2013, 2434, 2433, 2432, 2430, 2406, 2405, 2404])).
% 1.96/1.56 tff(2436,plain,(hskp5 | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.96/1.56 tff(2437,plain,
% 1.96/1.56 (hskp5),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2436, 21])).
% 1.96/1.56 tff(2438,plain,
% 1.96/1.56 (~c3_1(a467)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1169, 2437])).
% 1.96/1.56 tff(2439,plain,
% 1.96/1.56 (c0_1(a467)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[602, 2437])).
% 1.96/1.56 tff(2440,plain,
% 1.96/1.56 (c2_1(a467)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2272, 81, 363, 352, 341, 2439, 2438, 109])).
% 1.96/1.56 tff(2441,plain,
% 1.96/1.56 (~hskp30),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2125, 2440, 2439, 2438, 2396])).
% 1.96/1.56 tff(2442,plain,
% 1.96/1.56 ((~c2_1(a467)) | (~c3_1(a474))),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2110, 81, 2396, 352, 341, 2439, 2438, 1653])).
% 1.96/1.56 tff(2443,plain,
% 1.96/1.56 (~c3_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2442, 2440])).
% 1.96/1.56 tff(2444,plain,
% 1.96/1.56 (hskp30 | c3_1(a474)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1327, 81, 21, 363, 352, 167])).
% 1.96/1.56 tff(2445,plain,
% 1.96/1.56 ($false),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2444, 2443, 2441])).
% 1.96/1.56 tff(2446,plain,((~hskp29) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.96/1.56 tff(2447,plain,
% 1.96/1.56 (~hskp29),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2446, 21])).
% 1.96/1.56 tff(2448,plain,
% 1.96/1.56 (c2_1(a467)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2388, 2312, 2438, 385, 387, 386, 2439, 21])).
% 1.96/1.56 tff(2449,plain,
% 1.96/1.56 (~c1_1(a467)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[1064, 2437])).
% 1.96/1.56 tff(2450,plain,
% 1.96/1.56 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a487) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a487)) | (~c3_1(a487)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a487) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a487)) | (~c3_1(a487)))),
% 1.96/1.56 inference(rewrite,[status(thm)],[])).
% 1.96/1.56 tff(2451,plain,
% 1.96/1.56 ((hskp12 | (~ndr1_0) | c2_1(a487) | (~c3_1(a487)) | (~c0_1(a487)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467))) <=> (hskp12 | c2_1(a487) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a487)) | (~c3_1(a487)))),
% 1.96/1.56 inference(rewrite,[status(thm)],[])).
% 1.96/1.56 tff(2452,plain,
% 1.96/1.56 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a487) | (~c3_1(a487)) | (~c0_1(a487)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a487) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a487)) | (~c3_1(a487))))),
% 1.96/1.56 inference(monotonicity,[status(thm)],[2451])).
% 1.96/1.56 tff(2453,plain,
% 1.96/1.56 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a487) | (~c3_1(a487)) | (~c0_1(a487)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a487) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a487)) | (~c3_1(a487)))),
% 1.96/1.56 inference(transitivity,[status(thm)],[2452, 2450])).
% 1.96/1.56 tff(2454,plain,
% 1.96/1.56 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a487) | (~c3_1(a487)) | (~c0_1(a487)) | c1_1(a467) | (~c2_1(a467)) | (~c0_1(a467)))),
% 1.96/1.56 inference(quant_inst,[status(thm)],[])).
% 1.96/1.56 tff(2455,plain,
% 1.96/1.56 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a487) | c1_1(a467) | (~ndr1_0) | (~c0_1(a467)) | (~c2_1(a467)) | (~c0_1(a487)) | (~c3_1(a487))),
% 1.96/1.56 inference(modus_ponens,[status(thm)],[2454, 2453])).
% 1.96/1.56 tff(2456,plain,
% 1.96/1.56 ((~c2_1(a467)) | (~c3_1(a487))),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2455, 81, 21, 387, 2439, 385, 2449, 582])).
% 1.96/1.56 tff(2457,plain,
% 1.96/1.56 (~c3_1(a487)),
% 1.96/1.56 inference(unit_resolution,[status(thm)],[2456, 2448])).
