TSTP Solution File: SYN469-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN469-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:55:41 EDT 2022
% Result : Unsatisfiable 1.63s 1.36s
% Output : Proof 2.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SYN469-1 : TPTP v8.1.0. Released v2.1.0.
% 0.08/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Sep 5 04:02:57 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.14/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.37 Usage: tptp [options] [-file:]file
% 0.14/0.37 -h, -? prints this message.
% 0.14/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.37 -m, -model generate model.
% 0.14/0.37 -p, -proof generate proof.
% 0.14/0.37 -c, -core generate unsat core of named formulas.
% 0.14/0.37 -st, -statistics display statistics.
% 0.14/0.37 -t:timeout set timeout (in second).
% 0.14/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.37 -<param>:<value> configuration parameter and value.
% 0.14/0.37 -o:<output-file> file to place output in.
% 1.63/1.36 % SZS status Unsatisfiable
% 1.63/1.36 % SZS output start Proof
% 1.63/1.36 tff(c3_1_type, type, (
% 1.63/1.36 c3_1: $i > $o)).
% 1.63/1.36 tff(a451_type, type, (
% 1.63/1.36 a451: $i)).
% 1.63/1.36 tff(c1_1_type, type, (
% 1.63/1.36 c1_1: $i > $o)).
% 1.63/1.36 tff(a477_type, type, (
% 1.63/1.36 a477: $i)).
% 1.63/1.36 tff(c2_1_type, type, (
% 1.63/1.36 c2_1: $i > $o)).
% 1.63/1.36 tff(c0_1_type, type, (
% 1.63/1.36 c0_1: $i > $o)).
% 1.63/1.36 tff(ndr1_0_type, type, (
% 1.63/1.36 ndr1_0: $o)).
% 1.63/1.36 tff(a401_type, type, (
% 1.63/1.36 a401: $i)).
% 1.63/1.36 tff(hskp1_type, type, (
% 1.63/1.36 hskp1: $o)).
% 1.63/1.36 tff(a402_type, type, (
% 1.63/1.36 a402: $i)).
% 1.63/1.36 tff(hskp2_type, type, (
% 1.63/1.36 hskp2: $o)).
% 1.63/1.36 tff(a410_type, type, (
% 1.63/1.36 a410: $i)).
% 1.63/1.36 tff(hskp7_type, type, (
% 1.63/1.36 hskp7: $o)).
% 1.63/1.36 tff(a403_type, type, (
% 1.63/1.36 a403: $i)).
% 1.63/1.36 tff(hskp3_type, type, (
% 1.63/1.36 hskp3: $o)).
% 1.63/1.36 tff(a420_type, type, (
% 1.63/1.36 a420: $i)).
% 1.63/1.36 tff(a408_type, type, (
% 1.63/1.36 a408: $i)).
% 1.63/1.36 tff(hskp5_type, type, (
% 1.63/1.36 hskp5: $o)).
% 1.63/1.36 tff(hskp24_type, type, (
% 1.63/1.36 hskp24: $o)).
% 1.63/1.36 tff(a428_type, type, (
% 1.63/1.36 a428: $i)).
% 1.63/1.36 tff(a445_type, type, (
% 1.63/1.36 a445: $i)).
% 1.63/1.36 tff(hskp19_type, type, (
% 1.63/1.36 hskp19: $o)).
% 1.63/1.36 tff(a450_type, type, (
% 1.63/1.36 a450: $i)).
% 1.63/1.36 tff(hskp0_type, type, (
% 1.63/1.36 hskp0: $o)).
% 1.63/1.36 tff(hskp21_type, type, (
% 1.63/1.36 hskp21: $o)).
% 1.63/1.36 tff(a405_type, type, (
% 1.63/1.36 a405: $i)).
% 1.63/1.36 tff(hskp25_type, type, (
% 1.63/1.36 hskp25: $o)).
% 1.63/1.36 tff(a434_type, type, (
% 1.63/1.36 a434: $i)).
% 1.63/1.36 tff(a460_type, type, (
% 1.63/1.36 a460: $i)).
% 1.63/1.36 tff(hskp23_type, type, (
% 1.63/1.36 hskp23: $o)).
% 1.63/1.36 tff(hskp27_type, type, (
% 1.63/1.36 hskp27: $o)).
% 1.63/1.36 tff(a412_type, type, (
% 1.63/1.36 a412: $i)).
% 1.63/1.36 tff(a427_type, type, (
% 1.63/1.36 a427: $i)).
% 1.63/1.36 tff(hskp13_type, type, (
% 1.63/1.36 hskp13: $o)).
% 1.63/1.36 tff(hskp14_type, type, (
% 1.63/1.36 hskp14: $o)).
% 1.63/1.36 tff(a400_type, type, (
% 1.63/1.36 a400: $i)).
% 1.63/1.36 tff(hskp11_type, type, (
% 1.63/1.36 hskp11: $o)).
% 1.63/1.36 tff(a449_type, type, (
% 1.63/1.36 a449: $i)).
% 1.63/1.36 tff(hskp20_type, type, (
% 1.63/1.36 hskp20: $o)).
% 1.63/1.36 tff(a416_type, type, (
% 1.63/1.36 a416: $i)).
% 1.63/1.36 tff(a426_type, type, (
% 1.63/1.36 a426: $i)).
% 1.63/1.36 tff(hskp12_type, type, (
% 1.63/1.36 hskp12: $o)).
% 1.63/1.36 tff(hskp9_type, type, (
% 1.63/1.36 hskp9: $o)).
% 1.63/1.36 tff(hskp22_type, type, (
% 1.63/1.36 hskp22: $o)).
% 1.63/1.36 tff(hskp16_type, type, (
% 1.63/1.36 hskp16: $o)).
% 1.63/1.36 tff(a440_type, type, (
% 1.63/1.36 a440: $i)).
% 1.63/1.36 tff(hskp18_type, type, (
% 1.63/1.36 hskp18: $o)).
% 1.63/1.36 tff(a430_type, type, (
% 1.63/1.36 a430: $i)).
% 1.63/1.36 tff(hskp15_type, type, (
% 1.63/1.36 hskp15: $o)).
% 1.63/1.36 tff(a418_type, type, (
% 1.63/1.36 a418: $i)).
% 1.63/1.36 tff(hskp10_type, type, (
% 1.63/1.36 hskp10: $o)).
% 1.63/1.36 tff(hskp28_type, type, (
% 1.63/1.36 hskp28: $o)).
% 1.63/1.36 tff(a414_type, type, (
% 1.63/1.36 a414: $i)).
% 1.63/1.36 tff(a404_type, type, (
% 1.63/1.36 a404: $i)).
% 1.63/1.36 tff(hskp4_type, type, (
% 1.63/1.36 hskp4: $o)).
% 1.63/1.36 tff(a415_type, type, (
% 1.63/1.36 a415: $i)).
% 1.63/1.36 tff(hskp8_type, type, (
% 1.63/1.36 hskp8: $o)).
% 1.63/1.36 tff(1,assumption,(~c1_1(a477)), introduced(assumption)).
% 1.63/1.36 tff(2,plain,
% 1.63/1.36 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 1.63/1.36 inference(bind,[status(th)],[])).
% 1.63/1.36 tff(3,plain,
% 1.63/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.63/1.36 inference(quant_intro,[status(thm)],[2])).
% 1.63/1.36 tff(4,plain,
% 1.63/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(5,plain,
% 1.63/1.36 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 1.63/1.36 inference(bind,[status(th)],[])).
% 1.63/1.36 tff(6,plain,
% 1.63/1.36 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.63/1.36 inference(quant_intro,[status(thm)],[5])).
% 1.63/1.36 tff(7,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 1.63/1.36 tff(8,plain,
% 1.63/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[7, 6])).
% 1.63/1.36 tff(9,plain,
% 1.63/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[8, 4])).
% 1.63/1.36 tff(10,plain,(
% 1.63/1.36 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.63/1.36 inference(skolemize,[status(sab)],[9])).
% 1.63/1.36 tff(11,plain,
% 1.63/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[10, 3])).
% 1.63/1.36 tff(12,assumption,(~hskp1), introduced(assumption)).
% 1.63/1.36 tff(13,plain,
% 1.63/1.36 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 1.63/1.36 inference(bind,[status(th)],[])).
% 1.63/1.36 tff(14,plain,
% 1.63/1.36 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.63/1.36 inference(quant_intro,[status(thm)],[13])).
% 1.63/1.36 tff(15,plain,
% 1.63/1.36 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(16,plain,
% 1.63/1.36 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 1.63/1.36 inference(bind,[status(th)],[])).
% 1.63/1.36 tff(17,plain,
% 1.63/1.36 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.63/1.36 inference(quant_intro,[status(thm)],[16])).
% 1.63/1.36 tff(18,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 1.63/1.36 tff(19,plain,
% 1.63/1.36 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.63/1.36 tff(20,plain,
% 1.63/1.36 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[19, 15])).
% 1.63/1.36 tff(21,plain,(
% 1.63/1.36 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.63/1.36 inference(skolemize,[status(sab)],[20])).
% 1.63/1.36 tff(22,plain,
% 1.63/1.36 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[21, 14])).
% 1.63/1.36 tff(23,assumption,(~hskp2), introduced(assumption)).
% 1.63/1.36 tff(24,plain,
% 1.63/1.36 (^[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)))),
% 1.63/1.36 inference(bind,[status(th)],[])).
% 1.63/1.36 tff(25,plain,
% 1.63/1.36 (![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))),
% 1.63/1.36 inference(quant_intro,[status(thm)],[24])).
% 1.63/1.36 tff(26,plain,
% 1.63/1.36 (![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))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(27,plain,
% 1.63/1.36 (^[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))))),
% 1.63/1.36 inference(bind,[status(th)],[])).
% 1.63/1.36 tff(28,plain,
% 1.63/1.36 (![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))),
% 1.63/1.36 inference(quant_intro,[status(thm)],[27])).
% 1.63/1.36 tff(29,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 1.63/1.36 tff(30,plain,
% 1.63/1.36 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.63/1.36 tff(31,plain,
% 1.63/1.36 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.63/1.36 tff(32,plain,(
% 1.63/1.36 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.63/1.36 inference(skolemize,[status(sab)],[31])).
% 1.63/1.36 tff(33,plain,
% 1.63/1.36 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[32, 25])).
% 1.63/1.36 tff(34,plain,
% 1.63/1.36 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))))),
% 1.63/1.36 inference(bind,[status(th)],[])).
% 1.63/1.36 tff(35,plain,
% 1.63/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.63/1.36 inference(quant_intro,[status(thm)],[34])).
% 1.63/1.36 tff(36,plain,
% 1.63/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(37,plain,
% 1.63/1.36 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))))),
% 1.63/1.36 inference(bind,[status(th)],[])).
% 1.63/1.36 tff(38,plain,
% 1.63/1.36 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.63/1.36 inference(quant_intro,[status(thm)],[37])).
% 1.63/1.36 tff(39,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 1.63/1.36 tff(40,plain,
% 1.63/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.63/1.36 tff(41,plain,
% 1.63/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[40, 36])).
% 1.63/1.36 tff(42,plain,(
% 1.63/1.36 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.63/1.36 inference(skolemize,[status(sab)],[41])).
% 1.63/1.36 tff(43,plain,
% 1.63/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[42, 35])).
% 1.63/1.36 tff(44,assumption,(~hskp3), introduced(assumption)).
% 1.63/1.36 tff(45,plain,
% 1.63/1.36 (^[U: $i] : refl((hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.63/1.36 inference(bind,[status(th)],[])).
% 1.63/1.36 tff(46,plain,
% 1.63/1.36 (![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.63/1.37 inference(quant_intro,[status(thm)],[45])).
% 1.63/1.37 tff(47,plain,
% 1.63/1.37 (![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(48,plain,
% 1.63/1.37 (^[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) | hskp3) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp3))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp3) <=> (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp3) <=> (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.63/1.37 inference(bind,[status(th)],[])).
% 1.63/1.37 tff(49,plain,
% 1.63/1.37 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp3) <=> ![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.63/1.37 inference(quant_intro,[status(thm)],[48])).
% 1.63/1.37 tff(50,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp5) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 1.63/1.37 tff(51,plain,
% 1.63/1.37 (![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.63/1.37 tff(52,plain,
% 1.63/1.37 (![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[51, 47])).
% 1.63/1.37 tff(53,plain,(
% 1.63/1.37 ![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.63/1.37 inference(skolemize,[status(sab)],[52])).
% 1.63/1.37 tff(54,plain,
% 1.63/1.37 (![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[53, 46])).
% 1.63/1.37 tff(55,assumption,(~hskp24), introduced(assumption)).
% 1.63/1.37 tff(56,assumption,(~hskp21), introduced(assumption)).
% 1.63/1.37 tff(57,plain,
% 1.63/1.37 ((hskp25 | hskp24 | hskp21) <=> (hskp25 | hskp24 | hskp21)),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(58,plain,
% 1.63/1.37 (((hskp25 | hskp24) | hskp21) <=> (hskp25 | hskp24 | hskp21)),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(59,plain,
% 1.63/1.37 ((hskp25 | hskp24) <=> (hskp25 | hskp24)),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(60,plain,
% 1.63/1.37 (((hskp25 | hskp24) | hskp21) <=> ((hskp25 | hskp24) | hskp21)),
% 1.63/1.37 inference(monotonicity,[status(thm)],[59])).
% 1.63/1.37 tff(61,plain,
% 1.63/1.37 (((hskp25 | hskp24) | hskp21) <=> (hskp25 | hskp24 | hskp21)),
% 1.63/1.37 inference(transitivity,[status(thm)],[60, 58])).
% 1.63/1.37 tff(62,axiom,((hskp25 | hskp24) | hskp21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause30')).
% 1.63/1.37 tff(63,plain,
% 1.63/1.37 (hskp25 | hskp24 | hskp21),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[62, 61])).
% 1.63/1.37 tff(64,plain,
% 1.63/1.37 (hskp25 | hskp24 | hskp21),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[63, 57])).
% 1.63/1.37 tff(65,plain,
% 1.63/1.37 (hskp25 | hskp24 | hskp21),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[64, 57])).
% 1.63/1.37 tff(66,plain,
% 1.63/1.37 (hskp25 | hskp24 | hskp21),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[65, 57])).
% 1.63/1.37 tff(67,plain,
% 1.63/1.37 (hskp25 | hskp24 | hskp21),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[66, 57])).
% 1.63/1.37 tff(68,plain,
% 1.63/1.37 (hskp25 | hskp24 | hskp21),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[67, 57])).
% 1.63/1.37 tff(69,plain,
% 1.63/1.37 (hskp25 | hskp24 | hskp21),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[68, 57])).
% 1.63/1.37 tff(70,plain,
% 1.63/1.37 (hskp25 | hskp24 | hskp21),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[69, 57])).
% 1.63/1.37 tff(71,plain,
% 1.63/1.37 (hskp25),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[70, 56, 55])).
% 1.63/1.37 tff(72,plain,
% 1.63/1.37 (((~hskp25) | c3_1(a405)) <=> ((~hskp25) | c3_1(a405))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(73,axiom,((~hskp25) | c3_1(a405)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 1.63/1.37 tff(74,plain,
% 1.63/1.37 ((~hskp25) | c3_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.63/1.37 tff(75,plain,
% 1.63/1.37 ((~hskp25) | c3_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[74, 72])).
% 1.63/1.37 tff(76,plain,
% 1.63/1.37 ((~hskp25) | c3_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[75, 72])).
% 1.63/1.37 tff(77,plain,
% 1.63/1.37 ((~hskp25) | c3_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[76, 72])).
% 1.63/1.37 tff(78,plain,
% 1.63/1.37 ((~hskp25) | c3_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[77, 72])).
% 1.63/1.37 tff(79,plain,
% 1.63/1.37 ((~hskp25) | c3_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[78, 72])).
% 1.63/1.37 tff(80,plain,
% 1.63/1.37 ((~hskp25) | c3_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[79, 72])).
% 1.63/1.37 tff(81,plain,
% 1.63/1.37 ((~hskp25) | c3_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[80, 72])).
% 1.63/1.37 tff(82,plain,
% 1.63/1.37 (c3_1(a405)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[81, 71])).
% 1.63/1.37 tff(83,plain,
% 1.63/1.37 (((~hskp25) | c1_1(a405)) <=> ((~hskp25) | c1_1(a405))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(84,axiom,((~hskp25) | c1_1(a405)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 1.63/1.37 tff(85,plain,
% 1.63/1.37 ((~hskp25) | c1_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[84, 83])).
% 1.63/1.37 tff(86,plain,
% 1.63/1.37 ((~hskp25) | c1_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[85, 83])).
% 1.63/1.37 tff(87,plain,
% 1.63/1.37 ((~hskp25) | c1_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[86, 83])).
% 1.63/1.37 tff(88,plain,
% 1.63/1.37 ((~hskp25) | c1_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[87, 83])).
% 1.63/1.37 tff(89,plain,
% 1.63/1.37 ((~hskp25) | c1_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[88, 83])).
% 1.63/1.37 tff(90,plain,
% 1.63/1.37 ((~hskp25) | c1_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[89, 83])).
% 1.63/1.37 tff(91,plain,
% 1.63/1.37 ((~hskp25) | c1_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[90, 83])).
% 1.63/1.37 tff(92,plain,
% 1.63/1.37 ((~hskp25) | c1_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[91, 83])).
% 1.63/1.37 tff(93,plain,
% 1.63/1.37 (c1_1(a405)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[92, 71])).
% 1.63/1.37 tff(94,plain,
% 1.63/1.37 (((~hskp25) | c0_1(a405)) <=> ((~hskp25) | c0_1(a405))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(95,axiom,((~hskp25) | c0_1(a405)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 1.63/1.37 tff(96,plain,
% 1.63/1.37 ((~hskp25) | c0_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.63/1.37 tff(97,plain,
% 1.63/1.37 ((~hskp25) | c0_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[96, 94])).
% 1.63/1.37 tff(98,plain,
% 1.63/1.37 ((~hskp25) | c0_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[97, 94])).
% 1.63/1.37 tff(99,plain,
% 1.63/1.37 ((~hskp25) | c0_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[98, 94])).
% 1.63/1.37 tff(100,plain,
% 1.63/1.37 ((~hskp25) | c0_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[99, 94])).
% 1.63/1.37 tff(101,plain,
% 1.63/1.37 ((~hskp25) | c0_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[100, 94])).
% 1.63/1.37 tff(102,plain,
% 1.63/1.37 ((~hskp25) | c0_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[101, 94])).
% 1.63/1.37 tff(103,plain,
% 1.63/1.37 ((~hskp25) | c0_1(a405)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[102, 94])).
% 1.63/1.37 tff(104,plain,
% 1.63/1.37 (c0_1(a405)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[103, 71])).
% 1.63/1.37 tff(105,assumption,(~c1_1(a402)), introduced(assumption)).
% 1.63/1.37 tff(106,assumption,(c3_1(a405)), introduced(assumption)).
% 1.63/1.37 tff(107,assumption,(c1_1(a405)), introduced(assumption)).
% 1.63/1.37 tff(108,assumption,(c0_1(a405)), introduced(assumption)).
% 1.63/1.37 tff(109,plain,
% 1.63/1.37 (^[U: $i] : refl((hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.63/1.37 inference(bind,[status(th)],[])).
% 1.63/1.37 tff(110,plain,
% 1.63/1.37 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.63/1.37 inference(quant_intro,[status(thm)],[109])).
% 1.63/1.37 tff(111,plain,
% 1.63/1.37 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(112,plain,
% 1.63/1.37 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp7) <=> ((hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp7))), rewrite(((hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp7) <=> (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp7) <=> (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.63/1.37 inference(bind,[status(th)],[])).
% 1.63/1.37 tff(113,plain,
% 1.63/1.37 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp7) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.63/1.37 inference(quant_intro,[status(thm)],[112])).
% 1.63/1.37 tff(114,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.63/1.37 tff(115,plain,
% 1.63/1.37 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.63/1.37 tff(116,plain,
% 1.63/1.37 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[115, 111])).
% 1.63/1.37 tff(117,plain,(
% 1.63/1.37 ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.63/1.37 inference(skolemize,[status(sab)],[116])).
% 1.63/1.37 tff(118,plain,
% 1.63/1.37 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[117, 110])).
% 1.63/1.37 tff(119,assumption,(~hskp19), introduced(assumption)).
% 1.63/1.37 tff(120,plain,
% 1.63/1.37 (^[U: $i] : refl((hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 1.63/1.37 inference(bind,[status(th)],[])).
% 1.63/1.37 tff(121,plain,
% 1.63/1.37 (![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.37 inference(quant_intro,[status(thm)],[120])).
% 1.63/1.37 tff(122,plain,
% 1.63/1.37 (![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(123,plain,
% 1.63/1.37 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) | hskp24) <=> ((hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp24))), rewrite(((hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) | hskp24) <=> (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.63/1.37 inference(bind,[status(th)],[])).
% 1.63/1.37 tff(124,plain,
% 1.63/1.37 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) | hskp24) <=> ![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.37 inference(quant_intro,[status(thm)],[123])).
% 1.63/1.37 tff(125,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 1.63/1.37 tff(126,plain,
% 1.63/1.37 (![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[125, 124])).
% 1.63/1.37 tff(127,plain,
% 1.63/1.37 (![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[126, 122])).
% 1.63/1.37 tff(128,plain,(
% 1.63/1.37 ![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.37 inference(skolemize,[status(sab)],[127])).
% 1.63/1.37 tff(129,plain,
% 1.63/1.37 (![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[128, 121])).
% 1.63/1.37 tff(130,assumption,(~ndr1_0), introduced(assumption)).
% 1.63/1.37 tff(131,plain,
% 1.63/1.37 ((ndr1_0 | (~hskp21)) <=> (ndr1_0 | (~hskp21))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(132,plain,
% 1.63/1.37 (((~hskp21) | ndr1_0) <=> (ndr1_0 | (~hskp21))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(133,axiom,((~hskp21) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause8')).
% 1.63/1.37 tff(134,plain,
% 1.63/1.37 (ndr1_0 | (~hskp21)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[133, 132])).
% 1.63/1.37 tff(135,plain,
% 1.63/1.37 (ndr1_0 | (~hskp21)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[134, 131])).
% 1.63/1.37 tff(136,plain,
% 1.63/1.37 (~hskp21),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[135, 130])).
% 1.63/1.37 tff(137,plain,
% 1.63/1.37 ((ndr1_0 | (~hskp25)) <=> (ndr1_0 | (~hskp25))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(138,plain,
% 1.63/1.37 (((~hskp25) | ndr1_0) <=> (ndr1_0 | (~hskp25))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(139,axiom,((~hskp25) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause4')).
% 1.63/1.37 tff(140,plain,
% 1.63/1.37 (ndr1_0 | (~hskp25)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[139, 138])).
% 1.63/1.37 tff(141,plain,
% 1.63/1.37 (ndr1_0 | (~hskp25)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[140, 137])).
% 1.63/1.37 tff(142,plain,
% 1.63/1.37 (~hskp25),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[141, 130])).
% 1.63/1.37 tff(143,plain,
% 1.63/1.37 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(144,plain,
% 1.63/1.37 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(145,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause5')).
% 1.63/1.37 tff(146,plain,
% 1.63/1.37 (ndr1_0 | (~hskp24)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[145, 144])).
% 1.63/1.37 tff(147,plain,
% 1.63/1.37 (ndr1_0 | (~hskp24)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[146, 143])).
% 1.63/1.37 tff(148,plain,
% 1.63/1.37 (~hskp24),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[147, 130])).
% 1.63/1.37 tff(149,plain,
% 1.63/1.37 ($false),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[70, 148, 142, 136])).
% 1.63/1.37 tff(150,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.63/1.37 tff(151,plain,
% 1.63/1.37 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c1_1(a405)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c1_1(a405)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(152,plain,
% 1.63/1.37 ((hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a405)) | (~c1_1(a405)) | (~c0_1(a405))) <=> (hskp24 | hskp19 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c1_1(a405)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(153,plain,
% 1.63/1.37 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a405)) | (~c1_1(a405)) | (~c0_1(a405)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c1_1(a405))))),
% 1.63/1.37 inference(monotonicity,[status(thm)],[152])).
% 1.63/1.37 tff(154,plain,
% 1.63/1.37 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a405)) | (~c1_1(a405)) | (~c0_1(a405)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c1_1(a405)))),
% 1.63/1.37 inference(transitivity,[status(thm)],[153, 151])).
% 1.63/1.37 tff(155,plain,
% 1.63/1.37 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a405)) | (~c1_1(a405)) | (~c0_1(a405)))),
% 1.63/1.37 inference(quant_inst,[status(thm)],[])).
% 1.63/1.37 tff(156,plain,
% 1.63/1.37 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c1_1(a405))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[155, 154])).
% 1.63/1.37 tff(157,plain,
% 1.63/1.37 (hskp19 | (~c2_1(a405))),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[156, 150, 55, 108, 107, 129])).
% 1.63/1.37 tff(158,plain,
% 1.63/1.37 (~c2_1(a405)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[157, 119])).
% 1.63/1.37 tff(159,assumption,(hskp27), introduced(assumption)).
% 1.63/1.37 tff(160,plain,
% 1.63/1.37 (((~hskp27) | c2_1(a412)) <=> ((~hskp27) | c2_1(a412))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(161,axiom,((~hskp27) | c2_1(a412)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 1.63/1.37 tff(162,plain,
% 1.63/1.37 ((~hskp27) | c2_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[161, 160])).
% 1.63/1.37 tff(163,plain,
% 1.63/1.37 ((~hskp27) | c2_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[162, 160])).
% 1.63/1.37 tff(164,plain,
% 1.63/1.37 ((~hskp27) | c2_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[163, 160])).
% 1.63/1.37 tff(165,plain,
% 1.63/1.37 ((~hskp27) | c2_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[164, 160])).
% 1.63/1.37 tff(166,plain,
% 1.63/1.37 ((~hskp27) | c2_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[165, 160])).
% 1.63/1.37 tff(167,plain,
% 1.63/1.37 ((~hskp27) | c2_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[166, 160])).
% 1.63/1.37 tff(168,plain,
% 1.63/1.37 ((~hskp27) | c2_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[167, 160])).
% 1.63/1.37 tff(169,plain,
% 1.63/1.37 ((~hskp27) | c2_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[168, 160])).
% 1.63/1.37 tff(170,plain,
% 1.63/1.37 (c2_1(a412)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[169, 159])).
% 1.63/1.37 tff(171,plain,
% 1.63/1.37 (((~hskp27) | c1_1(a412)) <=> ((~hskp27) | c1_1(a412))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(172,axiom,((~hskp27) | c1_1(a412)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 1.63/1.37 tff(173,plain,
% 1.63/1.37 ((~hskp27) | c1_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[172, 171])).
% 1.63/1.37 tff(174,plain,
% 1.63/1.37 ((~hskp27) | c1_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[173, 171])).
% 1.63/1.37 tff(175,plain,
% 1.63/1.37 ((~hskp27) | c1_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[174, 171])).
% 1.63/1.37 tff(176,plain,
% 1.63/1.37 ((~hskp27) | c1_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[175, 171])).
% 1.63/1.37 tff(177,plain,
% 1.63/1.37 ((~hskp27) | c1_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[176, 171])).
% 1.63/1.37 tff(178,plain,
% 1.63/1.37 ((~hskp27) | c1_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[177, 171])).
% 1.63/1.37 tff(179,plain,
% 1.63/1.37 ((~hskp27) | c1_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[178, 171])).
% 1.63/1.37 tff(180,plain,
% 1.63/1.37 ((~hskp27) | c1_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[179, 171])).
% 1.63/1.37 tff(181,plain,
% 1.63/1.37 (c1_1(a412)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[180, 159])).
% 1.63/1.37 tff(182,plain,
% 1.63/1.37 (((~hskp27) | c0_1(a412)) <=> ((~hskp27) | c0_1(a412))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(183,axiom,((~hskp27) | c0_1(a412)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 1.63/1.37 tff(184,plain,
% 1.63/1.37 ((~hskp27) | c0_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[183, 182])).
% 1.63/1.37 tff(185,plain,
% 1.63/1.37 ((~hskp27) | c0_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[184, 182])).
% 1.63/1.37 tff(186,plain,
% 1.63/1.37 ((~hskp27) | c0_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[185, 182])).
% 1.63/1.37 tff(187,plain,
% 1.63/1.37 ((~hskp27) | c0_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[186, 182])).
% 1.63/1.37 tff(188,plain,
% 1.63/1.37 ((~hskp27) | c0_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[187, 182])).
% 1.63/1.37 tff(189,plain,
% 1.63/1.37 ((~hskp27) | c0_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[188, 182])).
% 1.63/1.37 tff(190,plain,
% 1.63/1.37 ((~hskp27) | c0_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[189, 182])).
% 1.63/1.37 tff(191,plain,
% 1.63/1.37 ((~hskp27) | c0_1(a412)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[190, 182])).
% 1.63/1.37 tff(192,plain,
% 1.63/1.37 (c0_1(a412)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[191, 159])).
% 1.63/1.37 tff(193,plain,
% 1.63/1.37 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(194,plain,
% 1.63/1.37 ((hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c1_1(a412)) | (~c0_1(a412))) <=> (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(195,plain,
% 1.63/1.37 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c1_1(a412)) | (~c0_1(a412)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412))))),
% 1.63/1.37 inference(monotonicity,[status(thm)],[194])).
% 1.63/1.37 tff(196,plain,
% 1.63/1.37 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c1_1(a412)) | (~c0_1(a412)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412)))),
% 1.63/1.37 inference(transitivity,[status(thm)],[195, 193])).
% 1.63/1.37 tff(197,plain,
% 1.63/1.37 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c1_1(a412)) | (~c0_1(a412)))),
% 1.63/1.37 inference(quant_inst,[status(thm)],[])).
% 1.63/1.37 tff(198,plain,
% 1.63/1.37 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[197, 196])).
% 1.63/1.37 tff(199,plain,
% 1.63/1.37 ($false),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[198, 150, 55, 119, 192, 181, 170, 129])).
% 1.63/1.37 tff(200,plain,((~hskp27) | hskp24 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.63/1.37 tff(201,plain,
% 1.63/1.37 (~hskp27),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[200, 119, 55])).
% 1.63/1.37 tff(202,plain,
% 1.63/1.37 (^[U: $i] : refl((hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.63/1.37 inference(bind,[status(th)],[])).
% 1.63/1.37 tff(203,plain,
% 1.63/1.37 (![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.37 inference(quant_intro,[status(thm)],[202])).
% 1.63/1.37 tff(204,plain,
% 1.63/1.37 (![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(205,plain,
% 1.63/1.37 (^[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)) | 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)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) | hskp23) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp23))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) | hskp23) <=> (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.63/1.37 inference(bind,[status(th)],[])).
% 1.63/1.37 tff(206,plain,
% 1.63/1.37 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) | hskp23) <=> ![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.37 inference(quant_intro,[status(thm)],[205])).
% 1.63/1.37 tff(207,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 1.63/1.37 tff(208,plain,
% 1.63/1.37 (![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[207, 206])).
% 1.63/1.37 tff(209,plain,
% 1.63/1.37 (![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[208, 204])).
% 1.63/1.37 tff(210,plain,(
% 1.63/1.37 ![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.37 inference(skolemize,[status(sab)],[209])).
% 1.63/1.37 tff(211,plain,
% 1.63/1.37 (![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[210, 203])).
% 1.63/1.37 tff(212,plain,
% 1.63/1.37 (((~![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp23 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c1_1(a405)))) <=> ((~![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp23 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c1_1(a405)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(213,plain,
% 1.63/1.37 ((hskp27 | hskp23 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c0_1(a405))) <=> (hskp27 | hskp23 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c1_1(a405)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(214,plain,
% 1.63/1.37 (((~![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp23 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c0_1(a405)))) <=> ((~![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp23 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c1_1(a405))))),
% 1.63/1.37 inference(monotonicity,[status(thm)],[213])).
% 1.63/1.37 tff(215,plain,
% 1.63/1.37 (((~![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp23 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c0_1(a405)))) <=> ((~![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp23 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c1_1(a405)))),
% 1.63/1.37 inference(transitivity,[status(thm)],[214, 212])).
% 1.63/1.37 tff(216,plain,
% 1.63/1.37 ((~![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp27 | hskp23 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c0_1(a405)))),
% 1.63/1.37 inference(quant_inst,[status(thm)],[])).
% 1.63/1.37 tff(217,plain,
% 1.63/1.37 ((~![U: $i] : (hskp27 | hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp27 | hskp23 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c1_1(a405))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[216, 215])).
% 1.63/1.37 tff(218,plain,
% 1.63/1.37 (hskp27 | hskp23 | c2_1(a405)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[217, 150, 108, 107, 211])).
% 1.63/1.37 tff(219,plain,
% 1.63/1.37 (hskp23),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[218, 201, 158])).
% 1.63/1.37 tff(220,plain,
% 1.63/1.37 (((~hskp23) | (~c3_1(a460))) <=> ((~hskp23) | (~c3_1(a460)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(221,plain,
% 1.63/1.37 (((~c3_1(a460)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a460)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(222,axiom,((~c3_1(a460)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 1.63/1.37 tff(223,plain,
% 1.63/1.37 ((~hskp23) | (~c3_1(a460))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[222, 221])).
% 1.63/1.37 tff(224,plain,
% 1.63/1.37 ((~hskp23) | (~c3_1(a460))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[223, 220])).
% 1.63/1.37 tff(225,plain,
% 1.63/1.37 (~c3_1(a460)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[224, 219])).
% 1.63/1.37 tff(226,plain,
% 1.63/1.37 (((~hskp23) | (~c2_1(a460))) <=> ((~hskp23) | (~c2_1(a460)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(227,plain,
% 1.63/1.37 (((~c2_1(a460)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a460)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(228,axiom,((~c2_1(a460)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 1.63/1.37 tff(229,plain,
% 1.63/1.37 ((~hskp23) | (~c2_1(a460))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[228, 227])).
% 1.63/1.37 tff(230,plain,
% 1.63/1.37 ((~hskp23) | (~c2_1(a460))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[229, 226])).
% 1.63/1.37 tff(231,plain,
% 1.63/1.37 (~c2_1(a460)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[230, 219])).
% 1.63/1.37 tff(232,plain,
% 1.63/1.37 (((~hskp23) | c1_1(a460)) <=> ((~hskp23) | c1_1(a460))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(233,axiom,((~hskp23) | c1_1(a460)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 1.63/1.37 tff(234,plain,
% 1.63/1.37 ((~hskp23) | c1_1(a460)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[233, 232])).
% 1.63/1.37 tff(235,plain,
% 1.63/1.37 ((~hskp23) | c1_1(a460)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[234, 232])).
% 1.63/1.37 tff(236,plain,
% 1.63/1.37 ((~hskp23) | c1_1(a460)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[235, 232])).
% 1.63/1.37 tff(237,plain,
% 1.63/1.37 ((~hskp23) | c1_1(a460)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[236, 232])).
% 1.63/1.37 tff(238,plain,
% 1.63/1.37 ((~hskp23) | c1_1(a460)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[237, 232])).
% 1.63/1.37 tff(239,plain,
% 1.63/1.37 ((~hskp23) | c1_1(a460)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[238, 232])).
% 1.63/1.37 tff(240,plain,
% 1.63/1.37 ((~hskp23) | c1_1(a460)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[239, 232])).
% 1.63/1.37 tff(241,plain,
% 1.63/1.37 ((~hskp23) | c1_1(a460)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[240, 232])).
% 1.63/1.37 tff(242,plain,
% 1.63/1.37 (c1_1(a460)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[241, 219])).
% 1.63/1.37 tff(243,plain,
% 1.63/1.37 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c1_1(a460)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c1_1(a460)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(244,plain,
% 1.63/1.37 ((hskp7 | hskp2 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460))) <=> (hskp7 | hskp2 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c1_1(a460)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(245,plain,
% 1.63/1.37 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c1_1(a460))))),
% 1.63/1.37 inference(monotonicity,[status(thm)],[244])).
% 1.63/1.37 tff(246,plain,
% 1.63/1.37 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c1_1(a460)))),
% 1.63/1.38 inference(transitivity,[status(thm)],[245, 243])).
% 1.63/1.38 tff(247,plain,
% 1.63/1.38 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)))),
% 1.63/1.38 inference(quant_inst,[status(thm)],[])).
% 1.63/1.38 tff(248,plain,
% 1.63/1.38 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | (~c1_1(a460))),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[247, 246])).
% 1.63/1.38 tff(249,plain,
% 1.63/1.38 (hskp7),
% 1.63/1.38 inference(unit_resolution,[status(thm)],[248, 150, 23, 242, 231, 225, 118])).
% 1.63/1.38 tff(250,plain,
% 1.63/1.38 (((~hskp7) | (~c3_1(a410))) <=> ((~hskp7) | (~c3_1(a410)))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(251,plain,
% 1.63/1.38 (((~c3_1(a410)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a410)))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(252,axiom,((~c3_1(a410)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 1.63/1.38 tff(253,plain,
% 1.63/1.38 ((~hskp7) | (~c3_1(a410))),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[252, 251])).
% 1.63/1.38 tff(254,plain,
% 1.63/1.38 ((~hskp7) | (~c3_1(a410))),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[253, 250])).
% 1.63/1.38 tff(255,plain,
% 1.63/1.38 (~c3_1(a410)),
% 1.63/1.38 inference(unit_resolution,[status(thm)],[254, 249])).
% 1.63/1.38 tff(256,plain,
% 1.63/1.38 (((~hskp7) | (~c1_1(a410))) <=> ((~hskp7) | (~c1_1(a410)))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(257,plain,
% 1.63/1.38 (((~c1_1(a410)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a410)))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(258,axiom,((~c1_1(a410)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 1.63/1.38 tff(259,plain,
% 1.63/1.38 ((~hskp7) | (~c1_1(a410))),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[258, 257])).
% 1.63/1.38 tff(260,plain,
% 1.63/1.38 ((~hskp7) | (~c1_1(a410))),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[259, 256])).
% 1.63/1.38 tff(261,plain,
% 1.63/1.38 (~c1_1(a410)),
% 1.63/1.38 inference(unit_resolution,[status(thm)],[260, 249])).
% 1.63/1.38 tff(262,plain,
% 1.63/1.38 (^[U: $i] : refl((hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 1.63/1.38 inference(bind,[status(th)],[])).
% 1.63/1.38 tff(263,plain,
% 1.63/1.38 (![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.63/1.38 inference(quant_intro,[status(thm)],[262])).
% 1.63/1.38 tff(264,plain,
% 1.63/1.38 (![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(265,plain,
% 1.63/1.38 (^[U: $i] : 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)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp2) | hskp13) <=> ((hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp13))), rewrite(((hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp13) <=> (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp2) | hskp13) <=> (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 1.63/1.38 inference(bind,[status(th)],[])).
% 1.63/1.38 tff(266,plain,
% 1.63/1.38 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp2) | hskp13) <=> ![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.63/1.38 inference(quant_intro,[status(thm)],[265])).
% 1.63/1.38 tff(267,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp2) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 1.63/1.38 tff(268,plain,
% 1.63/1.38 (![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[267, 266])).
% 1.63/1.38 tff(269,plain,
% 1.63/1.38 (![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[268, 264])).
% 1.63/1.38 tff(270,plain,(
% 1.63/1.38 ![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.63/1.38 inference(skolemize,[status(sab)],[269])).
% 1.63/1.38 tff(271,plain,
% 1.63/1.38 (![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[270, 263])).
% 1.63/1.38 tff(272,plain,
% 1.63/1.38 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(273,plain,
% 1.63/1.38 ((hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405))) <=> (hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(274,plain,
% 1.63/1.38 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405))))),
% 1.63/1.38 inference(monotonicity,[status(thm)],[273])).
% 1.63/1.38 tff(275,plain,
% 1.63/1.38 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 1.63/1.38 inference(transitivity,[status(thm)],[274, 272])).
% 1.63/1.38 tff(276,plain,
% 1.63/1.38 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)))),
% 1.63/1.38 inference(quant_inst,[status(thm)],[])).
% 1.63/1.38 tff(277,plain,
% 1.63/1.38 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405))),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[276, 275])).
% 1.63/1.38 tff(278,plain,
% 1.63/1.38 (hskp13 | hskp2 | c2_1(a405)),
% 1.63/1.38 inference(unit_resolution,[status(thm)],[277, 150, 107, 106, 271])).
% 1.63/1.38 tff(279,plain,
% 1.63/1.38 (hskp13),
% 1.63/1.38 inference(unit_resolution,[status(thm)],[278, 158, 23])).
% 1.63/1.38 tff(280,plain,
% 1.63/1.38 (((~hskp13) | (~c0_1(a427))) <=> ((~hskp13) | (~c0_1(a427)))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(281,plain,
% 1.63/1.38 (((~c0_1(a427)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a427)))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(282,axiom,((~c0_1(a427)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 1.63/1.38 tff(283,plain,
% 1.63/1.38 ((~hskp13) | (~c0_1(a427))),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[282, 281])).
% 1.63/1.38 tff(284,plain,
% 1.63/1.38 ((~hskp13) | (~c0_1(a427))),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[283, 280])).
% 1.63/1.38 tff(285,plain,
% 1.63/1.38 (~c0_1(a427)),
% 1.63/1.38 inference(unit_resolution,[status(thm)],[284, 279])).
% 1.63/1.38 tff(286,plain,
% 1.63/1.38 (((~hskp7) | c0_1(a410)) <=> ((~hskp7) | c0_1(a410))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(287,axiom,((~hskp7) | c0_1(a410)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 1.63/1.38 tff(288,plain,
% 1.63/1.38 ((~hskp7) | c0_1(a410)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[287, 286])).
% 1.63/1.38 tff(289,plain,
% 1.63/1.38 ((~hskp7) | c0_1(a410)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[288, 286])).
% 1.63/1.38 tff(290,plain,
% 1.63/1.38 ((~hskp7) | c0_1(a410)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[289, 286])).
% 1.63/1.38 tff(291,plain,
% 1.63/1.38 ((~hskp7) | c0_1(a410)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[290, 286])).
% 1.63/1.38 tff(292,plain,
% 1.63/1.38 ((~hskp7) | c0_1(a410)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[291, 286])).
% 1.63/1.38 tff(293,plain,
% 1.63/1.38 ((~hskp7) | c0_1(a410)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[292, 286])).
% 1.63/1.38 tff(294,plain,
% 1.63/1.38 ((~hskp7) | c0_1(a410)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[293, 286])).
% 1.63/1.38 tff(295,plain,
% 1.63/1.38 ((~hskp7) | c0_1(a410)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[294, 286])).
% 1.63/1.38 tff(296,plain,
% 1.63/1.38 (c0_1(a410)),
% 1.63/1.38 inference(unit_resolution,[status(thm)],[295, 249])).
% 1.63/1.38 tff(297,plain,
% 1.63/1.38 (((~hskp13) | c2_1(a427)) <=> ((~hskp13) | c2_1(a427))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(298,axiom,((~hskp13) | c2_1(a427)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 1.63/1.38 tff(299,plain,
% 1.63/1.38 ((~hskp13) | c2_1(a427)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[298, 297])).
% 1.63/1.38 tff(300,plain,
% 1.63/1.38 ((~hskp13) | c2_1(a427)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[299, 297])).
% 1.63/1.38 tff(301,plain,
% 1.63/1.38 ((~hskp13) | c2_1(a427)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[300, 297])).
% 1.63/1.38 tff(302,plain,
% 1.63/1.38 ((~hskp13) | c2_1(a427)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[301, 297])).
% 1.63/1.38 tff(303,plain,
% 1.63/1.38 ((~hskp13) | c2_1(a427)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[302, 297])).
% 1.63/1.38 tff(304,plain,
% 1.63/1.38 ((~hskp13) | c2_1(a427)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[303, 297])).
% 1.63/1.38 tff(305,plain,
% 1.63/1.38 ((~hskp13) | c2_1(a427)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[304, 297])).
% 1.63/1.38 tff(306,plain,
% 1.63/1.38 ((~hskp13) | c2_1(a427)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[305, 297])).
% 1.63/1.38 tff(307,plain,
% 1.63/1.38 (c2_1(a427)),
% 1.63/1.38 inference(unit_resolution,[status(thm)],[306, 279])).
% 1.63/1.38 tff(308,plain,
% 1.63/1.38 (((~hskp13) | c1_1(a427)) <=> ((~hskp13) | c1_1(a427))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(309,axiom,((~hskp13) | c1_1(a427)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 1.63/1.38 tff(310,plain,
% 1.63/1.38 ((~hskp13) | c1_1(a427)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[309, 308])).
% 1.63/1.38 tff(311,plain,
% 1.63/1.38 ((~hskp13) | c1_1(a427)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[310, 308])).
% 1.63/1.38 tff(312,plain,
% 1.63/1.38 ((~hskp13) | c1_1(a427)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[311, 308])).
% 1.63/1.38 tff(313,plain,
% 1.63/1.38 ((~hskp13) | c1_1(a427)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[312, 308])).
% 1.63/1.38 tff(314,plain,
% 1.63/1.38 ((~hskp13) | c1_1(a427)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[313, 308])).
% 1.63/1.38 tff(315,plain,
% 1.63/1.38 ((~hskp13) | c1_1(a427)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[314, 308])).