% 1.96/1.56 tff(2458,plain,
% 1.96/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a487) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a487) | (~c0_1(a487)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a487) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a487) | (~c0_1(a487)))),
% 1.96/1.56 inference(rewrite,[status(thm)],[])).
% 1.96/1.56 tff(2459,plain,
% 1.96/1.56 (((~ndr1_0) | c2_1(a487) | c3_1(a487) | (~c0_1(a487)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465))) <=> (c2_1(a487) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a487) | (~c0_1(a487)))),
% 1.96/1.56 inference(rewrite,[status(thm)],[])).
% 1.96/1.56 tff(2460,plain,
% 1.96/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a487) | c3_1(a487) | (~c0_1(a487)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a487) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a487) | (~c0_1(a487))))),
% 1.96/1.56 inference(monotonicity,[status(thm)],[2459])).
% 1.96/1.56 tff(2461,plain,
% 1.96/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a487) | c3_1(a487) | (~c0_1(a487)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a487) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a487) | (~c0_1(a487)))),
% 1.96/1.57 inference(transitivity,[status(thm)],[2460, 2458])).
% 1.96/1.57 tff(2462,plain,
% 1.96/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a487) | c3_1(a487) | (~c0_1(a487)) | c1_1(a465) | (~c3_1(a465)) | (~c2_1(a465)) | c1_1(a465) | c0_1(a465) | (~c2_1(a465)))),
% 1.96/1.57 inference(quant_inst,[status(thm)],[])).
% 1.96/1.57 tff(2463,plain,
% 1.96/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a487) | c0_1(a465) | c1_1(a465) | (~ndr1_0) | (~c3_1(a465)) | (~c2_1(a465)) | c3_1(a487) | (~c0_1(a487))),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2462, 2461])).
% 1.96/1.57 tff(2464,plain,
% 1.96/1.57 ($false),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2463, 81, 387, 2315, 385, 2314, 2317, 422, 2380, 2457])).
% 1.96/1.57 tff(2465,plain,(hskp29 | (~c0_1(a487)) | c2_1(a487) | c1_1(a487) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.96/1.57 tff(2466,plain,
% 1.96/1.57 ($false),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2465, 285, 296, 2447, 28, 21])).
% 1.96/1.57 tff(2467,plain,((~hskp16) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.96/1.57 tff(2468,plain,
% 1.96/1.57 (~hskp16),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2467, 21])).
% 1.96/1.57 tff(2469,plain,
% 1.96/1.57 (hskp16 | c2_1(a467)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[570, 81, 2439, 2449, 2438, 564])).
% 1.96/1.57 tff(2470,plain,
% 1.96/1.57 (c2_1(a467)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2469, 2468])).
% 1.96/1.57 tff(2471,plain,
% 1.96/1.57 (~hskp30),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2125, 2470, 2439, 2438, 2396])).
% 1.96/1.57 tff(2472,plain,
% 1.96/1.57 (^[U: $i] : refl((hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.96/1.57 inference(bind,[status(th)],[])).
% 1.96/1.57 tff(2473,plain,
% 1.96/1.57 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.96/1.57 inference(quant_intro,[status(thm)],[2472])).
% 1.96/1.57 tff(2474,plain,
% 1.96/1.57 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2475,plain,
% 1.96/1.57 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp30))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp21) <=> ((hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp21))), rewrite(((hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp21) <=> (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp21) <=> (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.96/1.57 inference(bind,[status(th)],[])).
% 1.96/1.57 tff(2476,plain,
% 1.96/1.57 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp21) <=> ![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.96/1.57 inference(quant_intro,[status(thm)],[2475])).
% 1.96/1.57 tff(2477,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 1.96/1.57 tff(2478,plain,
% 1.96/1.57 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2477, 2476])).
% 1.96/1.57 tff(2479,plain,
% 1.96/1.57 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2478, 2474])).
% 1.96/1.57 tff(2480,plain,(
% 1.96/1.57 ![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.96/1.57 inference(skolemize,[status(sab)],[2479])).