% 1.63/1.38 tff(316,plain,
% 1.63/1.38 ((~hskp13) | c1_1(a427)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[315, 308])).
% 1.63/1.38 tff(317,plain,
% 1.63/1.38 ((~hskp13) | c1_1(a427)),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[316, 308])).
% 1.63/1.38 tff(318,plain,
% 1.63/1.38 (c1_1(a427)),
% 1.63/1.38 inference(unit_resolution,[status(thm)],[317, 279])).
% 1.63/1.38 tff(319,plain,
% 1.63/1.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a427) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a427) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(320,plain,
% 1.63/1.38 ((hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427))) <=> (hskp1 | c0_1(a427) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(321,plain,
% 1.63/1.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a427) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a427)) | (~c1_1(a427))))),
% 1.63/1.38 inference(monotonicity,[status(thm)],[320])).
% 1.63/1.38 tff(322,plain,
% 1.63/1.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a427) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.63/1.38 inference(transitivity,[status(thm)],[321, 319])).
% 1.63/1.38 tff(323,plain,
% 1.63/1.38 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.63/1.38 inference(quant_inst,[status(thm)],[])).
% 1.63/1.38 tff(324,plain,
% 1.63/1.38 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a427) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a427)) | (~c1_1(a427))),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[323, 322])).
% 1.63/1.38 tff(325,plain,
% 1.63/1.38 ($false),
% 1.63/1.38 inference(unit_resolution,[status(thm)],[324, 150, 12, 318, 307, 296, 285, 261, 255, 22])).
% 1.63/1.38 tff(326,plain,(hskp19 | hskp1 | hskp2 | (~c0_1(a405)) | (~c1_1(a405)) | (~c3_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.63/1.38 tff(327,plain,
% 1.63/1.38 (hskp19),
% 1.63/1.38 inference(unit_resolution,[status(thm)],[326, 23, 12, 108, 107, 106, 55])).
% 1.63/1.38 tff(328,plain,
% 1.63/1.38 (((~hskp19) | (~c0_1(a445))) <=> ((~hskp19) | (~c0_1(a445)))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(329,plain,
% 1.63/1.38 (((~c0_1(a445)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a445)))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(330,axiom,((~c0_1(a445)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 1.63/1.38 tff(331,plain,
% 1.63/1.38 ((~hskp19) | (~c0_1(a445))),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[330, 329])).
% 1.63/1.38 tff(332,plain,
% 1.63/1.38 ((~hskp19) | (~c0_1(a445))),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[331, 328])).
% 1.63/1.38 tff(333,plain,
% 1.63/1.38 (~c0_1(a445)),
% 1.63/1.38 inference(unit_resolution,[status(thm)],[332, 327])).
% 1.63/1.38 tff(334,assumption,(~c3_1(a403)), introduced(assumption)).
% 1.63/1.38 tff(335,assumption,(~c2_1(a403)), introduced(assumption)).
% 1.63/1.38 tff(336,assumption,(~c0_1(a403)), introduced(assumption)).
% 1.63/1.38 tff(337,plain,
% 1.63/1.38 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)))),
% 1.63/1.38 inference(bind,[status(th)],[])).
% 1.63/1.38 tff(338,plain,
% 1.63/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.63/1.38 inference(quant_intro,[status(thm)],[337])).
% 1.63/1.38 tff(339,plain,
% 1.63/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(340,plain,
% 1.63/1.38 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c0_1(W))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c0_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c0_1(W) | c2_1(W))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c0_1(W) | c2_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))))),
% 1.63/1.38 inference(bind,[status(th)],[])).
% 1.63/1.38 tff(341,plain,
% 1.63/1.38 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.63/1.38 inference(quant_intro,[status(thm)],[340])).
% 1.63/1.38 tff(342,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 1.78/1.38 tff(343,plain,
% 1.78/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[342, 341])).
% 1.78/1.38 tff(344,plain,
% 1.78/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[343, 339])).
% 1.78/1.38 tff(345,plain,(
% 1.78/1.38 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.78/1.38 inference(skolemize,[status(sab)],[344])).
% 1.78/1.38 tff(346,plain,
% 1.78/1.38 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[345, 338])).
% 1.78/1.38 tff(347,plain,
% 1.78/1.38 (^[U: $i] : refl((hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 1.78/1.38 inference(bind,[status(th)],[])).
% 1.78/1.38 tff(348,plain,
% 1.78/1.38 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.78/1.38 inference(quant_intro,[status(thm)],[347])).
% 1.78/1.38 tff(349,plain,
% 1.78/1.38 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.78/1.38 inference(rewrite,[status(thm)],[])).
% 1.78/1.38 tff(350,plain,
% 1.78/1.38 (^[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)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp0) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp0))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp0) <=> (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp0) <=> (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 1.78/1.38 inference(bind,[status(th)],[])).
% 1.78/1.38 tff(351,plain,
% 1.78/1.38 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp0) <=> ![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.78/1.38 inference(quant_intro,[status(thm)],[350])).
% 1.78/1.38 tff(352,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 1.78/1.38 tff(353,plain,
% 1.78/1.38 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[352, 351])).
% 1.78/1.38 tff(354,plain,
% 1.78/1.38 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[353, 349])).
% 1.78/1.38 tff(355,plain,(
% 1.78/1.38 ![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.78/1.38 inference(skolemize,[status(sab)],[354])).
% 1.78/1.38 tff(356,plain,
% 1.78/1.38 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[355, 348])).
% 1.78/1.38 tff(357,plain,
% 1.78/1.38 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp0 | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0))),
% 1.78/1.38 inference(rewrite,[status(thm)],[])).
% 1.78/1.38 tff(358,plain,
% 1.78/1.38 ((hskp27 | hskp0 | (~ndr1_0) | c2_1(a403) | c0_1(a403) | c3_1(a403)) <=> (hskp27 | hskp0 | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0))),
% 1.78/1.38 inference(rewrite,[status(thm)],[])).
% 1.78/1.38 tff(359,plain,
% 1.78/1.38 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | (~ndr1_0) | c2_1(a403) | c0_1(a403) | c3_1(a403))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0)))),
% 1.78/1.38 inference(monotonicity,[status(thm)],[358])).
% 1.78/1.38 tff(360,plain,
% 1.78/1.38 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | (~ndr1_0) | c2_1(a403) | c0_1(a403) | c3_1(a403))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp0 | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0))),
% 1.78/1.38 inference(transitivity,[status(thm)],[359, 357])).
% 1.78/1.38 tff(361,plain,
% 1.78/1.38 ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | (~ndr1_0) | c2_1(a403) | c0_1(a403) | c3_1(a403))),
% 1.78/1.38 inference(quant_inst,[status(thm)],[])).
% 1.78/1.38 tff(362,plain,
% 1.78/1.38 ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp0 | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0)),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[361, 360])).
% 1.78/1.38 tff(363,plain,
% 1.78/1.38 (hskp27 | hskp0 | c0_1(a403) | c2_1(a403)),
% 1.78/1.38 inference(unit_resolution,[status(thm)],[362, 150, 334, 356])).
% 1.78/1.38 tff(364,plain,
% 1.78/1.38 (hskp0),
% 1.78/1.38 inference(unit_resolution,[status(thm)],[363, 201, 336, 335])).
% 1.78/1.38 tff(365,plain,
% 1.78/1.38 (((~hskp0) | c2_1(a400)) <=> ((~hskp0) | c2_1(a400))),
% 1.78/1.38 inference(rewrite,[status(thm)],[])).
% 1.78/1.38 tff(366,axiom,((~hskp0) | c2_1(a400)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 1.78/1.38 tff(367,plain,
% 1.78/1.38 ((~hskp0) | c2_1(a400)),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[366, 365])).
% 1.78/1.38 tff(368,plain,
% 1.78/1.38 ((~hskp0) | c2_1(a400)),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[367, 365])).
% 1.78/1.38 tff(369,plain,
% 1.78/1.38 ((~hskp0) | c2_1(a400)),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[368, 365])).
% 1.78/1.38 tff(370,plain,
% 1.78/1.38 ((~hskp0) | c2_1(a400)),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[369, 365])).
% 1.78/1.38 tff(371,plain,
% 1.78/1.38 ((~hskp0) | c2_1(a400)),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[370, 365])).
% 1.78/1.38 tff(372,plain,
% 1.78/1.38 ((~hskp0) | c2_1(a400)),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[371, 365])).
% 1.78/1.38 tff(373,plain,
% 1.78/1.38 ((~hskp0) | c2_1(a400)),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[372, 365])).
% 1.78/1.38 tff(374,plain,
% 1.78/1.38 ((~hskp0) | c2_1(a400)),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[373, 365])).
% 1.78/1.38 tff(375,plain,
% 1.78/1.38 (c2_1(a400)),
% 1.78/1.38 inference(unit_resolution,[status(thm)],[374, 364])).
% 1.78/1.38 tff(376,plain,
% 1.78/1.38 (((~hskp0) | c1_1(a400)) <=> ((~hskp0) | c1_1(a400))),
% 1.78/1.38 inference(rewrite,[status(thm)],[])).
% 1.78/1.38 tff(377,axiom,((~hskp0) | c1_1(a400)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 1.78/1.38 tff(378,plain,
% 1.78/1.38 ((~hskp0) | c1_1(a400)),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[377, 376])).
% 1.78/1.38 tff(379,plain,
% 1.78/1.38 ((~hskp0) | c1_1(a400)),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[378, 376])).
% 1.78/1.38 tff(380,plain,
% 1.78/1.38 ((~hskp0) | c1_1(a400)),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[379, 376])).
% 1.78/1.38 tff(381,plain,
% 1.78/1.38 ((~hskp0) | c1_1(a400)),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[380, 376])).
% 1.78/1.38 tff(382,plain,
% 1.78/1.38 ((~hskp0) | c1_1(a400)),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[381, 376])).
% 1.78/1.38 tff(383,plain,
% 1.78/1.38 ((~hskp0) | c1_1(a400)),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[382, 376])).
% 1.78/1.38 tff(384,plain,
% 1.78/1.38 ((~hskp0) | c1_1(a400)),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[383, 376])).
% 1.78/1.38 tff(385,plain,
% 1.78/1.38 ((~hskp0) | c1_1(a400)),
% 1.78/1.38 inference(modus_ponens,[status(thm)],[384, 376])).
% 1.78/1.39 tff(386,plain,
% 1.78/1.39 (c1_1(a400)),
% 1.78/1.39 inference(unit_resolution,[status(thm)],[385, 364])).
% 1.78/1.39 tff(387,plain,
% 1.78/1.39 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(388,plain,
% 1.78/1.39 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)))),
% 1.78/1.39 inference(quant_inst,[status(thm)],[])).
% 1.78/1.39 tff(389,plain,
% 1.78/1.39 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[388, 387])).
% 1.78/1.39 tff(390,plain,
% 1.78/1.39 (~c0_1(a400)),
% 1.78/1.39 inference(unit_resolution,[status(thm)],[389, 150, 55, 119, 386, 375, 129])).
% 1.78/1.39 tff(391,plain,
% 1.78/1.39 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.78/1.39 inference(bind,[status(th)],[])).
% 1.78/1.39 tff(392,plain,
% 1.78/1.39 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.78/1.39 inference(quant_intro,[status(thm)],[391])).
% 1.78/1.39 tff(393,plain,
% 1.78/1.39 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(394,plain,
% 1.78/1.39 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.78/1.39 inference(bind,[status(th)],[])).
% 1.78/1.39 tff(395,plain,
% 1.78/1.39 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.78/1.39 inference(quant_intro,[status(thm)],[394])).
% 1.78/1.39 tff(396,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 1.78/1.39 tff(397,plain,
% 1.78/1.39 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[396, 395])).
% 1.78/1.39 tff(398,plain,
% 1.78/1.39 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[397, 393])).
% 1.78/1.39 tff(399,plain,(
% 1.78/1.39 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.78/1.39 inference(skolemize,[status(sab)],[398])).
% 1.78/1.39 tff(400,plain,
% 1.78/1.39 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[399, 392])).
% 1.78/1.39 tff(401,plain,
% 1.78/1.39 (((~hskp0) | (~c3_1(a400))) <=> ((~hskp0) | (~c3_1(a400)))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(402,plain,
% 1.78/1.39 (((~c3_1(a400)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a400)))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(403,axiom,((~c3_1(a400)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 1.78/1.39 tff(404,plain,
% 1.78/1.39 ((~hskp0) | (~c3_1(a400))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[403, 402])).
% 1.78/1.39 tff(405,plain,
% 1.78/1.39 ((~hskp0) | (~c3_1(a400))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[404, 401])).
% 1.78/1.39 tff(406,plain,
% 1.78/1.39 (~c3_1(a400)),
% 1.78/1.39 inference(unit_resolution,[status(thm)],[405, 364])).
% 1.78/1.39 tff(407,assumption,(~hskp14), introduced(assumption)).
% 1.78/1.39 tff(408,plain,
% 1.78/1.39 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c2_1(a405) | (~c3_1(a405)) | c0_1(a400) | (~c1_1(a405)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c2_1(a405) | (~c3_1(a405)) | c0_1(a400) | (~c1_1(a405)))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(409,plain,
% 1.78/1.39 ((hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400))) <=> (hskp14 | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c2_1(a405) | (~c3_1(a405)) | c0_1(a400) | (~c1_1(a405)))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(410,plain,
% 1.78/1.39 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c2_1(a405) | (~c3_1(a405)) | c0_1(a400) | (~c1_1(a405))))),
% 1.78/1.39 inference(monotonicity,[status(thm)],[409])).
% 1.78/1.39 tff(411,plain,
% 1.78/1.39 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c2_1(a405) | (~c3_1(a405)) | c0_1(a400) | (~c1_1(a405)))),
% 1.78/1.39 inference(transitivity,[status(thm)],[410, 408])).
% 1.78/1.39 tff(412,plain,
% 1.78/1.39 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)))),
% 1.78/1.39 inference(quant_inst,[status(thm)],[])).
% 1.78/1.39 tff(413,plain,
% 1.78/1.39 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c2_1(a405) | (~c3_1(a405)) | c0_1(a400) | (~c1_1(a405))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[412, 411])).
% 1.78/1.39 tff(414,plain,
% 1.78/1.39 ($false),
% 1.78/1.39 inference(unit_resolution,[status(thm)],[413, 150, 407, 107, 106, 375, 406, 400, 158, 390])).
% 1.78/1.39 tff(415,plain,(hskp19 | hskp14 | (~c1_1(a405)) | (~c3_1(a405)) | hskp24 | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~c0_1(a405))), inference(lemma,lemma(discharge,[]))).
% 1.78/1.39 tff(416,plain,
% 1.78/1.39 (hskp14),
% 1.78/1.39 inference(unit_resolution,[status(thm)],[415, 119, 107, 106, 55, 336, 335, 334, 108])).
% 1.78/1.39 tff(417,plain,
% 1.78/1.39 (((~hskp14) | (~c1_1(a428))) <=> ((~hskp14) | (~c1_1(a428)))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(418,plain,
% 1.78/1.39 (((~c1_1(a428)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a428)))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(419,axiom,((~c1_1(a428)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 1.78/1.39 tff(420,plain,
% 1.78/1.39 ((~hskp14) | (~c1_1(a428))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[419, 418])).
% 1.78/1.39 tff(421,plain,
% 1.78/1.39 ((~hskp14) | (~c1_1(a428))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[420, 417])).
% 1.78/1.39 tff(422,plain,
% 1.78/1.39 (~c1_1(a428)),
% 1.78/1.39 inference(unit_resolution,[status(thm)],[421, 416])).
% 1.78/1.39 tff(423,plain,
% 1.78/1.39 (((~hskp14) | (~c0_1(a428))) <=> ((~hskp14) | (~c0_1(a428)))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(424,plain,
% 1.78/1.39 (((~c0_1(a428)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a428)))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(425,axiom,((~c0_1(a428)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 1.78/1.39 tff(426,plain,
% 1.78/1.39 ((~hskp14) | (~c0_1(a428))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[425, 424])).
% 1.78/1.39 tff(427,plain,
% 1.78/1.39 ((~hskp14) | (~c0_1(a428))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[426, 423])).
% 1.78/1.39 tff(428,plain,
% 1.78/1.39 (~c0_1(a428)),
% 1.78/1.39 inference(unit_resolution,[status(thm)],[427, 416])).
% 1.78/1.39 tff(429,plain,
% 1.78/1.39 (((~hskp14) | c2_1(a428)) <=> ((~hskp14) | c2_1(a428))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(430,axiom,((~hskp14) | c2_1(a428)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 1.78/1.39 tff(431,plain,
% 1.78/1.39 ((~hskp14) | c2_1(a428)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[430, 429])).
% 1.78/1.39 tff(432,plain,
% 1.78/1.39 ((~hskp14) | c2_1(a428)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[431, 429])).
% 1.78/1.39 tff(433,plain,
% 1.78/1.39 ((~hskp14) | c2_1(a428)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[432, 429])).
% 1.78/1.39 tff(434,plain,
% 1.78/1.39 ((~hskp14) | c2_1(a428)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[433, 429])).
% 1.78/1.39 tff(435,plain,
% 1.78/1.39 ((~hskp14) | c2_1(a428)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[434, 429])).
% 1.78/1.39 tff(436,plain,
% 1.78/1.39 ((~hskp14) | c2_1(a428)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[435, 429])).
% 1.78/1.39 tff(437,plain,
% 1.78/1.39 ((~hskp14) | c2_1(a428)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[436, 429])).
% 1.78/1.39 tff(438,plain,
% 1.78/1.39 ((~hskp14) | c2_1(a428)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[437, 429])).
% 1.78/1.39 tff(439,plain,
% 1.78/1.39 (c2_1(a428)),
% 1.78/1.39 inference(unit_resolution,[status(thm)],[438, 416])).
% 1.78/1.39 tff(440,plain,
% 1.78/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c1_1(a460)))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(441,plain,
% 1.78/1.39 (((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a428) | c0_1(a428) | (~c2_1(a428)) | c3_1(a403) | c0_1(a403) | c2_1(a403)) <=> (c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c1_1(a460)))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(442,plain,
% 1.78/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a428) | c0_1(a428) | (~c2_1(a428)) | c3_1(a403) | c0_1(a403) | c2_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c1_1(a460))))),
% 1.78/1.39 inference(monotonicity,[status(thm)],[441])).
% 1.78/1.39 tff(443,plain,
% 1.78/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a428) | c0_1(a428) | (~c2_1(a428)) | c3_1(a403) | c0_1(a403) | c2_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c1_1(a460)))),
% 1.78/1.39 inference(transitivity,[status(thm)],[442, 440])).
% 1.78/1.39 tff(444,plain,
% 1.78/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a428) | c0_1(a428) | (~c2_1(a428)) | c3_1(a403) | c0_1(a403) | c2_1(a403))),
% 1.78/1.39 inference(quant_inst,[status(thm)],[])).
% 1.78/1.39 tff(445,plain,
% 1.78/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c1_1(a460))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[444, 443])).
% 1.78/1.39 tff(446,plain,
% 1.78/1.39 ($false),
% 1.78/1.39 inference(unit_resolution,[status(thm)],[445, 150, 242, 439, 231, 225, 428, 422, 336, 335, 334, 346])).
% 1.78/1.39 tff(447,plain,(hskp19 | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~c0_1(a405)) | (~c1_1(a405)) | (~c3_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.78/1.39 tff(448,plain,
% 1.78/1.39 (hskp19),
% 1.78/1.39 inference(unit_resolution,[status(thm)],[447, 336, 335, 334, 108, 107, 106, 55])).
% 1.78/1.39 tff(449,plain,
% 1.78/1.39 (((~hskp19) | c1_1(a445)) <=> ((~hskp19) | c1_1(a445))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(450,axiom,((~hskp19) | c1_1(a445)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 1.78/1.39 tff(451,plain,
% 1.78/1.39 ((~hskp19) | c1_1(a445)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[450, 449])).
% 1.78/1.39 tff(452,plain,
% 1.78/1.39 ((~hskp19) | c1_1(a445)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[451, 449])).
% 1.78/1.39 tff(453,plain,
% 1.78/1.39 ((~hskp19) | c1_1(a445)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[452, 449])).
% 1.78/1.39 tff(454,plain,
% 1.78/1.39 ((~hskp19) | c1_1(a445)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[453, 449])).
% 1.78/1.39 tff(455,plain,
% 1.78/1.39 ((~hskp19) | c1_1(a445)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[454, 449])).
% 1.78/1.39 tff(456,plain,
% 1.78/1.39 ((~hskp19) | c1_1(a445)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[455, 449])).
% 1.78/1.39 tff(457,plain,
% 1.78/1.39 ((~hskp19) | c1_1(a445)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[456, 449])).
% 1.78/1.39 tff(458,plain,
% 1.78/1.39 ((~hskp19) | c1_1(a445)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[457, 449])).
% 1.78/1.39 tff(459,plain,
% 1.78/1.39 (c1_1(a445)),
% 1.78/1.39 inference(unit_resolution,[status(thm)],[458, 448])).
% 1.78/1.39 tff(460,plain,
% 1.78/1.39 (~c0_1(a445)),
% 1.78/1.39 inference(unit_resolution,[status(thm)],[332, 448])).
% 1.78/1.39 tff(461,plain,
% 1.78/1.39 (((~hskp19) | c3_1(a445)) <=> ((~hskp19) | c3_1(a445))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(462,axiom,((~hskp19) | c3_1(a445)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 1.78/1.39 tff(463,plain,
% 1.78/1.39 ((~hskp19) | c3_1(a445)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[462, 461])).
% 1.78/1.39 tff(464,plain,
% 1.78/1.39 ((~hskp19) | c3_1(a445)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[463, 461])).
% 1.78/1.39 tff(465,plain,
% 1.78/1.39 ((~hskp19) | c3_1(a445)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[464, 461])).
% 1.78/1.39 tff(466,plain,
% 1.78/1.39 ((~hskp19) | c3_1(a445)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[465, 461])).
% 1.78/1.39 tff(467,plain,
% 1.78/1.39 ((~hskp19) | c3_1(a445)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[466, 461])).
% 1.78/1.39 tff(468,plain,
% 1.78/1.39 ((~hskp19) | c3_1(a445)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[467, 461])).
% 1.78/1.39 tff(469,plain,
% 1.78/1.39 ((~hskp19) | c3_1(a445)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[468, 461])).
% 1.78/1.39 tff(470,plain,
% 1.78/1.39 ((~hskp19) | c3_1(a445)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[469, 461])).
% 1.78/1.39 tff(471,plain,
% 1.78/1.39 (c3_1(a445)),
% 1.78/1.39 inference(unit_resolution,[status(thm)],[470, 448])).
% 1.78/1.39 tff(472,assumption,(~c0_1(a445)), introduced(assumption)).
% 1.78/1.39 tff(473,assumption,(c3_1(a445)), introduced(assumption)).
% 1.78/1.39 tff(474,plain,
% 1.78/1.39 (^[U: $i] : refl((hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.78/1.39 inference(bind,[status(th)],[])).
% 1.78/1.39 tff(475,plain,
% 1.78/1.39 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.78/1.39 inference(quant_intro,[status(thm)],[474])).
% 1.78/1.39 tff(476,plain,
% 1.78/1.39 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(477,plain,
% 1.78/1.39 (^[U: $i] : 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)) | hskp20) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.78/1.39 inference(bind,[status(th)],[])).
% 1.78/1.39 tff(478,plain,
% 1.78/1.39 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp20) <=> ![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.78/1.39 inference(quant_intro,[status(thm)],[477])).
% 1.78/1.39 tff(479,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 1.78/1.39 tff(480,plain,
% 1.78/1.39 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[479, 478])).
% 1.78/1.39 tff(481,plain,
% 1.78/1.39 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[480, 476])).
% 1.78/1.39 tff(482,plain,(
% 1.78/1.39 ![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.78/1.39 inference(skolemize,[status(sab)],[481])).
% 1.78/1.39 tff(483,plain,
% 1.78/1.39 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[482, 475])).
% 1.78/1.39 tff(484,assumption,(c1_1(a445)), introduced(assumption)).
% 1.78/1.39 tff(485,assumption,(~hskp11), introduced(assumption)).
% 1.78/1.39 tff(486,plain,
% 1.78/1.39 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W))))),
% 1.78/1.39 inference(bind,[status(th)],[])).
% 1.78/1.39 tff(487,plain,
% 1.78/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 1.78/1.39 inference(quant_intro,[status(thm)],[486])).
% 1.78/1.39 tff(488,plain,
% 1.78/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(489,plain,
% 1.78/1.39 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))))),
% 1.78/1.39 inference(bind,[status(th)],[])).
% 1.78/1.39 tff(490,plain,
% 1.78/1.39 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 1.78/1.39 inference(quant_intro,[status(thm)],[489])).
% 1.78/1.39 tff(491,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 1.78/1.39 tff(492,plain,
% 1.78/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[491, 490])).
% 1.78/1.39 tff(493,plain,
% 1.78/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[492, 488])).
% 1.78/1.39 tff(494,plain,(
% 1.78/1.39 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 1.78/1.39 inference(skolemize,[status(sab)],[493])).
% 1.78/1.39 tff(495,plain,
% 1.78/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[494, 487])).
% 1.78/1.39 tff(496,assumption,(~c1_1(a403)), introduced(assumption)).
% 1.78/1.39 tff(497,plain,
% 1.78/1.39 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a403) | c2_1(a403) | (~ndr1_0) | c1_1(a403))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a403) | c2_1(a403) | (~ndr1_0) | c1_1(a403))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(498,plain,
% 1.78/1.39 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a403) | c1_1(a403) | c0_1(a403)) <=> (hskp2 | hskp1 | c0_1(a403) | c2_1(a403) | (~ndr1_0) | c1_1(a403))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(499,plain,
% 1.78/1.39 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a403) | c1_1(a403) | c0_1(a403))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a403) | c2_1(a403) | (~ndr1_0) | c1_1(a403)))),
% 1.78/1.39 inference(monotonicity,[status(thm)],[498])).
% 1.78/1.39 tff(500,plain,
% 1.78/1.39 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a403) | c1_1(a403) | c0_1(a403))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a403) | c2_1(a403) | (~ndr1_0) | c1_1(a403))),
% 1.78/1.39 inference(transitivity,[status(thm)],[499, 497])).
% 1.78/1.39 tff(501,plain,
% 1.78/1.39 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a403) | c1_1(a403) | c0_1(a403))),
% 1.78/1.39 inference(quant_inst,[status(thm)],[])).
% 1.78/1.39 tff(502,plain,
% 1.78/1.39 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a403) | c2_1(a403) | (~ndr1_0) | c1_1(a403)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[501, 500])).
% 1.78/1.39 tff(503,plain,
% 1.78/1.39 (hskp2 | hskp1 | c0_1(a403) | c1_1(a403)),
% 1.78/1.39 inference(unit_resolution,[status(thm)],[502, 150, 335, 33])).
% 1.78/1.39 tff(504,plain,
% 1.78/1.39 (hskp2),
% 1.78/1.39 inference(unit_resolution,[status(thm)],[503, 12, 336, 496])).
% 1.78/1.39 tff(505,plain,
% 1.78/1.39 (((~hskp2) | (~c2_1(a402))) <=> ((~hskp2) | (~c2_1(a402)))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(506,plain,
% 1.78/1.39 (((~c2_1(a402)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a402)))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(507,axiom,((~c2_1(a402)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 1.78/1.39 tff(508,plain,
% 1.78/1.39 ((~hskp2) | (~c2_1(a402))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[507, 506])).
% 1.78/1.39 tff(509,plain,
% 1.78/1.39 ((~hskp2) | (~c2_1(a402))),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[508, 505])).
% 1.78/1.39 tff(510,plain,
% 1.78/1.39 (~c2_1(a402)),
% 1.78/1.39 inference(unit_resolution,[status(thm)],[509, 504])).
% 1.78/1.39 tff(511,plain,
% 1.78/1.39 (((~hskp2) | c0_1(a402)) <=> ((~hskp2) | c0_1(a402))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(512,axiom,((~hskp2) | c0_1(a402)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.78/1.39 tff(513,plain,
% 1.78/1.39 ((~hskp2) | c0_1(a402)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[512, 511])).
% 1.78/1.39 tff(514,plain,
% 1.78/1.39 ((~hskp2) | c0_1(a402)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[513, 511])).
% 1.78/1.39 tff(515,plain,
% 1.78/1.39 ((~hskp2) | c0_1(a402)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[514, 511])).
% 1.78/1.39 tff(516,plain,
% 1.78/1.39 ((~hskp2) | c0_1(a402)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[515, 511])).
% 1.78/1.39 tff(517,plain,
% 1.78/1.39 ((~hskp2) | c0_1(a402)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[516, 511])).
% 1.78/1.39 tff(518,plain,
% 1.78/1.39 ((~hskp2) | c0_1(a402)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[517, 511])).
% 1.78/1.39 tff(519,plain,
% 1.78/1.39 ((~hskp2) | c0_1(a402)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[518, 511])).
% 1.78/1.39 tff(520,plain,
% 1.78/1.39 ((~hskp2) | c0_1(a402)),
% 1.78/1.39 inference(modus_ponens,[status(thm)],[519, 511])).
% 1.78/1.39 tff(521,plain,
% 1.78/1.39 (c0_1(a402)),
% 1.78/1.39 inference(unit_resolution,[status(thm)],[520, 504])).
% 1.78/1.39 tff(522,plain,
% 1.78/1.39 (^[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))) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.78/1.39 inference(bind,[status(th)],[])).
% 1.78/1.39 tff(523,plain,
% 1.78/1.39 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.78/1.39 inference(quant_intro,[status(thm)],[522])).
% 1.78/1.39 tff(524,plain,
% 1.78/1.39 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.78/1.39 inference(rewrite,[status(thm)],[])).
% 1.78/1.39 tff(525,plain,
% 1.78/1.39 (^[V: $i, U: $i] : 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)))))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(526,plain,
% 1.78/1.40 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.78/1.40 inference(quant_intro,[status(thm)],[525])).
% 1.78/1.40 tff(527,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 1.78/1.40 tff(528,plain,
% 1.78/1.40 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[527, 526])).
% 1.78/1.40 tff(529,plain,
% 1.78/1.40 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[528, 524])).
% 1.78/1.40 tff(530,plain,(
% 1.78/1.40 ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.78/1.40 inference(skolemize,[status(sab)],[529])).
% 1.78/1.40 tff(531,plain,
% 1.78/1.40 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[530, 523])).
% 1.78/1.40 tff(532,plain,
% 1.78/1.40 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a445) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a445)) | (~c3_1(a445)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a445) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a445)) | (~c3_1(a445)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(533,plain,
% 1.78/1.40 (((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445))) <=> (c0_1(a445) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a445)) | (~c3_1(a445)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(534,plain,
% 1.78/1.40 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a445) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a445)) | (~c3_1(a445))))),
% 1.78/1.40 inference(monotonicity,[status(thm)],[533])).
% 1.78/1.40 tff(535,plain,
% 1.78/1.40 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a445) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a445)) | (~c3_1(a445)))),
% 1.78/1.40 inference(transitivity,[status(thm)],[534, 532])).
% 1.78/1.40 tff(536,plain,
% 1.78/1.40 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445)))),
% 1.78/1.40 inference(quant_inst,[status(thm)],[])).
% 1.78/1.40 tff(537,plain,
% 1.78/1.40 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a445) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a445)) | (~c3_1(a445))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[536, 535])).
% 1.78/1.40 tff(538,plain,
% 1.78/1.40 ((~c3_1(a402)) | (~c0_1(a402))),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[537, 150, 484, 473, 472, 105, 531])).
% 1.78/1.40 tff(539,plain,
% 1.78/1.40 (~c3_1(a402)),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[538, 521])).
% 1.78/1.40 tff(540,plain,
% 1.78/1.40 (^[U: $i] : refl((hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(541,plain,
% 1.78/1.40 (![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.78/1.40 inference(quant_intro,[status(thm)],[540])).
% 1.78/1.40 tff(542,plain,
% 1.78/1.40 (![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(543,plain,
% 1.78/1.40 (^[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)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp12))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp1) <=> ((hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp1))), rewrite(((hskp12 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp1) <=> (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp1) <=> (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(544,plain,
% 1.78/1.40 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp1) <=> ![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.78/1.40 inference(quant_intro,[status(thm)],[543])).
% 1.78/1.40 tff(545,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 1.78/1.40 tff(546,plain,
% 1.78/1.40 (![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[545, 544])).
% 1.78/1.40 tff(547,plain,
% 1.78/1.40 (![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[546, 542])).
% 1.78/1.40 tff(548,plain,(
% 1.78/1.40 ![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.78/1.40 inference(skolemize,[status(sab)],[547])).
% 1.78/1.40 tff(549,plain,
% 1.78/1.40 (![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[548, 541])).
% 1.78/1.40 tff(550,plain,
% 1.78/1.40 (((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | hskp1 | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(551,plain,
% 1.78/1.40 ((hskp12 | hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402))) <=> (hskp12 | hskp1 | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(552,plain,
% 1.78/1.40 (((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402))))),
% 1.78/1.40 inference(monotonicity,[status(thm)],[551])).
% 1.78/1.40 tff(553,plain,
% 1.78/1.40 (((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | hskp1 | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)))),
% 1.78/1.40 inference(transitivity,[status(thm)],[552, 550])).
% 1.78/1.40 tff(554,plain,
% 1.78/1.40 ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)))),
% 1.78/1.40 inference(quant_inst,[status(thm)],[])).
% 1.78/1.40 tff(555,plain,
% 1.78/1.40 ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | hskp1 | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[554, 553])).
% 1.78/1.40 tff(556,plain,
% 1.78/1.40 (hskp12 | hskp1 | c3_1(a402) | (~c0_1(a402))),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[555, 150, 105, 549])).
% 1.78/1.40 tff(557,plain,
% 1.78/1.40 (hskp12),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[556, 539, 12, 521])).
% 1.78/1.40 tff(558,plain,
% 1.78/1.40 (((~hskp12) | (~c2_1(a426))) <=> ((~hskp12) | (~c2_1(a426)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(559,plain,
% 1.78/1.40 (((~c2_1(a426)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a426)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(560,axiom,((~c2_1(a426)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 1.78/1.40 tff(561,plain,
% 1.78/1.40 ((~hskp12) | (~c2_1(a426))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[560, 559])).
% 1.78/1.40 tff(562,plain,
% 1.78/1.40 ((~hskp12) | (~c2_1(a426))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[561, 558])).
% 1.78/1.40 tff(563,plain,
% 1.78/1.40 (~c2_1(a426)),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[562, 557])).
% 1.78/1.40 tff(564,plain,
% 1.78/1.40 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a445) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a445) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a445)) | (~c1_1(a445)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(565,plain,
% 1.78/1.40 ((hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445))) <=> (hskp1 | c0_1(a445) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a445)) | (~c1_1(a445)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(566,plain,
% 1.78/1.40 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a445) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a445)) | (~c1_1(a445))))),
% 1.78/1.40 inference(monotonicity,[status(thm)],[565])).
% 1.78/1.40 tff(567,plain,
% 1.78/1.40 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a445) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a445)) | (~c1_1(a445)))),
% 1.78/1.40 inference(transitivity,[status(thm)],[566, 564])).
% 1.78/1.40 tff(568,plain,
% 1.78/1.40 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445)))),
% 1.78/1.40 inference(quant_inst,[status(thm)],[])).
% 1.78/1.40 tff(569,plain,
% 1.78/1.40 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a445) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a445)) | (~c1_1(a445))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[568, 567])).
% 1.78/1.40 tff(570,plain,
% 1.78/1.40 (hskp1 | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a445))),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[569, 150, 484, 472, 105, 22])).
% 1.78/1.40 tff(571,plain,
% 1.78/1.40 (~c2_1(a445)),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[570, 539, 12, 521])).
% 1.78/1.40 tff(572,plain,
% 1.78/1.40 (^[U: $i] : refl((hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(573,plain,
% 1.78/1.40 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.78/1.40 inference(quant_intro,[status(thm)],[572])).
% 1.78/1.40 tff(574,plain,
% 1.78/1.40 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(575,plain,
% 1.78/1.40 (^[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)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp11) <=> ((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp11))), rewrite(((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp11) <=> (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp11) <=> (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(576,plain,
% 1.78/1.40 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp11) <=> ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.78/1.40 inference(quant_intro,[status(thm)],[575])).
% 1.78/1.40 tff(577,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 1.78/1.40 tff(578,plain,
% 1.78/1.40 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[577, 576])).
% 1.78/1.40 tff(579,plain,
% 1.78/1.40 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[578, 574])).
% 1.78/1.40 tff(580,plain,(
% 1.78/1.40 ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.78/1.40 inference(skolemize,[status(sab)],[579])).
% 1.78/1.40 tff(581,plain,
% 1.78/1.40 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[580, 573])).
% 1.78/1.40 tff(582,plain,
% 1.78/1.40 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp0 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp0 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(583,plain,
% 1.78/1.40 ((hskp11 | hskp0 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c3_1(a445))) <=> (hskp11 | hskp0 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(584,plain,
% 1.78/1.40 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp0 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445))))),
% 1.78/1.40 inference(monotonicity,[status(thm)],[583])).
% 1.78/1.40 tff(585,plain,
% 1.78/1.40 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp0 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445)))),
% 1.78/1.40 inference(transitivity,[status(thm)],[584, 582])).
% 1.78/1.40 tff(586,plain,
% 1.78/1.40 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c3_1(a445)))),
% 1.78/1.40 inference(quant_inst,[status(thm)],[])).
% 1.78/1.40 tff(587,plain,
% 1.78/1.40 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp0 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[586, 585])).
% 1.78/1.40 tff(588,plain,
% 1.78/1.40 (hskp11 | hskp0 | c2_1(a445)),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[587, 150, 473, 472, 581])).
% 1.78/1.40 tff(589,plain,
% 1.78/1.40 (hskp0),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[588, 571, 485])).
% 1.78/1.40 tff(590,plain,
% 1.78/1.40 (c2_1(a400)),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[374, 589])).
% 1.78/1.40 tff(591,plain,
% 1.78/1.40 (c1_1(a400)),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[385, 589])).
% 1.78/1.40 tff(592,plain,
% 1.78/1.40 (((~hskp12) | c1_1(a426)) <=> ((~hskp12) | c1_1(a426))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(593,axiom,((~hskp12) | c1_1(a426)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 1.78/1.40 tff(594,plain,
% 1.78/1.40 ((~hskp12) | c1_1(a426)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[593, 592])).
% 1.78/1.40 tff(595,plain,
% 1.78/1.40 ((~hskp12) | c1_1(a426)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[594, 592])).
% 1.78/1.40 tff(596,plain,
% 1.78/1.40 ((~hskp12) | c1_1(a426)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[595, 592])).
% 1.78/1.40 tff(597,plain,
% 1.78/1.40 ((~hskp12) | c1_1(a426)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[596, 592])).
% 1.78/1.40 tff(598,plain,
% 1.78/1.40 ((~hskp12) | c1_1(a426)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[597, 592])).
% 1.78/1.40 tff(599,plain,
% 1.78/1.40 ((~hskp12) | c1_1(a426)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[598, 592])).
% 1.78/1.40 tff(600,plain,
% 1.78/1.40 ((~hskp12) | c1_1(a426)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[599, 592])).
% 1.78/1.40 tff(601,plain,
% 1.78/1.40 ((~hskp12) | c1_1(a426)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[600, 592])).
% 1.78/1.40 tff(602,plain,
% 1.78/1.40 (c1_1(a426)),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[601, 557])).
% 1.78/1.40 tff(603,plain,
% 1.78/1.40 (((~hskp12) | c0_1(a426)) <=> ((~hskp12) | c0_1(a426))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(604,axiom,((~hskp12) | c0_1(a426)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 1.78/1.40 tff(605,plain,
% 1.78/1.40 ((~hskp12) | c0_1(a426)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[604, 603])).
% 1.78/1.40 tff(606,plain,
% 1.78/1.40 ((~hskp12) | c0_1(a426)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[605, 603])).
% 1.78/1.40 tff(607,plain,
% 1.78/1.40 ((~hskp12) | c0_1(a426)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[606, 603])).
% 1.78/1.40 tff(608,plain,
% 1.78/1.40 ((~hskp12) | c0_1(a426)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[607, 603])).
% 1.78/1.40 tff(609,plain,
% 1.78/1.40 ((~hskp12) | c0_1(a426)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[608, 603])).
% 1.78/1.40 tff(610,plain,
% 1.78/1.40 ((~hskp12) | c0_1(a426)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[609, 603])).
% 1.78/1.40 tff(611,plain,
% 1.78/1.40 ((~hskp12) | c0_1(a426)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[610, 603])).
% 1.78/1.40 tff(612,plain,
% 1.78/1.40 ((~hskp12) | c0_1(a426)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[611, 603])).
% 1.78/1.40 tff(613,plain,
% 1.78/1.40 (c0_1(a426)),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[612, 557])).
% 1.78/1.40 tff(614,plain,
% 1.78/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(615,plain,
% 1.78/1.40 (((~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402))) <=> (c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(616,plain,
% 1.78/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426))))),
% 1.78/1.40 inference(monotonicity,[status(thm)],[615])).
% 1.78/1.40 tff(617,plain,
% 1.78/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)))),
% 1.78/1.40 inference(transitivity,[status(thm)],[616, 614])).
% 1.78/1.40 tff(618,plain,
% 1.78/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)))),
% 1.78/1.40 inference(quant_inst,[status(thm)],[])).
% 1.78/1.40 tff(619,plain,
% 1.78/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | (~c0_1(a400)) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[618, 617])).
% 1.78/1.40 tff(620,plain,
% 1.78/1.40 (~c0_1(a400)),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[619, 150, 613, 602, 521, 591, 590, 563, 105, 510, 495])).
% 1.78/1.40 tff(621,plain,
% 1.78/1.40 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c1_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c1_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a402) | (~c0_1(a402)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(622,plain,
% 1.78/1.40 ((hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400))) <=> (hskp1 | c1_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a402) | (~c0_1(a402)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(623,plain,
% 1.78/1.40 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c1_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a402) | (~c0_1(a402))))),
% 1.78/1.40 inference(monotonicity,[status(thm)],[622])).
% 1.78/1.40 tff(624,plain,
% 1.78/1.40 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c1_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a402) | (~c0_1(a402)))),
% 1.78/1.40 inference(transitivity,[status(thm)],[623, 621])).
% 1.78/1.40 tff(625,plain,
% 1.78/1.40 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))),
% 1.78/1.40 inference(quant_inst,[status(thm)],[])).
% 1.78/1.40 tff(626,plain,
% 1.78/1.40 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c1_1(a402) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a402) | (~c0_1(a402))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[625, 624])).
% 1.78/1.40 tff(627,plain,
% 1.78/1.40 ($false),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[626, 150, 12, 521, 591, 590, 105, 22, 539, 620])).
% 1.78/1.40 tff(628,plain,(hskp1 | c1_1(a402) | hskp11 | (~c3_1(a445)) | c0_1(a445) | (~c1_1(a445)) | c0_1(a403) | c1_1(a403) | c2_1(a403)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.40 tff(629,plain,
% 1.78/1.40 (c1_1(a403)),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[628, 12, 105, 473, 472, 484, 336, 485, 335])).
% 1.78/1.40 tff(630,assumption,(c1_1(a403)), introduced(assumption)).
% 1.78/1.40 tff(631,plain,
% 1.78/1.40 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(632,plain,
% 1.78/1.40 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.78/1.40 inference(quant_intro,[status(thm)],[631])).
% 1.78/1.40 tff(633,plain,
% 1.78/1.40 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(634,plain,
% 1.78/1.40 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_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)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.78/1.41 inference(bind,[status(th)],[])).
% 1.78/1.41 tff(635,plain,
% 1.78/1.41 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.78/1.41 inference(quant_intro,[status(thm)],[634])).
% 1.78/1.41 tff(636,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 1.78/1.41 tff(637,plain,
% 1.78/1.41 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[636, 635])).
% 1.78/1.41 tff(638,plain,
% 1.78/1.41 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[637, 633])).
% 1.78/1.41 tff(639,plain,(
% 1.78/1.41 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.78/1.41 inference(skolemize,[status(sab)],[638])).
% 1.78/1.41 tff(640,plain,
% 1.78/1.41 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[639, 632])).
% 1.78/1.41 tff(641,plain,
% 1.78/1.41 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(642,plain,
% 1.78/1.41 ((hskp7 | hskp2 | (~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403))) <=> (hskp7 | hskp2 | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(643,plain,
% 1.78/1.41 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403))))),
% 1.78/1.41 inference(monotonicity,[status(thm)],[642])).
% 1.78/1.41 tff(644,plain,
% 1.78/1.41 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)))),
% 1.78/1.41 inference(transitivity,[status(thm)],[643, 641])).
% 1.78/1.41 tff(645,plain,
% 1.78/1.41 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)))),
% 1.78/1.41 inference(quant_inst,[status(thm)],[])).
% 1.78/1.41 tff(646,plain,
% 1.78/1.41 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[645, 644])).
% 1.78/1.41 tff(647,plain,
% 1.78/1.41 (hskp7 | hskp2 | c2_1(a403) | (~c1_1(a403))),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[646, 150, 334, 118])).