% 1.96/1.57 tff(2481,plain,
% 1.96/1.57 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2480, 2473])).
% 1.96/1.57 tff(2482,plain,
% 1.96/1.57 (((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp21 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)))) <=> ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp30 | hskp21 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2483,plain,
% 1.96/1.57 ((hskp30 | hskp21 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c2_1(a467))) <=> (hskp30 | hskp21 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2484,plain,
% 1.96/1.57 (((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp21 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c2_1(a467)))) <=> ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp21 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467))))),
% 1.96/1.57 inference(monotonicity,[status(thm)],[2483])).
% 1.96/1.57 tff(2485,plain,
% 1.96/1.57 (((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp21 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c2_1(a467)))) <=> ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp30 | hskp21 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467)))),
% 1.96/1.57 inference(transitivity,[status(thm)],[2484, 2482])).
% 1.96/1.57 tff(2486,plain,
% 1.96/1.57 ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp21 | (~ndr1_0) | c1_1(a467) | c3_1(a467) | (~c2_1(a467)))),
% 1.96/1.57 inference(quant_inst,[status(thm)],[])).
% 1.96/1.57 tff(2487,plain,
% 1.96/1.57 ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp30 | hskp21 | c1_1(a467) | c3_1(a467) | (~ndr1_0) | (~c2_1(a467))),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2486, 2485])).
% 1.96/1.57 tff(2488,plain,
% 1.96/1.57 (hskp30 | hskp21 | (~c2_1(a467))),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2487, 81, 2449, 2438, 2481])).
% 1.96/1.57 tff(2489,plain,
% 1.96/1.57 (hskp21),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2488, 2471, 2470])).
% 1.96/1.57 tff(2490,plain,
% 1.96/1.57 (((~hskp21) | (~c0_1(a507))) <=> ((~hskp21) | (~c0_1(a507)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2491,plain,
% 1.96/1.57 (((~c0_1(a507)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a507)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2492,axiom,((~c0_1(a507)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.96/1.57 tff(2493,plain,
% 1.96/1.57 ((~hskp21) | (~c0_1(a507))),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2492, 2491])).
% 1.96/1.57 tff(2494,plain,
% 1.96/1.57 ((~hskp21) | (~c0_1(a507))),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2493, 2490])).
% 1.96/1.57 tff(2495,plain,
% 1.96/1.57 (~c0_1(a507)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2494, 2489])).
% 1.96/1.57 tff(2496,plain,
% 1.96/1.57 (((~hskp21) | c2_1(a507)) <=> ((~hskp21) | c2_1(a507))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2497,axiom,((~hskp21) | c2_1(a507)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 1.96/1.57 tff(2498,plain,
% 1.96/1.57 ((~hskp21) | c2_1(a507)),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2497, 2496])).
% 1.96/1.57 tff(2499,plain,
% 1.96/1.57 ((~hskp21) | c2_1(a507)),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2498, 2496])).
% 1.96/1.57 tff(2500,plain,
% 1.96/1.57 ((~hskp21) | c2_1(a507)),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2499, 2496])).
% 1.96/1.57 tff(2501,plain,
% 1.96/1.57 ((~hskp21) | c2_1(a507)),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2500, 2496])).
% 1.96/1.57 tff(2502,plain,
% 1.96/1.57 ((~hskp21) | c2_1(a507)),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2501, 2496])).
% 1.96/1.57 tff(2503,plain,
% 1.96/1.57 ((~hskp21) | c2_1(a507)),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2502, 2496])).
% 1.96/1.57 tff(2504,plain,
% 1.96/1.57 ((~hskp21) | c2_1(a507)),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2503, 2496])).
% 1.96/1.57 tff(2505,plain,
% 1.96/1.57 ((~hskp21) | c2_1(a507)),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2504, 2496])).
% 1.96/1.57 tff(2506,plain,
% 1.96/1.57 (c2_1(a507)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2505, 2489])).
% 1.96/1.57 tff(2507,plain,
% 1.96/1.57 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a507) | (~ndr1_0) | c3_1(a507) | (~c2_1(a507)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a507) | (~ndr1_0) | c3_1(a507) | (~c2_1(a507)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2508,plain,
% 1.96/1.57 ((hskp16 | hskp7 | (~ndr1_0) | c0_1(a507) | c3_1(a507) | (~c2_1(a507))) <=> (hskp16 | hskp7 | c0_1(a507) | (~ndr1_0) | c3_1(a507) | (~c2_1(a507)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2509,plain,
% 1.96/1.57 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a507) | c3_1(a507) | (~c2_1(a507)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a507) | (~ndr1_0) | c3_1(a507) | (~c2_1(a507))))),
% 1.96/1.57 inference(monotonicity,[status(thm)],[2508])).
% 1.96/1.57 tff(2510,plain,
% 1.96/1.57 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a507) | c3_1(a507) | (~c2_1(a507)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a507) | (~ndr1_0) | c3_1(a507) | (~c2_1(a507)))),
% 1.96/1.57 inference(transitivity,[status(thm)],[2509, 2507])).
% 1.96/1.57 tff(2511,plain,
% 1.96/1.57 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a507) | c3_1(a507) | (~c2_1(a507)))),
% 1.96/1.57 inference(quant_inst,[status(thm)],[])).
% 1.96/1.57 tff(2512,plain,
% 1.96/1.57 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a507) | (~ndr1_0) | c3_1(a507) | (~c2_1(a507))),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2511, 2510])).
% 1.96/1.57 tff(2513,plain,
% 1.96/1.57 (c3_1(a507)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2512, 81, 2468, 2396, 2506, 2495, 20])).
% 1.96/1.57 tff(2514,plain,
% 1.96/1.57 (~hskp19),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[233, 2468, 21])).
% 1.96/1.57 tff(2515,plain,
% 1.96/1.57 (hskp31),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1523, 2514])).
% 1.96/1.57 tff(2516,plain,
% 1.96/1.57 (c3_1(a529)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1545, 2515])).
% 1.96/1.57 tff(2517,plain,
% 1.96/1.57 (c1_1(a529)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1556, 2515])).
% 1.96/1.57 tff(2518,plain,
% 1.96/1.57 (c0_1(a529)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1534, 2515])).
% 1.96/1.57 tff(2519,plain,
% 1.96/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a507) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c3_1(a507)) | (~c2_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a507) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c3_1(a507)) | (~c2_1(a507)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2520,plain,
% 1.96/1.57 (((~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c2_1(a529)) | (~c0_1(a529)) | c0_1(a507) | (~c3_1(a507)) | (~c2_1(a507))) <=> (c0_1(a507) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c3_1(a507)) | (~c2_1(a507)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2521,plain,
% 1.96/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c2_1(a529)) | (~c0_1(a529)) | c0_1(a507) | (~c3_1(a507)) | (~c2_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a507) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c3_1(a507)) | (~c2_1(a507))))),
% 1.96/1.57 inference(monotonicity,[status(thm)],[2520])).
% 1.96/1.57 tff(2522,plain,
% 1.96/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c2_1(a529)) | (~c0_1(a529)) | c0_1(a507) | (~c3_1(a507)) | (~c2_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a507) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c3_1(a507)) | (~c2_1(a507)))),
% 1.96/1.57 inference(transitivity,[status(thm)],[2521, 2519])).
% 1.96/1.57 tff(2523,plain,
% 1.96/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a529)) | (~c3_1(a529)) | (~c0_1(a529)) | (~c1_1(a529)) | (~c2_1(a529)) | (~c0_1(a529)) | c0_1(a507) | (~c3_1(a507)) | (~c2_1(a507)))),
% 1.96/1.57 inference(quant_inst,[status(thm)],[])).
% 1.96/1.57 tff(2524,plain,
% 1.96/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a507) | (~ndr1_0) | (~c3_1(a529)) | (~c0_1(a529)) | (~c2_1(a529)) | (~c1_1(a529)) | (~c3_1(a507)) | (~c2_1(a507))),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2523, 2522])).
% 1.96/1.57 tff(2525,plain,
% 1.96/1.57 (~c2_1(a529)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2524, 81, 2518, 2517, 2516, 2506, 2495, 919, 2513])).