% 1.78/1.41 tff(648,plain,
% 1.78/1.41 (hskp7),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[647, 23, 335, 630])).
% 1.78/1.41 tff(649,plain,
% 1.78/1.41 (~c3_1(a410)),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[254, 648])).
% 1.78/1.41 tff(650,plain,
% 1.78/1.41 (~c1_1(a410)),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[260, 648])).
% 1.78/1.41 tff(651,plain,
% 1.78/1.41 (c0_1(a410)),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[295, 648])).
% 1.78/1.41 tff(652,plain,
% 1.78/1.41 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c1_1(a410) | c3_1(a410) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c0_1(a410)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c1_1(a410) | c3_1(a410) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c0_1(a410)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(653,plain,
% 1.78/1.41 ((hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a403) | c3_1(a403) | (~c1_1(a403))) <=> (hskp9 | c1_1(a410) | c3_1(a410) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c0_1(a410)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(654,plain,
% 1.78/1.41 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a403) | c3_1(a403) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c1_1(a410) | c3_1(a410) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c0_1(a410))))),
% 1.78/1.41 inference(monotonicity,[status(thm)],[653])).
% 1.78/1.41 tff(655,plain,
% 1.78/1.41 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a403) | c3_1(a403) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c1_1(a410) | c3_1(a410) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c0_1(a410)))),
% 1.78/1.41 inference(transitivity,[status(thm)],[654, 652])).
% 1.78/1.41 tff(656,plain,
% 1.78/1.41 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a403) | c3_1(a403) | (~c1_1(a403)))),
% 1.78/1.41 inference(quant_inst,[status(thm)],[])).
% 1.78/1.41 tff(657,plain,
% 1.78/1.41 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c1_1(a410) | c3_1(a410) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c0_1(a410))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[656, 655])).
% 1.78/1.41 tff(658,plain,
% 1.78/1.41 (hskp9),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[657, 150, 651, 650, 649, 336, 334, 640, 630])).
% 1.78/1.41 tff(659,plain,
% 1.78/1.41 (((~hskp9) | (~c1_1(a416))) <=> ((~hskp9) | (~c1_1(a416)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(660,plain,
% 1.78/1.41 (((~c1_1(a416)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a416)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(661,axiom,((~c1_1(a416)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 1.78/1.41 tff(662,plain,
% 1.78/1.41 ((~hskp9) | (~c1_1(a416))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[661, 660])).
% 1.78/1.41 tff(663,plain,
% 1.78/1.41 ((~hskp9) | (~c1_1(a416))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[662, 659])).
% 1.78/1.41 tff(664,plain,
% 1.78/1.41 (~c1_1(a416)),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[663, 658])).
% 1.78/1.41 tff(665,plain,
% 1.78/1.41 (((~hskp9) | (~c0_1(a416))) <=> ((~hskp9) | (~c0_1(a416)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(666,plain,
% 1.78/1.41 (((~c0_1(a416)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a416)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(667,axiom,((~c0_1(a416)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 1.78/1.41 tff(668,plain,
% 1.78/1.41 ((~hskp9) | (~c0_1(a416))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[667, 666])).
% 1.78/1.41 tff(669,plain,
% 1.78/1.41 ((~hskp9) | (~c0_1(a416))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[668, 665])).
% 1.78/1.41 tff(670,plain,
% 1.78/1.41 (~c0_1(a416)),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[669, 658])).
% 1.78/1.41 tff(671,plain,
% 1.78/1.41 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(672,plain,
% 1.78/1.41 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | c0_1(a416)) <=> (hskp2 | hskp1 | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(673,plain,
% 1.78/1.41 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | c0_1(a416))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416)))),
% 1.78/1.41 inference(monotonicity,[status(thm)],[672])).
% 1.78/1.41 tff(674,plain,
% 1.78/1.41 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | c0_1(a416))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416))),
% 1.78/1.41 inference(transitivity,[status(thm)],[673, 671])).
% 1.78/1.41 tff(675,plain,
% 1.78/1.41 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | c0_1(a416))),
% 1.78/1.41 inference(quant_inst,[status(thm)],[])).
% 1.78/1.41 tff(676,plain,
% 1.78/1.41 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[675, 674])).
% 1.78/1.41 tff(677,plain,
% 1.78/1.41 (c2_1(a416)),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[676, 150, 23, 12, 670, 664, 33])).
% 1.78/1.41 tff(678,plain,
% 1.78/1.41 (^[U: $i] : refl((hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.78/1.41 inference(bind,[status(th)],[])).
% 1.78/1.41 tff(679,plain,
% 1.78/1.41 (![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.78/1.41 inference(quant_intro,[status(thm)],[678])).
% 1.78/1.41 tff(680,plain,
% 1.78/1.41 (![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(681,plain,
% 1.78/1.41 (^[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)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp11) <=> ((hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp11))), rewrite(((hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp11) <=> (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp11) <=> (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.78/1.41 inference(bind,[status(th)],[])).
% 1.78/1.41 tff(682,plain,
% 1.78/1.41 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp11) <=> ![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.78/1.41 inference(quant_intro,[status(thm)],[681])).
% 1.78/1.41 tff(683,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 1.78/1.41 tff(684,plain,
% 1.78/1.41 (![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[683, 682])).
% 1.78/1.41 tff(685,plain,
% 1.78/1.41 (![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[684, 680])).
% 1.78/1.41 tff(686,plain,(
% 1.78/1.41 ![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.78/1.41 inference(skolemize,[status(sab)],[685])).
% 1.78/1.41 tff(687,plain,
% 1.78/1.41 (![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[686, 679])).
% 1.78/1.41 tff(688,plain,
% 1.78/1.41 (((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410))) <=> ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp11 | hskp2 | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(689,plain,
% 1.78/1.41 ((hskp11 | hskp2 | (~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410))) <=> (hskp11 | hskp2 | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(690,plain,
% 1.78/1.41 (((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)))) <=> ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410)))),
% 1.78/1.41 inference(monotonicity,[status(thm)],[689])).
% 1.78/1.41 tff(691,plain,
% 1.78/1.41 (((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)))) <=> ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp11 | hskp2 | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410))),
% 1.78/1.41 inference(transitivity,[status(thm)],[690, 688])).
% 1.78/1.41 tff(692,plain,
% 1.78/1.41 ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)))),
% 1.78/1.41 inference(quant_inst,[status(thm)],[])).
% 1.78/1.41 tff(693,plain,
% 1.78/1.41 ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp11 | hskp2 | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[692, 691])).
% 1.78/1.41 tff(694,plain,
% 1.78/1.41 (c2_1(a410)),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[693, 150, 485, 23, 651, 649, 687])).
% 1.78/1.41 tff(695,plain,
% 1.78/1.41 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 1.78/1.41 inference(bind,[status(th)],[])).
% 1.78/1.41 tff(696,plain,
% 1.78/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.78/1.41 inference(quant_intro,[status(thm)],[695])).
% 1.78/1.41 tff(697,plain,
% 1.78/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(698,plain,
% 1.78/1.41 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 1.81/1.41 inference(bind,[status(th)],[])).
% 1.81/1.41 tff(699,plain,
% 1.81/1.41 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.81/1.41 inference(quant_intro,[status(thm)],[698])).
% 1.81/1.41 tff(700,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 1.81/1.41 tff(701,plain,
% 1.81/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.81/1.41 inference(modus_ponens,[status(thm)],[700, 699])).
% 1.81/1.41 tff(702,plain,
% 1.81/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.81/1.41 inference(modus_ponens,[status(thm)],[701, 697])).
% 1.81/1.41 tff(703,plain,(
% 1.81/1.41 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.81/1.41 inference(skolemize,[status(sab)],[702])).
% 1.81/1.41 tff(704,plain,
% 1.81/1.41 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.81/1.41 inference(modus_ponens,[status(thm)],[703, 696])).
% 1.81/1.41 tff(705,plain,
% 1.81/1.41 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a445) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a445) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a445)) | (~c1_1(a445)))),
% 1.81/1.41 inference(rewrite,[status(thm)],[])).
% 1.81/1.41 tff(706,plain,
% 1.81/1.41 ((hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445))) <=> (hskp1 | c0_1(a445) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a445)) | (~c1_1(a445)))),
% 1.81/1.41 inference(rewrite,[status(thm)],[])).
% 1.81/1.41 tff(707,plain,
% 1.81/1.41 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a445) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a445)) | (~c1_1(a445))))),
% 1.81/1.41 inference(monotonicity,[status(thm)],[706])).
% 1.81/1.41 tff(708,plain,
% 1.81/1.41 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a445) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a445)) | (~c1_1(a445)))),
% 1.81/1.41 inference(transitivity,[status(thm)],[707, 705])).
% 1.81/1.41 tff(709,plain,
% 1.81/1.41 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445)))),
% 1.81/1.41 inference(quant_inst,[status(thm)],[])).
% 1.81/1.41 tff(710,plain,
% 1.81/1.41 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a445) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a445)) | (~c1_1(a445))),
% 1.81/1.41 inference(modus_ponens,[status(thm)],[709, 708])).
% 1.81/1.41 tff(711,plain,
% 1.81/1.41 (~c2_1(a445)),
% 1.81/1.41 inference(unit_resolution,[status(thm)],[710, 150, 12, 484, 651, 472, 650, 649, 22])).
% 1.81/1.41 tff(712,plain,
% 1.81/1.41 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a445) | (~c1_1(a445)) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | (~ndr1_0) | c2_1(a445) | (~c1_1(a445)) | (~c3_1(a445)))),
% 1.81/1.41 inference(rewrite,[status(thm)],[])).
% 1.81/1.41 tff(713,plain,
% 1.81/1.41 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a445) | (~c1_1(a445)) | (~c3_1(a445)))),
% 1.81/1.41 inference(quant_inst,[status(thm)],[])).
% 1.81/1.41 tff(714,plain,
% 1.81/1.41 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | (~ndr1_0) | c2_1(a445) | (~c1_1(a445)) | (~c3_1(a445))),
% 1.81/1.41 inference(modus_ponens,[status(thm)],[713, 712])).
% 1.81/1.41 tff(715,plain,
% 1.81/1.41 (hskp13 | hskp2 | c2_1(a445)),
% 1.81/1.41 inference(unit_resolution,[status(thm)],[714, 150, 484, 473, 271])).
% 1.81/1.41 tff(716,plain,
% 1.81/1.41 (hskp13),
% 1.81/1.41 inference(unit_resolution,[status(thm)],[715, 711, 23])).
% 1.81/1.41 tff(717,plain,
% 1.81/1.41 (~c0_1(a427)),
% 1.81/1.41 inference(unit_resolution,[status(thm)],[284, 716])).
% 1.81/1.41 tff(718,plain,
% 1.81/1.41 (((~hskp9) | c3_1(a416)) <=> ((~hskp9) | c3_1(a416))),
% 1.81/1.41 inference(rewrite,[status(thm)],[])).
% 1.81/1.41 tff(719,axiom,((~hskp9) | c3_1(a416)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 1.81/1.41 tff(720,plain,
% 1.81/1.41 ((~hskp9) | c3_1(a416)),
% 1.81/1.41 inference(modus_ponens,[status(thm)],[719, 718])).
% 1.81/1.41 tff(721,plain,
% 1.81/1.41 ((~hskp9) | c3_1(a416)),
% 1.81/1.41 inference(modus_ponens,[status(thm)],[720, 718])).
% 1.81/1.41 tff(722,plain,
% 1.81/1.41 ((~hskp9) | c3_1(a416)),
% 1.81/1.41 inference(modus_ponens,[status(thm)],[721, 718])).
% 1.81/1.41 tff(723,plain,
% 1.81/1.41 ((~hskp9) | c3_1(a416)),
% 1.81/1.41 inference(modus_ponens,[status(thm)],[722, 718])).
% 1.81/1.41 tff(724,plain,
% 1.81/1.41 ((~hskp9) | c3_1(a416)),
% 1.81/1.41 inference(modus_ponens,[status(thm)],[723, 718])).
% 1.81/1.41 tff(725,plain,
% 1.81/1.41 ((~hskp9) | c3_1(a416)),
% 1.81/1.41 inference(modus_ponens,[status(thm)],[724, 718])).
% 1.81/1.41 tff(726,plain,
% 1.81/1.41 ((~hskp9) | c3_1(a416)),
% 1.81/1.41 inference(modus_ponens,[status(thm)],[725, 718])).
% 1.81/1.41 tff(727,plain,
% 1.81/1.41 ((~hskp9) | c3_1(a416)),
% 1.81/1.41 inference(modus_ponens,[status(thm)],[726, 718])).
% 1.81/1.41 tff(728,plain,
% 1.81/1.41 (c3_1(a416)),
% 1.81/1.41 inference(unit_resolution,[status(thm)],[727, 658])).
% 1.81/1.41 tff(729,plain,
% 1.81/1.41 (c2_1(a427)),
% 1.81/1.41 inference(unit_resolution,[status(thm)],[306, 716])).
% 1.81/1.41 tff(730,plain,
% 1.81/1.41 (c1_1(a427)),
% 1.81/1.41 inference(unit_resolution,[status(thm)],[317, 716])).
% 1.81/1.41 tff(731,plain,
% 1.81/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.81/1.41 inference(rewrite,[status(thm)],[])).
% 1.81/1.41 tff(732,plain,
% 1.81/1.41 (((~ndr1_0) | c3_1(a410) | (~c2_1(a410)) | (~c0_1(a410)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427))) <=> (c0_1(a427) | c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(733,plain,
% 1.81/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a410) | (~c2_1(a410)) | (~c0_1(a410)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427))))),
% 1.81/1.42 inference(monotonicity,[status(thm)],[732])).
% 1.81/1.42 tff(734,plain,
% 1.81/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a410) | (~c2_1(a410)) | (~c0_1(a410)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.81/1.42 inference(transitivity,[status(thm)],[733, 731])).
% 1.81/1.42 tff(735,plain,
% 1.81/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a410) | (~c2_1(a410)) | (~c0_1(a410)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.81/1.42 inference(quant_inst,[status(thm)],[])).
% 1.81/1.42 tff(736,plain,
% 1.81/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a410)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[735, 734])).
% 1.81/1.42 tff(737,plain,
% 1.81/1.42 ($false),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[736, 150, 730, 729, 728, 651, 717, 664, 649, 704, 694, 677])).
% 1.81/1.42 tff(738,plain,(hskp2 | hskp1 | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a403) | c3_1(a403) | (~c1_1(a403)) | c0_1(a445) | hskp11 | c2_1(a403)), inference(lemma,lemma(discharge,[]))).
% 1.81/1.42 tff(739,plain,
% 1.81/1.42 (hskp2),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[738, 12, 484, 473, 336, 334, 629, 472, 485, 335])).
% 1.81/1.42 tff(740,plain,
% 1.81/1.42 (c0_1(a402)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[520, 739])).
% 1.81/1.42 tff(741,plain,
% 1.81/1.42 (~c3_1(a402)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[538, 740])).
% 1.81/1.42 tff(742,plain,
% 1.81/1.42 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a403) | c3_1(a403) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a403) | c3_1(a403) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403)))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(743,plain,
% 1.81/1.42 ((hskp9 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a403) | c3_1(a403) | (~c1_1(a403))) <=> (hskp9 | c0_1(a403) | c3_1(a403) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403)))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(744,plain,
% 1.81/1.42 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a403) | c3_1(a403) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a403) | c3_1(a403) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403))))),
% 1.81/1.42 inference(monotonicity,[status(thm)],[743])).
% 1.81/1.42 tff(745,plain,
% 1.81/1.42 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a403) | c3_1(a403) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a403) | c3_1(a403) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403)))),
% 1.81/1.42 inference(transitivity,[status(thm)],[744, 742])).
% 1.81/1.42 tff(746,plain,
% 1.81/1.42 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a403) | c3_1(a403) | (~c1_1(a403)))),
% 1.81/1.42 inference(quant_inst,[status(thm)],[])).
% 1.81/1.42 tff(747,plain,
% 1.81/1.42 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a403) | c3_1(a403) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[746, 745])).
% 1.81/1.42 tff(748,plain,
% 1.81/1.42 (hskp9 | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403))),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[747, 150, 336, 334, 105, 640])).
% 1.81/1.42 tff(749,plain,
% 1.81/1.42 (hskp9),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[748, 741, 629, 740])).
% 1.81/1.42 tff(750,plain,
% 1.81/1.42 (~c1_1(a416)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[663, 749])).
% 1.81/1.42 tff(751,plain,
% 1.81/1.42 (~c0_1(a416)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[669, 749])).
% 1.81/1.42 tff(752,plain,
% 1.81/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a416) | c1_1(a416) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a416) | c1_1(a416) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a416)))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(753,plain,
% 1.81/1.42 (((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a403) | c0_1(a403) | c2_1(a403)) <=> (c0_1(a416) | c1_1(a416) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a416)))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(754,plain,
% 1.81/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a403) | c0_1(a403) | c2_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a416) | c1_1(a416) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a416))))),
% 1.81/1.42 inference(monotonicity,[status(thm)],[753])).
% 1.81/1.42 tff(755,plain,
% 1.81/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a403) | c0_1(a403) | c2_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a416) | c1_1(a416) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a416)))),
% 1.81/1.42 inference(transitivity,[status(thm)],[754, 752])).
% 1.81/1.42 tff(756,plain,
% 1.81/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a403) | c0_1(a403) | c2_1(a403))),
% 1.81/1.42 inference(quant_inst,[status(thm)],[])).
% 1.81/1.42 tff(757,plain,
% 1.81/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a416) | c1_1(a416) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a416))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[756, 755])).
% 1.81/1.42 tff(758,plain,
% 1.81/1.42 (~c2_1(a416)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[757, 150, 751, 750, 336, 335, 334, 346, 629])).
% 1.81/1.42 tff(759,plain,
% 1.81/1.42 (~c2_1(a402)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[509, 739])).
% 1.81/1.42 tff(760,plain,
% 1.81/1.42 (hskp12),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[556, 741, 12, 740])).
% 1.81/1.42 tff(761,plain,
% 1.81/1.42 (~c2_1(a426)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[562, 760])).
% 1.81/1.42 tff(762,plain,
% 1.81/1.42 (~c2_1(a445)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[570, 741, 12, 740])).
% 1.81/1.42 tff(763,plain,
% 1.81/1.42 (hskp0),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[588, 762, 485])).
% 1.81/1.42 tff(764,plain,
% 1.81/1.42 (c2_1(a400)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[374, 763])).
% 1.81/1.42 tff(765,plain,
% 1.81/1.42 (c1_1(a400)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[385, 763])).
% 1.81/1.42 tff(766,plain,
% 1.81/1.42 (c1_1(a426)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[601, 760])).
% 1.81/1.42 tff(767,plain,
% 1.81/1.42 (c0_1(a426)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[612, 760])).
% 1.81/1.42 tff(768,plain,
% 1.81/1.42 (~c0_1(a400)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[619, 150, 767, 766, 740, 765, 764, 761, 105, 759, 495])).
% 1.81/1.42 tff(769,plain,
% 1.81/1.42 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.81/1.42 inference(bind,[status(th)],[])).
% 1.81/1.42 tff(770,plain,
% 1.81/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.81/1.42 inference(quant_intro,[status(thm)],[769])).
% 1.81/1.42 tff(771,plain,
% 1.81/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(772,plain,
% 1.81/1.42 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.81/1.42 inference(bind,[status(th)],[])).
% 1.81/1.42 tff(773,plain,
% 1.81/1.42 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.81/1.42 inference(quant_intro,[status(thm)],[772])).
% 1.81/1.42 tff(774,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 1.81/1.42 tff(775,plain,
% 1.81/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[774, 773])).
% 1.81/1.42 tff(776,plain,
% 1.81/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[775, 771])).
% 1.81/1.42 tff(777,plain,(
% 1.81/1.42 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.81/1.42 inference(skolemize,[status(sab)],[776])).
% 1.81/1.42 tff(778,plain,
% 1.81/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[777, 770])).
% 1.81/1.42 tff(779,plain,
% 1.81/1.42 (~c3_1(a400)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[405, 763])).
% 1.81/1.42 tff(780,plain,
% 1.81/1.42 (c3_1(a416)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[727, 749])).
% 1.81/1.42 tff(781,plain,
% 1.81/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a416) | c1_1(a416) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | c2_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a416) | c1_1(a416) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | c2_1(a416) | (~c3_1(a416)))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(782,plain,
% 1.81/1.42 (((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416))) <=> (c0_1(a416) | c1_1(a416) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | c2_1(a416) | (~c3_1(a416)))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(783,plain,
% 1.81/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a416) | c1_1(a416) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | c2_1(a416) | (~c3_1(a416))))),
% 1.81/1.42 inference(monotonicity,[status(thm)],[782])).
% 1.81/1.42 tff(784,plain,
% 1.81/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a416) | c1_1(a416) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | c2_1(a416) | (~c3_1(a416)))),
% 1.81/1.42 inference(transitivity,[status(thm)],[783, 781])).
% 1.81/1.42 tff(785,plain,
% 1.81/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)))),
% 1.81/1.42 inference(quant_inst,[status(thm)],[])).
% 1.81/1.42 tff(786,plain,
% 1.81/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a416) | c1_1(a416) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | c2_1(a416) | (~c3_1(a416))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[785, 784])).
% 1.81/1.42 tff(787,plain,
% 1.81/1.42 ($false),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[786, 150, 780, 764, 751, 750, 779, 778, 768, 758])).
% 1.81/1.42 tff(788,plain,(hskp1 | c1_1(a402) | c0_1(a403) | c2_1(a403) | c3_1(a403) | hskp11 | (~c3_1(a445)) | c0_1(a445) | (~c1_1(a445))), inference(lemma,lemma(discharge,[]))).
% 1.81/1.42 tff(789,plain,
% 1.81/1.42 (hskp1),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[788, 485, 336, 335, 334, 105, 473, 472, 484])).
% 1.81/1.42 tff(790,plain,
% 1.81/1.42 (((~hskp1) | (~c3_1(a401))) <=> ((~hskp1) | (~c3_1(a401)))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(791,plain,
% 1.81/1.42 (((~c3_1(a401)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a401)))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(792,axiom,((~c3_1(a401)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 1.81/1.42 tff(793,plain,
% 1.81/1.42 ((~hskp1) | (~c3_1(a401))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[792, 791])).
% 1.81/1.42 tff(794,plain,
% 1.81/1.42 ((~hskp1) | (~c3_1(a401))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[793, 790])).
% 1.81/1.42 tff(795,plain,
% 1.81/1.42 (~c3_1(a401)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[794, 789])).
% 1.81/1.42 tff(796,plain,
% 1.81/1.42 (((~hskp1) | c1_1(a401)) <=> ((~hskp1) | c1_1(a401))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(797,axiom,((~hskp1) | c1_1(a401)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 1.81/1.42 tff(798,plain,
% 1.81/1.42 ((~hskp1) | c1_1(a401)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[797, 796])).
% 1.81/1.42 tff(799,plain,
% 1.81/1.42 ((~hskp1) | c1_1(a401)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[798, 796])).
% 1.81/1.42 tff(800,plain,
% 1.81/1.42 ((~hskp1) | c1_1(a401)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[799, 796])).
% 1.81/1.42 tff(801,plain,
% 1.81/1.42 ((~hskp1) | c1_1(a401)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[800, 796])).
% 1.81/1.42 tff(802,plain,
% 1.81/1.42 ((~hskp1) | c1_1(a401)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[801, 796])).
% 1.81/1.42 tff(803,plain,
% 1.81/1.42 ((~hskp1) | c1_1(a401)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[802, 796])).
% 1.81/1.42 tff(804,plain,
% 1.81/1.42 ((~hskp1) | c1_1(a401)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[803, 796])).
% 1.81/1.42 tff(805,plain,
% 1.81/1.42 ((~hskp1) | c1_1(a401)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[804, 796])).
% 1.81/1.42 tff(806,plain,
% 1.81/1.42 (c1_1(a401)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[805, 789])).
% 1.81/1.42 tff(807,plain,
% 1.81/1.42 (((~hskp1) | c0_1(a401)) <=> ((~hskp1) | c0_1(a401))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(808,axiom,((~hskp1) | c0_1(a401)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 1.81/1.42 tff(809,plain,
% 1.81/1.42 ((~hskp1) | c0_1(a401)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[808, 807])).
% 1.81/1.42 tff(810,plain,
% 1.81/1.42 ((~hskp1) | c0_1(a401)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[809, 807])).
% 1.81/1.42 tff(811,plain,
% 1.81/1.42 ((~hskp1) | c0_1(a401)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[810, 807])).
% 1.81/1.42 tff(812,plain,
% 1.81/1.42 ((~hskp1) | c0_1(a401)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[811, 807])).
% 1.81/1.42 tff(813,plain,
% 1.81/1.42 ((~hskp1) | c0_1(a401)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[812, 807])).
% 1.81/1.42 tff(814,plain,
% 1.81/1.42 ((~hskp1) | c0_1(a401)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[813, 807])).
% 1.81/1.42 tff(815,plain,
% 1.81/1.42 ((~hskp1) | c0_1(a401)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[814, 807])).
% 1.81/1.42 tff(816,plain,
% 1.81/1.42 ((~hskp1) | c0_1(a401)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[815, 807])).
% 1.81/1.42 tff(817,plain,
% 1.81/1.42 (c0_1(a401)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[816, 789])).
% 1.81/1.42 tff(818,plain,
% 1.81/1.42 (((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(819,plain,
% 1.81/1.42 ((hskp20 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401))) <=> (hskp20 | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(820,plain,
% 1.81/1.42 (((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401))))),
% 1.81/1.42 inference(monotonicity,[status(thm)],[819])).
% 1.81/1.42 tff(821,plain,
% 1.81/1.42 (((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.81/1.42 inference(transitivity,[status(thm)],[820, 818])).
% 1.81/1.42 tff(822,plain,
% 1.81/1.42 ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.81/1.42 inference(quant_inst,[status(thm)],[])).
% 1.81/1.42 tff(823,plain,
% 1.81/1.42 ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[822, 821])).
% 1.81/1.42 tff(824,plain,
% 1.81/1.42 (hskp20),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[823, 150, 817, 806, 795, 483])).
% 1.81/1.42 tff(825,plain,
% 1.81/1.42 (((~hskp20) | c1_1(a449)) <=> ((~hskp20) | c1_1(a449))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(826,axiom,((~hskp20) | c1_1(a449)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 1.81/1.42 tff(827,plain,
% 1.81/1.42 ((~hskp20) | c1_1(a449)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[826, 825])).
% 1.81/1.42 tff(828,plain,
% 1.81/1.42 ((~hskp20) | c1_1(a449)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[827, 825])).
% 1.81/1.42 tff(829,plain,
% 1.81/1.42 ((~hskp20) | c1_1(a449)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[828, 825])).
% 1.81/1.42 tff(830,plain,
% 1.81/1.42 ((~hskp20) | c1_1(a449)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[829, 825])).
% 1.81/1.42 tff(831,plain,
% 1.81/1.42 ((~hskp20) | c1_1(a449)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[830, 825])).
% 1.81/1.42 tff(832,plain,
% 1.81/1.42 ((~hskp20) | c1_1(a449)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[831, 825])).
% 1.81/1.42 tff(833,plain,
% 1.81/1.42 ((~hskp20) | c1_1(a449)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[832, 825])).
% 1.81/1.42 tff(834,plain,
% 1.81/1.42 ((~hskp20) | c1_1(a449)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[833, 825])).
% 1.81/1.42 tff(835,plain,
% 1.81/1.42 (c1_1(a449)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[834, 824])).
% 1.81/1.42 tff(836,assumption,(c0_1(a401)), introduced(assumption)).
% 1.81/1.42 tff(837,assumption,(~c3_1(a401)), introduced(assumption)).
% 1.81/1.42 tff(838,assumption,(c1_1(a401)), introduced(assumption)).
% 1.81/1.42 tff(839,assumption,(hskp22), introduced(assumption)).
% 1.81/1.42 tff(840,plain,
% 1.81/1.42 (((~hskp22) | (~c1_1(a451))) <=> ((~hskp22) | (~c1_1(a451)))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(841,plain,
% 1.81/1.42 (((~c1_1(a451)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a451)))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(842,axiom,((~c1_1(a451)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 1.81/1.42 tff(843,plain,
% 1.81/1.42 ((~hskp22) | (~c1_1(a451))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[842, 841])).
% 1.81/1.42 tff(844,plain,
% 1.81/1.42 ((~hskp22) | (~c1_1(a451))),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[843, 840])).
% 1.81/1.42 tff(845,plain,
% 1.81/1.42 (~c1_1(a451)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[844, 839])).
% 1.81/1.42 tff(846,plain,
% 1.81/1.42 (((~hskp22) | c2_1(a451)) <=> ((~hskp22) | c2_1(a451))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(847,axiom,((~hskp22) | c2_1(a451)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 1.81/1.42 tff(848,plain,
% 1.81/1.42 ((~hskp22) | c2_1(a451)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[847, 846])).
% 1.81/1.42 tff(849,plain,
% 1.81/1.42 ((~hskp22) | c2_1(a451)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[848, 846])).
% 1.81/1.42 tff(850,plain,
% 1.81/1.42 ((~hskp22) | c2_1(a451)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[849, 846])).
% 1.81/1.42 tff(851,plain,
% 1.81/1.42 ((~hskp22) | c2_1(a451)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[850, 846])).
% 1.81/1.42 tff(852,plain,
% 1.81/1.42 ((~hskp22) | c2_1(a451)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[851, 846])).
% 1.81/1.42 tff(853,plain,
% 1.81/1.42 ((~hskp22) | c2_1(a451)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[852, 846])).
% 1.81/1.42 tff(854,plain,
% 1.81/1.42 ((~hskp22) | c2_1(a451)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[853, 846])).
% 1.81/1.42 tff(855,plain,
% 1.81/1.42 ((~hskp22) | c2_1(a451)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[854, 846])).
% 1.81/1.42 tff(856,plain,
% 1.81/1.42 (c2_1(a451)),
% 1.81/1.42 inference(unit_resolution,[status(thm)],[855, 839])).
% 1.81/1.42 tff(857,plain,
% 1.81/1.42 (((~hskp22) | c0_1(a451)) <=> ((~hskp22) | c0_1(a451))),
% 1.81/1.42 inference(rewrite,[status(thm)],[])).
% 1.81/1.42 tff(858,axiom,((~hskp22) | c0_1(a451)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 1.81/1.42 tff(859,plain,
% 1.81/1.42 ((~hskp22) | c0_1(a451)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[858, 857])).
% 1.81/1.42 tff(860,plain,
% 1.81/1.42 ((~hskp22) | c0_1(a451)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[859, 857])).
% 1.81/1.42 tff(861,plain,
% 1.81/1.42 ((~hskp22) | c0_1(a451)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[860, 857])).
% 1.81/1.42 tff(862,plain,
% 1.81/1.42 ((~hskp22) | c0_1(a451)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[861, 857])).
% 1.81/1.42 tff(863,plain,
% 1.81/1.42 ((~hskp22) | c0_1(a451)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[862, 857])).
% 1.81/1.42 tff(864,plain,
% 1.81/1.42 ((~hskp22) | c0_1(a451)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[863, 857])).
% 1.81/1.42 tff(865,plain,
% 1.81/1.42 ((~hskp22) | c0_1(a451)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[864, 857])).
% 1.81/1.42 tff(866,plain,
% 1.81/1.42 ((~hskp22) | c0_1(a451)),
% 1.81/1.42 inference(modus_ponens,[status(thm)],[865, 857])).
% 1.81/1.42 tff(867,plain,
% 1.81/1.43 (c0_1(a451)),
% 1.81/1.43 inference(unit_resolution,[status(thm)],[866, 839])).
% 1.81/1.43 tff(868,assumption,(~c1_1(a451)), introduced(assumption)).
% 1.81/1.43 tff(869,plain,
% 1.81/1.43 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c1_1(a451) | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)) | (~c3_1(a451)) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c1_1(a451) | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.81/1.43 inference(rewrite,[status(thm)],[])).
% 1.81/1.43 tff(870,plain,
% 1.81/1.43 (((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445))) <=> (c1_1(a451) | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.81/1.43 inference(rewrite,[status(thm)],[])).
% 1.81/1.43 tff(871,plain,
% 1.81/1.43 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c1_1(a451) | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)) | (~c3_1(a451)) | (~c0_1(a451))))),
% 1.81/1.43 inference(monotonicity,[status(thm)],[870])).
% 1.81/1.43 tff(872,plain,
% 1.81/1.43 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c1_1(a451) | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.81/1.43 inference(transitivity,[status(thm)],[871, 869])).
% 1.81/1.43 tff(873,plain,
% 1.81/1.43 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445)))),
% 1.81/1.43 inference(quant_inst,[status(thm)],[])).
% 1.81/1.43 tff(874,plain,
% 1.81/1.43 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c1_1(a451) | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)) | (~c3_1(a451)) | (~c0_1(a451))),
% 1.81/1.43 inference(modus_ponens,[status(thm)],[873, 872])).
% 1.81/1.43 tff(875,plain,
% 1.81/1.43 ((~c1_1(a445)) | (~c3_1(a445)) | (~c3_1(a451)) | (~c0_1(a451))),
% 1.81/1.43 inference(unit_resolution,[status(thm)],[874, 150, 868, 472, 531])).
% 1.81/1.43 tff(876,plain,
% 1.81/1.43 (~c3_1(a451)),
% 1.81/1.43 inference(unit_resolution,[status(thm)],[875, 867, 473, 484])).
% 1.81/1.43 tff(877,plain,
% 1.81/1.43 (^[V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.81/1.43 inference(bind,[status(th)],[])).
% 1.81/1.43 tff(878,plain,
% 1.81/1.43 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.81/1.43 inference(quant_intro,[status(thm)],[877])).
% 1.81/1.43 tff(879,plain,
% 1.81/1.43 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.81/1.43 inference(rewrite,[status(thm)],[])).
% 1.81/1.43 tff(880,plain,
% 1.81/1.43 (^[V: $i, U: $i] : 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(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.82/1.43 inference(bind,[status(th)],[])).
% 1.82/1.43 tff(881,plain,
% 1.82/1.43 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.43 inference(quant_intro,[status(thm)],[880])).
% 1.82/1.43 tff(882,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 1.82/1.43 tff(883,plain,
% 1.82/1.43 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[882, 881])).
% 1.82/1.43 tff(884,plain,
% 1.82/1.43 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[883, 879])).
% 1.82/1.43 tff(885,plain,(
% 1.82/1.43 ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.43 inference(skolemize,[status(sab)],[884])).
% 1.82/1.43 tff(886,plain,
% 1.82/1.43 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[885, 878])).
% 1.82/1.43 tff(887,plain,
% 1.82/1.43 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a451) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | c3_1(a451))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a451) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | c3_1(a451))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(888,plain,
% 1.82/1.43 (((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451))) <=> (c1_1(a451) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | c3_1(a451))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(889,plain,
% 1.82/1.43 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a451) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | c3_1(a451)))),
% 1.82/1.43 inference(monotonicity,[status(thm)],[888])).
% 1.82/1.43 tff(890,plain,
% 1.82/1.43 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a451) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | c3_1(a451))),
% 1.82/1.43 inference(transitivity,[status(thm)],[889, 887])).
% 1.82/1.43 tff(891,plain,
% 1.82/1.43 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))),
% 1.82/1.43 inference(quant_inst,[status(thm)],[])).
% 1.82/1.43 tff(892,plain,
% 1.82/1.43 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a451) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | c3_1(a451)),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[891, 890])).
% 1.82/1.43 tff(893,plain,
% 1.82/1.43 ((~c2_1(a451)) | c3_1(a451)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[892, 150, 836, 838, 868, 837, 886])).
% 1.82/1.43 tff(894,plain,
% 1.82/1.43 ($false),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[893, 876, 856])).
% 1.82/1.43 tff(895,plain,((~hskp22) | (~c0_1(a401)) | (~c1_1(a401)) | c1_1(a451) | c3_1(a401) | (~c3_1(a445)) | (~c1_1(a445)) | c0_1(a445)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.43 tff(896,plain,
% 1.82/1.43 ($false),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[895, 845, 839, 473, 838, 837, 836, 484, 472])).
% 1.82/1.43 tff(897,plain,((~hskp22) | (~c3_1(a445)) | (~c1_1(a401)) | c3_1(a401) | (~c0_1(a401)) | (~c1_1(a445)) | c0_1(a445)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.43 tff(898,plain,
% 1.82/1.43 (~hskp22),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[897, 795, 473, 806, 817, 484, 472])).
% 1.82/1.43 tff(899,plain,
% 1.82/1.43 (((~hskp20) | c3_1(a449)) <=> ((~hskp20) | c3_1(a449))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(900,axiom,((~hskp20) | c3_1(a449)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 1.82/1.43 tff(901,plain,
% 1.82/1.43 ((~hskp20) | c3_1(a449)),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[900, 899])).
% 1.82/1.43 tff(902,plain,
% 1.82/1.43 ((~hskp20) | c3_1(a449)),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[901, 899])).
% 1.82/1.43 tff(903,plain,
% 1.82/1.43 ((~hskp20) | c3_1(a449)),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[902, 899])).
% 1.82/1.43 tff(904,plain,
% 1.82/1.43 ((~hskp20) | c3_1(a449)),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[903, 899])).
% 1.82/1.43 tff(905,plain,
% 1.82/1.43 ((~hskp20) | c3_1(a449)),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[904, 899])).
% 1.82/1.43 tff(906,plain,
% 1.82/1.43 ((~hskp20) | c3_1(a449)),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[905, 899])).
% 1.82/1.43 tff(907,plain,
% 1.82/1.43 ((~hskp20) | c3_1(a449)),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[906, 899])).
% 1.82/1.43 tff(908,plain,
% 1.82/1.43 ((~hskp20) | c3_1(a449)),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[907, 899])).
% 1.82/1.43 tff(909,plain,
% 1.82/1.43 (c3_1(a449)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[908, 824])).
% 1.82/1.43 tff(910,plain,
% 1.82/1.43 (((~hskp20) | (~c2_1(a449))) <=> ((~hskp20) | (~c2_1(a449)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(911,plain,
% 1.82/1.43 (((~c2_1(a449)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a449)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(912,axiom,((~c2_1(a449)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 1.82/1.43 tff(913,plain,
% 1.82/1.43 ((~hskp20) | (~c2_1(a449))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[912, 911])).
% 1.82/1.43 tff(914,plain,
% 1.82/1.43 ((~hskp20) | (~c2_1(a449))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[913, 910])).
% 1.82/1.43 tff(915,plain,
% 1.82/1.43 (~c2_1(a449)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[914, 824])).
% 1.82/1.43 tff(916,assumption,(hskp2), introduced(assumption)).
% 1.82/1.43 tff(917,plain,
% 1.82/1.43 (c0_1(a402)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[520, 916])).
% 1.82/1.43 tff(918,plain,
% 1.82/1.43 ((~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a445)) | (~c3_1(a445))),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[537, 150, 472, 105, 531])).
% 1.82/1.43 tff(919,plain,
% 1.82/1.43 (~c3_1(a402)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[918, 917, 484, 473])).
% 1.82/1.43 tff(920,plain,
% 1.82/1.43 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.82/1.43 inference(bind,[status(th)],[])).
% 1.82/1.43 tff(921,plain,
% 1.82/1.43 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.82/1.43 inference(quant_intro,[status(thm)],[920])).
% 1.82/1.43 tff(922,plain,
% 1.82/1.43 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(923,plain,
% 1.82/1.43 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.82/1.43 inference(bind,[status(th)],[])).
% 1.82/1.43 tff(924,plain,
% 1.82/1.43 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.82/1.43 inference(quant_intro,[status(thm)],[923])).
% 1.82/1.43 tff(925,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 1.82/1.43 tff(926,plain,
% 1.82/1.43 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[925, 924])).
% 1.82/1.43 tff(927,plain,
% 1.82/1.43 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[926, 922])).
% 1.82/1.43 tff(928,plain,(
% 1.82/1.43 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.82/1.43 inference(skolemize,[status(sab)],[927])).
% 1.82/1.43 tff(929,plain,
% 1.82/1.43 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[928, 921])).
% 1.82/1.43 tff(930,plain,
% 1.82/1.43 (~c2_1(a402)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[509, 916])).
% 1.82/1.43 tff(931,assumption,(~c2_1(a449)), introduced(assumption)).
% 1.82/1.43 tff(932,assumption,(c3_1(a449)), introduced(assumption)).
% 1.82/1.43 tff(933,assumption,(c1_1(a449)), introduced(assumption)).
% 1.82/1.43 tff(934,assumption,(~hskp22), introduced(assumption)).
% 1.82/1.43 tff(935,plain,
% 1.82/1.43 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a449) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a449)) | (~c1_1(a449)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(936,plain,
% 1.82/1.43 ((hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402))) <=> (hskp22 | c2_1(a449) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(937,plain,
% 1.82/1.43 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a449) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a449)) | (~c1_1(a449))))),
% 1.82/1.43 inference(monotonicity,[status(thm)],[936])).
% 1.82/1.43 tff(938,plain,
% 1.82/1.43 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.82/1.43 inference(transitivity,[status(thm)],[937, 935])).
% 1.82/1.43 tff(939,plain,
% 1.82/1.43 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))),
% 1.82/1.43 inference(quant_inst,[status(thm)],[])).
% 1.82/1.43 tff(940,plain,
% 1.82/1.43 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a449)) | (~c1_1(a449))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[939, 938])).
% 1.82/1.43 tff(941,plain,
% 1.82/1.43 ($false),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[940, 150, 934, 933, 932, 917, 931, 930, 929, 919])).
% 1.82/1.43 tff(942,plain,((~hskp2) | hskp22 | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a449) | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | c1_1(a402)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.43 tff(943,plain,
% 1.82/1.43 (~hskp2),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[942, 915, 484, 909, 898, 835, 473, 472, 105])).
% 1.82/1.43 tff(944,plain,
% 1.82/1.43 (((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c0_1(a401)))) <=> ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp11 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c0_1(a401)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(945,plain,
% 1.82/1.43 ((hskp11 | hskp2 | (~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c0_1(a401))) <=> (hskp11 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c0_1(a401)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(946,plain,
% 1.82/1.43 (((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c0_1(a401)))) <=> ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c0_1(a401))))),
% 1.82/1.43 inference(monotonicity,[status(thm)],[945])).
% 1.82/1.43 tff(947,plain,
% 1.82/1.43 (((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c0_1(a401)))) <=> ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp11 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c0_1(a401)))),
% 1.82/1.43 inference(transitivity,[status(thm)],[946, 944])).
% 1.82/1.43 tff(948,plain,
% 1.82/1.43 ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c0_1(a401)))),
% 1.82/1.43 inference(quant_inst,[status(thm)],[])).
% 1.82/1.43 tff(949,plain,
% 1.82/1.43 ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp11 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c0_1(a401))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[948, 947])).
% 1.82/1.43 tff(950,plain,
% 1.82/1.43 (hskp2 | c2_1(a401)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[949, 150, 485, 817, 795, 687])).
% 1.82/1.43 tff(951,plain,
% 1.82/1.43 (c2_1(a401)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[950, 943])).
% 1.82/1.43 tff(952,plain,
% 1.82/1.43 (^[U: $i] : refl((hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 1.82/1.43 inference(bind,[status(th)],[])).
% 1.82/1.43 tff(953,plain,
% 1.82/1.43 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.43 inference(quant_intro,[status(thm)],[952])).
% 1.82/1.43 tff(954,plain,
% 1.82/1.43 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(955,plain,
% 1.82/1.43 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp11) <=> ((hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp11))), rewrite(((hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp11) <=> (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.82/1.43 inference(bind,[status(th)],[])).
% 1.82/1.43 tff(956,plain,
% 1.82/1.43 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp11) <=> ![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.43 inference(quant_intro,[status(thm)],[955])).
% 1.82/1.43 tff(957,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 1.82/1.43 tff(958,plain,
% 1.82/1.43 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[957, 956])).
% 1.82/1.43 tff(959,plain,
% 1.82/1.43 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[958, 954])).
% 1.82/1.43 tff(960,plain,(
% 1.82/1.43 ![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.43 inference(skolemize,[status(sab)],[959])).
% 1.82/1.43 tff(961,plain,
% 1.82/1.43 (![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[960, 953])).
% 1.82/1.43 tff(962,plain,
% 1.82/1.43 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp11 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(963,plain,
% 1.82/1.43 ((hskp22 | hskp11 | (~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405))) <=> (hskp22 | hskp11 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(964,plain,
% 1.82/1.43 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405))))),
% 1.82/1.43 inference(monotonicity,[status(thm)],[963])).
% 1.82/1.43 tff(965,plain,
% 1.82/1.43 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp11 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)))),
% 1.82/1.43 inference(transitivity,[status(thm)],[964, 962])).
% 1.82/1.43 tff(966,plain,
% 1.82/1.43 ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)))),
% 1.82/1.43 inference(quant_inst,[status(thm)],[])).
% 1.82/1.43 tff(967,plain,
% 1.82/1.43 ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp11 | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[966, 965])).
% 1.82/1.43 tff(968,plain,
% 1.82/1.43 (hskp22 | hskp11 | (~c2_1(a405))),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[967, 150, 108, 106, 961])).
% 1.82/1.43 tff(969,plain,
% 1.82/1.43 (~c2_1(a405)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[968, 898, 485])).