% 1.96/1.57 tff(2526,plain,
% 1.96/1.57 ($false),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1776, 81, 21, 2518, 2516, 2439, 2449, 582, 2470, 2525])).
% 1.96/1.57 tff(2527,plain,(hskp12), inference(lemma,lemma(discharge,[]))).
% 1.96/1.57 tff(2528,plain,
% 1.96/1.57 (~c3_1(a481)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[463, 2527])).
% 1.96/1.57 tff(2529,plain,
% 1.96/1.57 (~c0_1(a481)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[469, 2527])).
% 1.96/1.57 tff(2530,plain,
% 1.96/1.57 (c1_1(a481)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[480, 2527])).
% 1.96/1.57 tff(2531,plain,
% 1.96/1.57 (c2_1(a481)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[487, 81, 2530, 2529, 2528, 10])).
% 1.96/1.57 tff(2532,plain,
% 1.96/1.57 ($false),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1242, 81, 296, 2530, 28, 285, 2529, 405, 2531])).
% 1.96/1.57 tff(2533,plain,(~hskp16), inference(lemma,lemma(discharge,[]))).
% 1.96/1.57 tff(2534,plain,
% 1.96/1.57 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c2_1(a481)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c2_1(a481)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2535,plain,
% 1.96/1.57 ((hskp16 | hskp7 | (~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c2_1(a481))) <=> (hskp16 | hskp7 | c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c2_1(a481)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2536,plain,
% 1.96/1.57 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c2_1(a481)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c2_1(a481))))),
% 1.96/1.57 inference(monotonicity,[status(thm)],[2535])).
% 1.96/1.57 tff(2537,plain,
% 1.96/1.57 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c2_1(a481)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c2_1(a481)))),
% 1.96/1.57 inference(transitivity,[status(thm)],[2536, 2534])).
% 1.96/1.57 tff(2538,plain,
% 1.96/1.57 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c0_1(a481) | c3_1(a481) | (~c2_1(a481)))),
% 1.96/1.57 inference(quant_inst,[status(thm)],[])).
% 1.96/1.57 tff(2539,plain,
% 1.96/1.57 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp7 | c0_1(a481) | c3_1(a481) | (~ndr1_0) | (~c2_1(a481))),
% 1.96/1.57 inference(modus_ponens,[status(thm)],[2538, 2537])).
% 1.96/1.57 tff(2540,plain,
% 1.96/1.57 (hskp16 | hskp7),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2539, 81, 2529, 2528, 20, 2531])).
% 1.96/1.57 tff(2541,plain,
% 1.96/1.57 (hskp7),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2540, 2533])).
% 1.96/1.57 tff(2542,plain,
% 1.96/1.57 (~c2_1(a471)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[528, 2541])).
% 1.96/1.57 tff(2543,plain,
% 1.96/1.57 (c0_1(a471)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[550, 2541])).
% 1.96/1.57 tff(2544,plain,
% 1.96/1.57 (c1_1(a471)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1009, 81, 2530, 2543, 2529, 2542, 405, 2531])).
% 1.96/1.57 tff(2545,plain,
% 1.96/1.57 (hskp29 | (~c1_1(a471))),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1051, 81, 2530, 2543, 2528, 2542, 1045, 2531])).
% 1.96/1.57 tff(2546,plain,
% 1.96/1.57 (hskp29),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2545, 2544])).
% 1.96/1.57 tff(2547,plain,
% 1.96/1.57 (c2_1(a474)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[340, 2546])).
% 1.96/1.57 tff(2548,plain,
% 1.96/1.57 (c0_1(a474)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[362, 2546])).
% 1.96/1.57 tff(2549,plain,
% 1.96/1.57 (hskp31),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1516, 2541, 2530, 2528, 2529])).
% 1.96/1.57 tff(2550,plain,
% 1.96/1.57 (c1_1(a529)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1556, 2549])).
% 1.96/1.57 tff(2551,plain,
% 1.96/1.57 (c3_1(a529)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1545, 2549])).
% 1.96/1.57 tff(2552,plain,
% 1.96/1.57 (c0_1(a529)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[1534, 2549])).
% 1.96/1.57 tff(2553,plain,
% 1.96/1.57 (c1_1(a474)),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[351, 2546])).
% 1.96/1.57 tff(2554,plain,
% 1.96/1.57 (~hskp17),
% 1.96/1.57 inference(unit_resolution,[status(thm)],[2013, 2553, 2552, 2551, 2550, 2548, 2547])).
% 1.96/1.57 tff(2555,plain,
% 1.96/1.57 (^[U: $i] : refl((hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 1.96/1.57 inference(bind,[status(th)],[])).
% 1.96/1.57 tff(2556,plain,
% 1.96/1.57 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.96/1.57 inference(quant_intro,[status(thm)],[2555])).
% 1.96/1.57 tff(2557,plain,
% 1.96/1.57 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.96/1.57 inference(rewrite,[status(thm)],[])).
% 1.96/1.57 tff(2558,plain,
% 1.96/1.57 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp18))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp17) <=> ((hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp17))), rewrite(((hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp17) <=> (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp17) <=> (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.96/1.58 inference(bind,[status(th)],[])).
% 1.96/1.58 tff(2559,plain,
% 1.96/1.58 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp17) <=> ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.96/1.58 inference(quant_intro,[status(thm)],[2558])).
% 1.96/1.58 tff(2560,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 1.96/1.58 tff(2561,plain,
% 1.96/1.58 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2560, 2559])).
% 1.96/1.58 tff(2562,plain,
% 1.96/1.58 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2561, 2557])).
% 1.96/1.58 tff(2563,plain,(
% 1.96/1.58 ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.96/1.58 inference(skolemize,[status(sab)],[2562])).
% 1.96/1.58 tff(2564,plain,
% 1.96/1.58 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2563, 2556])).
% 1.96/1.58 tff(2565,plain,
% 1.96/1.58 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp18 | hskp17 | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp18 | hskp17 | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(2566,plain,
% 1.96/1.58 ((hskp18 | hskp17 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481))) <=> (hskp18 | hskp17 | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.96/1.58 inference(rewrite,[status(thm)],[])).
% 1.96/1.58 tff(2567,plain,
% 1.96/1.58 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp18 | hskp17 | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481))))),
% 1.96/1.58 inference(monotonicity,[status(thm)],[2566])).
% 1.96/1.58 tff(2568,plain,
% 1.96/1.58 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp18 | hskp17 | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.96/1.58 inference(transitivity,[status(thm)],[2567, 2565])).
% 1.96/1.58 tff(2569,plain,
% 1.96/1.58 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c3_1(a481) | (~c1_1(a481)) | (~c2_1(a481)))),
% 1.96/1.58 inference(quant_inst,[status(thm)],[])).
% 1.96/1.58 tff(2570,plain,
% 1.96/1.58 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp18 | hskp17 | c3_1(a481) | (~ndr1_0) | (~c1_1(a481)) | (~c2_1(a481))),
% 1.96/1.58 inference(modus_ponens,[status(thm)],[2569, 2568])).
% 1.96/1.58 tff(2571,plain,
% 1.96/1.58 (hskp18 | hskp17 | (~c2_1(a481))),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[2570, 81, 2530, 2528, 2564])).
% 1.96/1.58 tff(2572,plain,
% 1.96/1.58 (hskp18),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[2571, 2554, 2531])).
% 1.96/1.58 tff(2573,plain,
% 1.96/1.58 (~c3_1(a494)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[308, 2572])).
% 1.96/1.58 tff(2574,plain,
% 1.96/1.58 (c0_1(a494)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[325, 2572])).
% 1.96/1.58 tff(2575,plain,
% 1.96/1.58 (~c2_1(a494)),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[314, 2572])).
% 1.96/1.58 tff(2576,plain,
% 1.96/1.58 ($false),
% 1.96/1.58 inference(unit_resolution,[status(thm)],[371, 2575, 2574, 2546, 2573])).
% 1.96/1.58 % SZS output end Proof
%------------------------------------------------------------------------------