% 1.82/1.43 tff(970,assumption,(hskp7), introduced(assumption)).
% 1.82/1.43 tff(971,plain,
% 1.82/1.43 (~c3_1(a410)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[254, 970])).
% 1.82/1.43 tff(972,plain,
% 1.82/1.43 (~c1_1(a410)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[260, 970])).
% 1.82/1.43 tff(973,plain,
% 1.82/1.43 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a410) | c3_1(a410) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a410)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a410) | c3_1(a410) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a410)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(974,plain,
% 1.82/1.43 (((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410))) <=> (c1_1(a410) | c3_1(a410) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a410)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(975,plain,
% 1.82/1.43 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a410) | c3_1(a410) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a410))))),
% 1.82/1.43 inference(monotonicity,[status(thm)],[974])).
% 1.82/1.43 tff(976,plain,
% 1.82/1.43 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a410) | c3_1(a410) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a410)))),
% 1.82/1.43 inference(transitivity,[status(thm)],[975, 973])).
% 1.82/1.43 tff(977,plain,
% 1.82/1.43 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410)))),
% 1.82/1.43 inference(quant_inst,[status(thm)],[])).
% 1.82/1.43 tff(978,plain,
% 1.82/1.43 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a410) | c3_1(a410) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a410))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[977, 976])).
% 1.82/1.43 tff(979,plain,
% 1.82/1.43 (~c2_1(a410)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[978, 150, 836, 838, 972, 971, 837, 886])).
% 1.82/1.43 tff(980,plain,
% 1.82/1.43 (hskp20),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[823, 150, 836, 838, 837, 483])).
% 1.82/1.43 tff(981,plain,
% 1.82/1.43 (~c2_1(a449)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[914, 980])).
% 1.82/1.43 tff(982,plain,
% 1.82/1.43 (c0_1(a410)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[295, 970])).
% 1.82/1.43 tff(983,plain,
% 1.82/1.43 (c3_1(a449)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[908, 980])).
% 1.82/1.43 tff(984,plain,
% 1.82/1.43 (c1_1(a449)),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[834, 980])).
% 1.82/1.43 tff(985,plain,
% 1.82/1.43 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a449) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | (~c3_1(a449)) | (~c1_1(a449)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(986,plain,
% 1.82/1.43 ((hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a410) | c3_1(a410) | (~c0_1(a410))) <=> (hskp22 | c2_1(a449) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.82/1.43 inference(rewrite,[status(thm)],[])).
% 1.82/1.43 tff(987,plain,
% 1.82/1.43 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a449) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | (~c3_1(a449)) | (~c1_1(a449))))),
% 1.82/1.43 inference(monotonicity,[status(thm)],[986])).
% 1.82/1.43 tff(988,plain,
% 1.82/1.43 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.82/1.43 inference(transitivity,[status(thm)],[987, 985])).
% 1.82/1.43 tff(989,plain,
% 1.82/1.43 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)))),
% 1.82/1.43 inference(quant_inst,[status(thm)],[])).
% 1.82/1.43 tff(990,plain,
% 1.82/1.43 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | (~c3_1(a449)) | (~c1_1(a449))),
% 1.82/1.43 inference(modus_ponens,[status(thm)],[989, 988])).
% 1.82/1.43 tff(991,plain,
% 1.82/1.43 ($false),
% 1.82/1.43 inference(unit_resolution,[status(thm)],[990, 150, 934, 984, 983, 982, 981, 971, 929, 979])).
% 1.82/1.44 tff(992,plain,((~hskp7) | hskp22 | (~c0_1(a401)) | (~c1_1(a401)) | c3_1(a401)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.44 tff(993,plain,
% 1.82/1.44 (~hskp7),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[992, 898, 817, 806, 795])).
% 1.82/1.44 tff(994,plain,
% 1.82/1.44 (^[U: $i] : refl((hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.82/1.44 inference(bind,[status(th)],[])).
% 1.82/1.44 tff(995,plain,
% 1.82/1.44 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.44 inference(quant_intro,[status(thm)],[994])).
% 1.82/1.44 tff(996,plain,
% 1.82/1.44 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(997,plain,
% 1.82/1.44 (^[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)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp7) | hskp16) <=> ((hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp16))), rewrite(((hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp7) | hskp16) <=> (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.82/1.44 inference(bind,[status(th)],[])).
% 1.82/1.44 tff(998,plain,
% 1.82/1.44 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp7) | hskp16) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.44 inference(quant_intro,[status(thm)],[997])).
% 1.82/1.44 tff(999,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp7) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 1.82/1.44 tff(1000,plain,
% 1.82/1.44 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[999, 998])).
% 1.82/1.44 tff(1001,plain,
% 1.82/1.44 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1000, 996])).
% 1.82/1.44 tff(1002,plain,(
% 1.82/1.44 ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.44 inference(skolemize,[status(sab)],[1001])).
% 1.82/1.44 tff(1003,plain,
% 1.82/1.44 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1002, 995])).
% 1.82/1.44 tff(1004,plain,
% 1.82/1.44 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c3_1(a405)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c3_1(a405)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1005,plain,
% 1.82/1.44 ((hskp16 | hskp7 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c0_1(a405))) <=> (hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c3_1(a405)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1006,plain,
% 1.82/1.44 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c0_1(a405)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c3_1(a405))))),
% 1.82/1.44 inference(monotonicity,[status(thm)],[1005])).
% 1.82/1.44 tff(1007,plain,
% 1.82/1.44 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c0_1(a405)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c3_1(a405)))),
% 1.82/1.44 inference(transitivity,[status(thm)],[1006, 1004])).
% 1.82/1.44 tff(1008,plain,
% 1.82/1.44 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c0_1(a405)))),
% 1.82/1.44 inference(quant_inst,[status(thm)],[])).
% 1.82/1.44 tff(1009,plain,
% 1.82/1.44 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a405)) | c2_1(a405) | (~c3_1(a405))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1008, 1007])).
% 1.82/1.44 tff(1010,plain,
% 1.82/1.44 (hskp16 | hskp7 | c2_1(a405)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1009, 150, 108, 106, 1003])).
% 1.82/1.44 tff(1011,plain,
% 1.82/1.44 (hskp16),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1010, 993, 969])).
% 1.82/1.44 tff(1012,plain,
% 1.82/1.44 (((~hskp16) | (~c3_1(a434))) <=> ((~hskp16) | (~c3_1(a434)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1013,plain,
% 1.82/1.44 (((~c3_1(a434)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a434)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1014,axiom,((~c3_1(a434)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 1.82/1.44 tff(1015,plain,
% 1.82/1.44 ((~hskp16) | (~c3_1(a434))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1014, 1013])).
% 1.82/1.44 tff(1016,plain,
% 1.82/1.44 ((~hskp16) | (~c3_1(a434))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1015, 1012])).
% 1.82/1.44 tff(1017,plain,
% 1.82/1.44 (~c3_1(a434)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1016, 1011])).
% 1.82/1.44 tff(1018,plain,
% 1.82/1.44 (((~hskp16) | (~c0_1(a434))) <=> ((~hskp16) | (~c0_1(a434)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1019,plain,
% 1.82/1.44 (((~c0_1(a434)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a434)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1020,axiom,((~c0_1(a434)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 1.82/1.44 tff(1021,plain,
% 1.82/1.44 ((~hskp16) | (~c0_1(a434))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1020, 1019])).
% 1.82/1.44 tff(1022,plain,
% 1.82/1.44 ((~hskp16) | (~c0_1(a434))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1021, 1018])).
% 1.82/1.44 tff(1023,plain,
% 1.82/1.44 (~c0_1(a434)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1022, 1011])).
% 1.82/1.44 tff(1024,assumption,(~c2_1(a434)), introduced(assumption)).
% 1.82/1.44 tff(1025,assumption,(~hskp7), introduced(assumption)).
% 1.82/1.44 tff(1026,assumption,(~c3_1(a434)), introduced(assumption)).
% 1.82/1.44 tff(1027,plain,
% 1.82/1.44 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1028,plain,
% 1.82/1.44 ((hskp7 | hskp2 | (~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434))) <=> (hskp7 | hskp2 | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1029,plain,
% 1.82/1.44 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434))))),
% 1.82/1.44 inference(monotonicity,[status(thm)],[1028])).
% 1.82/1.44 tff(1030,plain,
% 1.82/1.44 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)))),
% 1.82/1.44 inference(transitivity,[status(thm)],[1029, 1027])).
% 1.82/1.44 tff(1031,plain,
% 1.82/1.44 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)))),
% 1.82/1.44 inference(quant_inst,[status(thm)],[])).
% 1.82/1.44 tff(1032,plain,
% 1.82/1.44 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 1.82/1.44 tff(1033,plain,
% 1.82/1.44 (hskp7 | hskp2 | c2_1(a434) | (~c1_1(a434))),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1032, 150, 1026, 118])).
% 1.82/1.44 tff(1034,plain,
% 1.82/1.44 (~c1_1(a434)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1033, 1024, 23, 1025])).
% 1.82/1.44 tff(1035,plain,
% 1.82/1.44 (((~hskp16) | c1_1(a434)) <=> ((~hskp16) | c1_1(a434))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1036,axiom,((~hskp16) | c1_1(a434)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 1.82/1.44 tff(1037,plain,
% 1.82/1.44 ((~hskp16) | c1_1(a434)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 1.82/1.44 tff(1038,plain,
% 1.82/1.44 ((~hskp16) | c1_1(a434)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1037, 1035])).
% 1.82/1.44 tff(1039,plain,
% 1.82/1.44 ((~hskp16) | c1_1(a434)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1038, 1035])).
% 1.82/1.44 tff(1040,plain,
% 1.82/1.44 ((~hskp16) | c1_1(a434)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1039, 1035])).
% 1.82/1.44 tff(1041,plain,
% 1.82/1.44 ((~hskp16) | c1_1(a434)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1040, 1035])).
% 1.82/1.44 tff(1042,plain,
% 1.82/1.44 ((~hskp16) | c1_1(a434)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1041, 1035])).
% 1.82/1.44 tff(1043,plain,
% 1.82/1.44 ((~hskp16) | c1_1(a434)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1042, 1035])).
% 1.82/1.44 tff(1044,plain,
% 1.82/1.44 ((~hskp16) | c1_1(a434)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1043, 1035])).
% 1.82/1.44 tff(1045,plain,
% 1.82/1.44 (~hskp16),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1044, 1034])).
% 1.82/1.44 tff(1046,plain,
% 1.82/1.44 (c2_1(a405)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1010, 1045, 1025])).
% 1.82/1.44 tff(1047,assumption,(~c0_1(a434)), introduced(assumption)).
% 1.82/1.44 tff(1048,plain,
% 1.82/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a434) | c0_1(a434) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a434) | c0_1(a434) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)) | c2_1(a434))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1049,plain,
% 1.82/1.44 (((~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a434) | c0_1(a434) | c2_1(a434)) <=> (c1_1(a434) | c0_1(a434) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)) | c2_1(a434))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1050,plain,
% 1.82/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a434) | c0_1(a434) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)) | c2_1(a434)))),
% 1.82/1.44 inference(monotonicity,[status(thm)],[1049])).
% 1.82/1.44 tff(1051,plain,
% 1.82/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a434) | c0_1(a434) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)) | c2_1(a434))),
% 1.82/1.44 inference(transitivity,[status(thm)],[1050, 1048])).
% 1.82/1.44 tff(1052,plain,
% 1.82/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a434) | c0_1(a434) | c2_1(a434))),
% 1.82/1.44 inference(quant_inst,[status(thm)],[])).
% 1.82/1.44 tff(1053,plain,
% 1.82/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a434) | c0_1(a434) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)) | c2_1(a434)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1052, 1051])).
% 1.82/1.44 tff(1054,plain,
% 1.82/1.44 ($false),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1053, 150, 108, 106, 1034, 836, 838, 1047, 837, 11, 1046, 1024])).
% 1.82/1.44 tff(1055,plain,(c2_1(a434) | (~c0_1(a405)) | (~c3_1(a405)) | (~c0_1(a401)) | (~c1_1(a401)) | c0_1(a434) | c3_1(a401) | hskp7 | hskp2 | c3_1(a434)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.44 tff(1056,plain,
% 1.82/1.44 (c2_1(a434)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1055, 943, 106, 817, 806, 1023, 795, 993, 1017, 108])).
% 1.82/1.44 tff(1057,assumption,(~c2_1(a405)), introduced(assumption)).
% 1.82/1.44 tff(1058,assumption,(hskp16), introduced(assumption)).
% 1.82/1.44 tff(1059,plain,
% 1.82/1.44 (~c0_1(a434)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1022, 1058])).
% 1.82/1.44 tff(1060,plain,
% 1.82/1.44 (~c3_1(a434)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1016, 1058])).
% 1.82/1.44 tff(1061,plain,
% 1.82/1.44 (c2_1(a434)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1055, 1026, 106, 836, 838, 1047, 837, 1025, 23, 108])).
% 1.82/1.44 tff(1062,plain,
% 1.82/1.44 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a449) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c3_1(a449)) | (~c1_1(a449)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a449) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1063,plain,
% 1.82/1.44 ((hskp14 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434))) <=> (hskp14 | c2_1(a449) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1064,plain,
% 1.82/1.44 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a449) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c3_1(a449)) | (~c1_1(a449))))),
% 1.82/1.44 inference(monotonicity,[status(thm)],[1063])).
% 1.82/1.44 tff(1065,plain,
% 1.82/1.44 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a449) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.82/1.44 inference(transitivity,[status(thm)],[1064, 1062])).
% 1.82/1.44 tff(1066,plain,
% 1.82/1.44 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))),
% 1.82/1.44 inference(quant_inst,[status(thm)],[])).
% 1.82/1.44 tff(1067,plain,
% 1.82/1.44 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a449) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c3_1(a449)) | (~c1_1(a449))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 1.82/1.44 tff(1068,plain,
% 1.82/1.44 (c3_1(a434) | (~c2_1(a434))),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1067, 150, 407, 984, 983, 981, 1047, 400])).
% 1.82/1.44 tff(1069,plain,
% 1.82/1.44 ($false),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1068, 1061, 1026])).
% 1.82/1.44 tff(1070,plain,(c3_1(a434) | hskp14 | c0_1(a434) | (~c3_1(a405)) | (~c0_1(a401)) | (~c1_1(a401)) | c3_1(a401) | hskp7 | hskp2 | (~c0_1(a405))), inference(lemma,lemma(discharge,[]))).
% 1.82/1.44 tff(1071,plain,
% 1.82/1.44 ($false),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1070, 1060, 1059, 407, 106, 836, 838, 837, 1025, 23, 108])).
% 1.82/1.44 tff(1072,plain,((~hskp16) | hskp14 | (~c3_1(a405)) | (~c0_1(a401)) | (~c1_1(a401)) | c3_1(a401) | hskp7 | hskp2 | (~c0_1(a405))), inference(lemma,lemma(discharge,[]))).
% 1.82/1.44 tff(1073,plain,
% 1.82/1.44 (~hskp16),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1072, 1025, 106, 836, 838, 837, 407, 23, 108])).
% 1.82/1.44 tff(1074,plain,
% 1.82/1.44 ($false),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1010, 1073, 1025, 1057])).
% 1.82/1.44 tff(1075,plain,(hskp7 | c2_1(a405) | (~c0_1(a405)) | (~c3_1(a405)) | (~c0_1(a401)) | (~c1_1(a401)) | c3_1(a401) | hskp14 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.82/1.44 tff(1076,plain,
% 1.82/1.44 (hskp14),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1075, 943, 108, 106, 817, 806, 795, 969, 993])).
% 1.82/1.44 tff(1077,plain,
% 1.82/1.44 (~c1_1(a428)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[421, 1076])).
% 1.82/1.44 tff(1078,plain,
% 1.82/1.44 (c2_1(a428)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[438, 1076])).
% 1.82/1.44 tff(1079,plain,
% 1.82/1.44 (c1_1(a434)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1044, 1011])).
% 1.82/1.44 tff(1080,plain,
% 1.82/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a434) | c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a434) | c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1081,plain,
% 1.82/1.44 (((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434))) <=> (c0_1(a434) | c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1082,plain,
% 1.82/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a434) | c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a434)) | (~c1_1(a434))))),
% 1.82/1.44 inference(monotonicity,[status(thm)],[1081])).
% 1.82/1.44 tff(1083,plain,
% 1.82/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a434) | c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.82/1.44 inference(transitivity,[status(thm)],[1082, 1080])).
% 1.82/1.44 tff(1084,plain,
% 1.82/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.82/1.44 inference(quant_inst,[status(thm)],[])).
% 1.82/1.44 tff(1085,plain,
% 1.82/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a434) | c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a434)) | (~c1_1(a434))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1084, 1083])).
% 1.82/1.44 tff(1086,plain,
% 1.82/1.44 (~c3_1(a428)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1085, 150, 1079, 1078, 817, 1023, 1077, 795, 704, 1056, 951])).
% 1.82/1.44 tff(1087,plain,
% 1.82/1.44 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | c3_1(a428))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | c3_1(a428))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1088,plain,
% 1.82/1.44 (((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a428) | c3_1(a428) | (~c2_1(a428))) <=> (c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | c3_1(a428))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1089,plain,
% 1.82/1.44 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a428) | c3_1(a428) | (~c2_1(a428)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | c3_1(a428)))),
% 1.82/1.44 inference(monotonicity,[status(thm)],[1088])).
% 1.82/1.44 tff(1090,plain,
% 1.82/1.44 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a428) | c3_1(a428) | (~c2_1(a428)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | c3_1(a428))),
% 1.82/1.44 inference(transitivity,[status(thm)],[1089, 1087])).
% 1.82/1.44 tff(1091,plain,
% 1.82/1.44 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a428) | c3_1(a428) | (~c2_1(a428)))),
% 1.82/1.44 inference(quant_inst,[status(thm)],[])).
% 1.82/1.44 tff(1092,plain,
% 1.82/1.44 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a428) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a428)) | c3_1(a428)),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1091, 1090])).
% 1.82/1.44 tff(1093,plain,
% 1.82/1.44 ($false),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1092, 150, 1078, 817, 806, 1077, 795, 886, 1086])).
% 1.82/1.44 tff(1094,plain,(hskp11 | (~c3_1(a405)) | (~c0_1(a405)) | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | c1_1(a402) | c0_1(a403) | c2_1(a403) | c3_1(a403)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.44 tff(1095,plain,
% 1.82/1.44 (hskp11),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1094, 459, 108, 106, 471, 460, 105, 336, 335, 334])).
% 1.82/1.44 tff(1096,plain,
% 1.82/1.44 (((~hskp11) | (~c0_1(a420))) <=> ((~hskp11) | (~c0_1(a420)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1097,plain,
% 1.82/1.44 (((~c0_1(a420)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a420)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1098,axiom,((~c0_1(a420)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 1.82/1.44 tff(1099,plain,
% 1.82/1.44 ((~hskp11) | (~c0_1(a420))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 1.82/1.44 tff(1100,plain,
% 1.82/1.44 ((~hskp11) | (~c0_1(a420))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1099, 1096])).
% 1.82/1.44 tff(1101,plain,
% 1.82/1.44 (~c0_1(a420)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1100, 1095])).
% 1.82/1.44 tff(1102,plain,
% 1.82/1.44 (((~hskp11) | (~c1_1(a420))) <=> ((~hskp11) | (~c1_1(a420)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1103,plain,
% 1.82/1.44 (((~c1_1(a420)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a420)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1104,axiom,((~c1_1(a420)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 1.82/1.44 tff(1105,plain,
% 1.82/1.44 ((~hskp11) | (~c1_1(a420))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1104, 1103])).
% 1.82/1.44 tff(1106,plain,
% 1.82/1.44 ((~hskp11) | (~c1_1(a420))),
% 1.82/1.44 inference(modus_ponens,[status(thm)],[1105, 1102])).
% 1.82/1.44 tff(1107,plain,
% 1.82/1.44 (~c1_1(a420)),
% 1.82/1.44 inference(unit_resolution,[status(thm)],[1106, 1095])).
% 1.82/1.44 tff(1108,plain,
% 1.82/1.44 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 1.82/1.44 inference(bind,[status(th)],[])).
% 1.82/1.44 tff(1109,plain,
% 1.82/1.44 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.82/1.44 inference(quant_intro,[status(thm)],[1108])).
% 1.82/1.44 tff(1110,plain,
% 1.82/1.44 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.82/1.44 inference(rewrite,[status(thm)],[])).
% 1.82/1.44 tff(1111,plain,
% 1.82/1.44 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_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))))), (((((((~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)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_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)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 1.82/1.45 inference(bind,[status(th)],[])).
% 1.82/1.45 tff(1112,plain,
% 1.82/1.45 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.82/1.45 inference(quant_intro,[status(thm)],[1111])).
% 1.82/1.45 tff(1113,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 1.82/1.45 tff(1114,plain,
% 1.82/1.45 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 1.82/1.45 tff(1115,plain,
% 1.82/1.45 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1114, 1110])).
% 1.82/1.45 tff(1116,plain,(
% 1.82/1.45 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.82/1.45 inference(skolemize,[status(sab)],[1115])).
% 1.82/1.45 tff(1117,plain,
% 1.82/1.45 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1116, 1109])).
% 1.82/1.45 tff(1118,assumption,(~c0_1(a420)), introduced(assumption)).
% 1.82/1.45 tff(1119,assumption,(~c1_1(a420)), introduced(assumption)).
% 1.82/1.45 tff(1120,assumption,(~c2_1(a420)), introduced(assumption)).
% 1.82/1.45 tff(1121,plain,
% 1.82/1.45 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1122,plain,
% 1.82/1.45 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a420) | c1_1(a420) | c0_1(a420)) <=> (hskp2 | hskp1 | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1123,plain,
% 1.82/1.45 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a420) | c1_1(a420) | c0_1(a420))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0)))),
% 1.82/1.45 inference(monotonicity,[status(thm)],[1122])).
% 1.82/1.45 tff(1124,plain,
% 1.82/1.45 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a420) | c1_1(a420) | c0_1(a420))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0))),
% 1.82/1.45 inference(transitivity,[status(thm)],[1123, 1121])).
% 1.82/1.45 tff(1125,plain,
% 1.82/1.45 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a420) | c1_1(a420) | c0_1(a420))),
% 1.82/1.45 inference(quant_inst,[status(thm)],[])).
% 1.82/1.45 tff(1126,plain,
% 1.82/1.45 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1125, 1124])).
% 1.82/1.45 tff(1127,plain,
% 1.82/1.45 (hskp2 | hskp1 | c0_1(a420) | c1_1(a420)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1126, 150, 1120, 33])).
% 1.82/1.45 tff(1128,plain,
% 1.82/1.45 (hskp2),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1127, 12, 1118, 1119])).
% 1.82/1.45 tff(1129,plain,
% 1.82/1.45 (c0_1(a402)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[520, 1128])).
% 1.82/1.45 tff(1130,assumption,(~c2_1(a426)), introduced(assumption)).
% 1.82/1.45 tff(1131,plain,
% 1.82/1.45 (~c2_1(a402)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[509, 1128])).
% 1.82/1.45 tff(1132,plain,
% 1.82/1.45 (~c3_1(a402)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[918, 1129, 484, 473])).
% 1.82/1.45 tff(1133,plain,
% 1.82/1.45 (hskp12),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[556, 1129, 12, 1132])).
% 1.82/1.45 tff(1134,plain,
% 1.82/1.45 (c0_1(a426)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[612, 1133])).
% 1.82/1.45 tff(1135,plain,
% 1.82/1.45 (c1_1(a426)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[601, 1133])).
% 1.82/1.45 tff(1136,assumption,(c2_1(a412)), introduced(assumption)).
% 1.82/1.45 tff(1137,assumption,(c1_1(a412)), introduced(assumption)).
% 1.82/1.45 tff(1138,assumption,(c0_1(a412)), introduced(assumption)).
% 1.82/1.45 tff(1139,plain,
% 1.82/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1140,plain,
% 1.82/1.45 (((~ndr1_0) | (~c2_1(a412)) | (~c1_1(a412)) | (~c0_1(a412)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402))) <=> (c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1141,plain,
% 1.82/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a412)) | (~c1_1(a412)) | (~c0_1(a412)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412))))),
% 1.82/1.45 inference(monotonicity,[status(thm)],[1140])).
% 1.82/1.45 tff(1142,plain,
% 1.82/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a412)) | (~c1_1(a412)) | (~c0_1(a412)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412)))),
% 1.82/1.45 inference(transitivity,[status(thm)],[1141, 1139])).
% 1.82/1.45 tff(1143,plain,
% 1.82/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a412)) | (~c1_1(a412)) | (~c0_1(a412)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)))),
% 1.82/1.45 inference(quant_inst,[status(thm)],[])).
% 1.82/1.45 tff(1144,plain,
% 1.82/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a412)) | (~c0_1(a412)) | (~c1_1(a412))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1143, 1142])).
% 1.82/1.45 tff(1145,plain,
% 1.82/1.45 (c2_1(a402) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426))),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1144, 150, 1138, 1137, 1136, 1130, 105, 495])).
% 1.82/1.45 tff(1146,plain,
% 1.82/1.45 ($false),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1145, 1135, 1134, 1129, 1131])).
% 1.82/1.45 tff(1147,plain,(hskp1 | (~c0_1(a412)) | (~c1_1(a412)) | (~c2_1(a412)) | c2_1(a426) | c1_1(a402) | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | c0_1(a420) | c1_1(a420) | c2_1(a420)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.45 tff(1148,plain,
% 1.82/1.45 ($false),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1147, 170, 192, 484, 12, 1130, 105, 181, 473, 472, 1118, 1119, 1120])).
% 1.82/1.45 tff(1149,plain,((~hskp27) | (~c1_1(a445)) | hskp1 | c2_1(a426) | c1_1(a402) | (~c3_1(a445)) | c0_1(a445) | c0_1(a420) | c1_1(a420) | c2_1(a420)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.45 tff(1150,plain,
% 1.82/1.45 (~hskp27),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1149, 12, 484, 1130, 105, 473, 472, 1118, 1119, 1120])).
% 1.82/1.45 tff(1151,plain,
% 1.82/1.45 (hskp0),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[363, 1150, 336, 335])).
% 1.82/1.45 tff(1152,plain,
% 1.82/1.45 (c1_1(a400)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[385, 1151])).
% 1.82/1.45 tff(1153,plain,
% 1.82/1.45 (c2_1(a400)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[374, 1151])).
% 1.82/1.45 tff(1154,plain,
% 1.82/1.45 (hskp12),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[556, 1132, 12, 1129])).
% 1.82/1.45 tff(1155,plain,
% 1.82/1.45 (c0_1(a426)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[612, 1154])).
% 1.82/1.45 tff(1156,plain,
% 1.82/1.45 (c1_1(a426)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[601, 1154])).
% 1.82/1.45 tff(1157,assumption,(c2_1(a400)), introduced(assumption)).
% 1.82/1.45 tff(1158,assumption,(c1_1(a400)), introduced(assumption)).
% 1.82/1.45 tff(1159,plain,
% 1.82/1.45 (c2_1(a402) | (~c0_1(a400)) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426))),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[619, 150, 1158, 1157, 1130, 105, 495])).
% 1.82/1.45 tff(1160,plain,
% 1.82/1.45 (~c0_1(a400)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1159, 1156, 1129, 1131, 1155])).
% 1.82/1.45 tff(1161,plain,
% 1.82/1.45 ($false),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[626, 150, 12, 1129, 1158, 1157, 105, 22, 1132, 1160])).
% 1.82/1.45 tff(1162,plain,(hskp1 | (~c1_1(a400)) | (~c2_1(a400)) | c1_1(a402) | c2_1(a426) | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | c0_1(a420) | c1_1(a420) | c2_1(a420)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.45 tff(1163,plain,
% 1.82/1.45 ($false),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1162, 1153, 1152, 12, 105, 1130, 484, 473, 472, 1118, 1119, 1120])).
% 1.82/1.45 tff(1164,plain,(hskp1 | c1_1(a402) | c2_1(a426) | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a403) | c2_1(a403) | c3_1(a403)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.45 tff(1165,plain,
% 1.82/1.45 (c2_1(a426)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1164, 12, 484, 105, 473, 472, 1118, 1119, 1120, 336, 335, 334])).
% 1.82/1.45 tff(1166,plain,
% 1.82/1.45 (~hskp12),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[562, 1165])).
% 1.82/1.45 tff(1167,plain,
% 1.82/1.45 (~c3_1(a402)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[538, 1129])).
% 1.82/1.45 tff(1168,plain,
% 1.82/1.45 ($false),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[556, 1167, 1166, 12, 1129])).
% 1.82/1.45 tff(1169,plain,(hskp1 | c1_1(a402) | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a403) | c2_1(a403) | c3_1(a403)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.45 tff(1170,plain,
% 1.82/1.45 (hskp1),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1169, 1120, 105, 473, 472, 484, 1118, 1119, 336, 335, 334])).
% 1.82/1.45 tff(1171,plain,
% 1.82/1.45 (~c3_1(a401)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[794, 1170])).
% 1.82/1.45 tff(1172,plain,
% 1.82/1.45 (c1_1(a401)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[805, 1170])).
% 1.82/1.45 tff(1173,plain,
% 1.82/1.45 (c0_1(a401)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[816, 1170])).
% 1.82/1.45 tff(1174,plain,
% 1.82/1.45 (hskp20),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[823, 150, 1173, 1172, 1171, 483])).
% 1.82/1.45 tff(1175,plain,
% 1.82/1.45 (c1_1(a449)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[834, 1174])).
% 1.82/1.45 tff(1176,plain,
% 1.82/1.45 (~hskp22),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[897, 1172, 473, 1171, 1173, 484, 472])).
% 1.82/1.45 tff(1177,plain,
% 1.82/1.45 (c3_1(a449)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[908, 1174])).
% 1.82/1.45 tff(1178,plain,
% 1.82/1.45 (~c2_1(a449)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[914, 1174])).
% 1.82/1.45 tff(1179,plain,
% 1.82/1.45 (~hskp2),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[942, 1178, 484, 1177, 1176, 1175, 473, 472, 105])).
% 1.82/1.45 tff(1180,plain,
% 1.82/1.45 (~hskp7),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[992, 1176, 1173, 1172, 1171])).
% 1.82/1.45 tff(1181,plain,
% 1.82/1.45 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c1_1(a401)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c1_1(a401)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1182,plain,
% 1.82/1.45 ((hskp7 | hskp2 | (~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c1_1(a401))) <=> (hskp7 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c1_1(a401)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1183,plain,
% 1.82/1.45 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c1_1(a401)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c1_1(a401))))),
% 1.82/1.45 inference(monotonicity,[status(thm)],[1182])).
% 1.82/1.45 tff(1184,plain,
% 1.82/1.45 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c1_1(a401)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c1_1(a401)))),
% 1.82/1.45 inference(transitivity,[status(thm)],[1183, 1181])).
% 1.82/1.45 tff(1185,plain,
% 1.82/1.45 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c1_1(a401)))),
% 1.82/1.45 inference(quant_inst,[status(thm)],[])).
% 1.82/1.45 tff(1186,plain,
% 1.82/1.45 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp7 | hskp2 | c3_1(a401) | (~ndr1_0) | c2_1(a401) | (~c1_1(a401))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 1.82/1.45 tff(1187,plain,
% 1.82/1.45 (hskp7 | hskp2 | c2_1(a401)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1186, 150, 1172, 1171, 118])).
% 1.82/1.45 tff(1188,plain,
% 1.82/1.45 (c2_1(a401)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1187, 1180, 1179])).
% 1.82/1.45 tff(1189,assumption,(c2_1(a405)), introduced(assumption)).
% 1.82/1.45 tff(1190,plain,
% 1.82/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1191,plain,
% 1.82/1.45 (((~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420)) <=> (c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1192,plain,
% 1.82/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401))))),
% 1.82/1.45 inference(monotonicity,[status(thm)],[1191])).
% 1.82/1.45 tff(1193,plain,
% 1.82/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.82/1.45 inference(transitivity,[status(thm)],[1192, 1190])).
% 1.82/1.45 tff(1194,plain,
% 1.82/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420))),
% 1.82/1.45 inference(quant_inst,[status(thm)],[])).
% 1.82/1.45 tff(1195,plain,
% 1.82/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c1_1(a401)) | (~c0_1(a401))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1194, 1193])).
% 1.82/1.45 tff(1196,plain,
% 1.82/1.45 ($false),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1195, 150, 108, 106, 836, 838, 1118, 1119, 1120, 837, 11, 1189])).
% 1.82/1.45 tff(1197,plain,((~c2_1(a405)) | (~c0_1(a405)) | (~c3_1(a405)) | (~c0_1(a401)) | (~c1_1(a401)) | c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.45 tff(1198,plain,
% 1.82/1.45 (~c2_1(a405)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1197, 1173, 106, 108, 1172, 1118, 1119, 1120, 1171])).
% 1.82/1.45 tff(1199,plain,
% 1.82/1.45 (hskp16),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1010, 1180, 1198])).
% 1.82/1.45 tff(1200,plain,
% 1.82/1.45 (~c0_1(a434)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1022, 1199])).
% 1.82/1.45 tff(1201,plain,
% 1.82/1.45 (~c3_1(a434)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1016, 1199])).
% 1.82/1.45 tff(1202,plain,
% 1.82/1.45 (c2_1(a434)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1055, 1201, 106, 1173, 1172, 1200, 1171, 1180, 1179, 108])).
% 1.82/1.45 tff(1203,plain,
% 1.82/1.45 (hskp14),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1075, 1180, 108, 106, 1173, 1172, 1171, 1198, 1179])).
% 1.82/1.45 tff(1204,plain,
% 1.82/1.45 (~c1_1(a428)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[421, 1203])).
% 1.82/1.45 tff(1205,plain,
% 1.82/1.45 (c2_1(a428)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[438, 1203])).
% 1.82/1.45 tff(1206,plain,
% 1.82/1.45 (c1_1(a434)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1044, 1199])).
% 1.82/1.45 tff(1207,plain,
% 1.82/1.45 (~c3_1(a428)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1085, 150, 1206, 1205, 1173, 1200, 1204, 1171, 704, 1202, 1188])).
% 1.82/1.45 tff(1208,plain,
% 1.82/1.45 ($false),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1092, 150, 1205, 1173, 1172, 1204, 1171, 886, 1207])).
% 1.82/1.45 tff(1209,plain,(c2_1(a420) | (~c3_1(a405)) | (~c0_1(a405)) | c0_1(a420) | c1_1(a420) | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | c1_1(a402) | c0_1(a403) | c2_1(a403) | c3_1(a403)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.45 tff(1210,plain,
% 1.82/1.45 (c2_1(a420)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1209, 1119, 108, 1118, 106, 484, 473, 472, 105, 336, 335, 334])).
% 1.82/1.45 tff(1211,plain,
% 1.82/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1212,plain,
% 1.82/1.45 (((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a420) | c0_1(a420) | (~c2_1(a420)) | c3_1(a403) | c0_1(a403) | c2_1(a403)) <=> (c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1213,plain,
% 1.82/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a420) | c0_1(a420) | (~c2_1(a420)) | c3_1(a403) | c0_1(a403) | c2_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403))))),
% 1.82/1.45 inference(monotonicity,[status(thm)],[1212])).
% 1.82/1.45 tff(1214,plain,
% 1.82/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a420) | c0_1(a420) | (~c2_1(a420)) | c3_1(a403) | c0_1(a403) | c2_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)))),
% 1.82/1.45 inference(transitivity,[status(thm)],[1213, 1211])).
% 1.82/1.45 tff(1215,plain,
% 1.82/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a420) | c0_1(a420) | (~c2_1(a420)) | c3_1(a403) | c0_1(a403) | c2_1(a403))),
% 1.82/1.45 inference(quant_inst,[status(thm)],[])).
% 1.82/1.45 tff(1216,plain,
% 1.82/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1215, 1214])).
% 1.82/1.45 tff(1217,plain,
% 1.82/1.45 ((~c2_1(a420)) | (~c1_1(a403))),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1216, 150, 1118, 1119, 336, 335, 334, 346])).
% 1.82/1.45 tff(1218,plain,
% 1.82/1.45 (~c1_1(a403)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1217, 1210])).
% 1.82/1.45 tff(1219,plain,
% 1.82/1.45 (((~hskp11) | (~c2_1(a420))) <=> ((~hskp11) | (~c2_1(a420)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1220,plain,
% 1.82/1.45 (((~c2_1(a420)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a420)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1221,axiom,((~c2_1(a420)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 1.82/1.45 tff(1222,plain,
% 1.82/1.45 ((~hskp11) | (~c2_1(a420))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1221, 1220])).
% 1.82/1.45 tff(1223,plain,
% 1.82/1.45 ((~hskp11) | (~c2_1(a420))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1222, 1219])).
% 1.82/1.45 tff(1224,plain,
% 1.82/1.45 (~hskp11),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1223, 1210])).
% 1.82/1.45 tff(1225,plain,
% 1.82/1.45 (hskp1),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[628, 1224, 105, 473, 472, 484, 336, 1218, 335])).
% 1.82/1.45 tff(1226,plain,
% 1.82/1.45 (~c3_1(a401)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[794, 1225])).
% 1.82/1.45 tff(1227,plain,
% 1.82/1.45 (c1_1(a401)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[805, 1225])).
% 1.82/1.45 tff(1228,plain,
% 1.82/1.45 (c0_1(a401)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[816, 1225])).
% 1.82/1.45 tff(1229,plain,
% 1.82/1.45 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c0_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c3_1(a420)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c3_1(a420)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1230,plain,
% 1.82/1.45 ((hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a420) | (~c2_1(a420)) | (~c3_1(a420))) <=> (hskp11 | c0_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c3_1(a420)))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1231,plain,
% 1.82/1.45 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a420) | (~c2_1(a420)) | (~c3_1(a420)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c0_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c3_1(a420))))),
% 1.82/1.45 inference(monotonicity,[status(thm)],[1230])).
% 1.82/1.45 tff(1232,plain,
% 1.82/1.45 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a420) | (~c2_1(a420)) | (~c3_1(a420)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c3_1(a420)))),
% 1.82/1.45 inference(transitivity,[status(thm)],[1231, 1229])).
% 1.82/1.45 tff(1233,plain,
% 1.82/1.45 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a420) | (~c2_1(a420)) | (~c3_1(a420)))),
% 1.82/1.45 inference(quant_inst,[status(thm)],[])).
% 1.82/1.45 tff(1234,plain,
% 1.82/1.45 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c3_1(a420))),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1233, 1232])).
% 1.82/1.45 tff(1235,plain,
% 1.82/1.45 (~c3_1(a420)),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1234, 150, 1224, 1228, 1227, 1118, 1210, 1226, 1117])).
% 1.82/1.45 tff(1236,plain,
% 1.82/1.45 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | c3_1(a420))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | c3_1(a420))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1237,plain,
% 1.82/1.45 (((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c3_1(a420) | (~c2_1(a420))) <=> (c1_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | c3_1(a420))),
% 1.82/1.45 inference(rewrite,[status(thm)],[])).
% 1.82/1.45 tff(1238,plain,
% 1.82/1.45 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c3_1(a420) | (~c2_1(a420)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | c3_1(a420)))),
% 1.82/1.45 inference(monotonicity,[status(thm)],[1237])).
% 1.82/1.45 tff(1239,plain,
% 1.82/1.45 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c3_1(a420) | (~c2_1(a420)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | c3_1(a420))),
% 1.82/1.45 inference(transitivity,[status(thm)],[1238, 1236])).
% 1.82/1.45 tff(1240,plain,
% 1.82/1.45 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c3_1(a420) | (~c2_1(a420)))),
% 1.82/1.45 inference(quant_inst,[status(thm)],[])).
% 1.82/1.45 tff(1241,plain,
% 1.82/1.45 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a420) | (~c2_1(a420)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | c3_1(a420)),
% 1.82/1.45 inference(modus_ponens,[status(thm)],[1240, 1239])).
% 1.82/1.45 tff(1242,plain,
% 1.82/1.45 ($false),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1241, 150, 1228, 1227, 1119, 1210, 1226, 886, 1235])).
% 1.82/1.45 tff(1243,plain,(c1_1(a420) | c0_1(a420) | c1_1(a402) | (~c3_1(a445)) | c0_1(a445) | (~c1_1(a445)) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~c0_1(a405)) | (~c3_1(a405))), inference(lemma,lemma(discharge,[]))).
% 1.82/1.45 tff(1244,plain,
% 1.82/1.45 ($false),
% 1.82/1.45 inference(unit_resolution,[status(thm)],[1243, 1107, 1101, 105, 471, 460, 459, 336, 335, 334, 108, 106])).
% 1.82/1.45 tff(1245,plain,(c0_1(a403) | c1_1(a402) | c2_1(a403) | c3_1(a403) | (~c0_1(a405)) | (~c3_1(a405)) | (~c1_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.82/1.46 tff(1246,plain,
% 1.82/1.46 (c0_1(a403)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1245, 335, 105, 334, 108, 106, 107, 55])).
% 1.82/1.46 tff(1247,plain,
% 1.82/1.46 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.82/1.46 inference(bind,[status(th)],[])).
% 1.82/1.46 tff(1248,plain,
% 1.82/1.46 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.82/1.46 inference(quant_intro,[status(thm)],[1247])).
% 1.82/1.46 tff(1249,plain,
% 1.82/1.46 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1250,plain,
% 1.82/1.46 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | 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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp3) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp3))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.82/1.46 inference(bind,[status(th)],[])).
% 1.82/1.46 tff(1251,plain,
% 1.82/1.46 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.82/1.46 inference(quant_intro,[status(thm)],[1250])).
% 1.82/1.46 tff(1252,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 1.82/1.46 tff(1253,plain,
% 1.82/1.46 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 1.82/1.46 tff(1254,plain,
% 1.82/1.46 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1253, 1249])).
% 1.82/1.46 tff(1255,plain,(
% 1.82/1.46 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.82/1.46 inference(skolemize,[status(sab)],[1254])).
% 1.82/1.46 tff(1256,plain,
% 1.82/1.46 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1255, 1248])).
% 1.82/1.46 tff(1257,assumption,(c0_1(a403)), introduced(assumption)).
% 1.82/1.46 tff(1258,plain,
% 1.82/1.46 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1259,plain,
% 1.82/1.46 ((hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a403) | c3_1(a403) | (~c0_1(a403))) <=> (hskp22 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1260,plain,
% 1.82/1.46 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a403) | c3_1(a403) | (~c0_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405))))),
% 1.82/1.46 inference(monotonicity,[status(thm)],[1259])).
% 1.82/1.46 tff(1261,plain,
% 1.82/1.46 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a403) | c3_1(a403) | (~c0_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 1.82/1.46 inference(transitivity,[status(thm)],[1260, 1258])).
% 1.82/1.46 tff(1262,plain,
% 1.82/1.46 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a403) | c3_1(a403) | (~c0_1(a403)))),
% 1.82/1.46 inference(quant_inst,[status(thm)],[])).
% 1.82/1.46 tff(1263,plain,
% 1.82/1.46 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 1.82/1.46 tff(1264,plain,
% 1.82/1.46 (hskp22),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1263, 150, 107, 106, 1257, 335, 334, 929, 158])).
% 1.82/1.46 tff(1265,plain,
% 1.82/1.46 (~c1_1(a451)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[844, 1264])).
% 1.82/1.46 tff(1266,plain,
% 1.82/1.46 (c2_1(a451)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[855, 1264])).
% 1.82/1.46 tff(1267,plain,
% 1.82/1.46 (c0_1(a451)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[866, 1264])).
% 1.82/1.46 tff(1268,plain,
% 1.82/1.46 (((~hskp3) | (~c0_1(a403))) <=> ((~hskp3) | (~c0_1(a403)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1269,plain,
% 1.82/1.46 (((~c0_1(a403)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a403)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1270,axiom,((~c0_1(a403)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 1.82/1.46 tff(1271,plain,
% 1.82/1.46 ((~hskp3) | (~c0_1(a403))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1270, 1269])).
% 1.82/1.46 tff(1272,plain,
% 1.82/1.46 ((~hskp3) | (~c0_1(a403))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1271, 1268])).
% 1.82/1.46 tff(1273,plain,
% 1.82/1.46 (~hskp3),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1272, 1257])).
% 1.82/1.46 tff(1274,plain,
% 1.82/1.46 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1275,plain,
% 1.82/1.46 ((hskp3 | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451))) <=> (hskp3 | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1276,plain,
% 1.82/1.46 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451))))),
% 1.82/1.46 inference(monotonicity,[status(thm)],[1275])).
% 1.82/1.46 tff(1277,plain,
% 1.82/1.46 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.82/1.46 inference(transitivity,[status(thm)],[1276, 1274])).
% 1.82/1.46 tff(1278,plain,
% 1.82/1.46 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)))),
% 1.82/1.46 inference(quant_inst,[status(thm)],[])).
% 1.82/1.46 tff(1279,plain,
% 1.82/1.46 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1278, 1277])).
% 1.82/1.46 tff(1280,plain,
% 1.82/1.46 (~c3_1(a451)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1279, 150, 1273, 1267, 1266, 1265, 1256])).
% 1.82/1.46 tff(1281,plain,
% 1.82/1.46 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c3_1(a460) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a460)) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c3_1(a460) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1282,plain,
% 1.82/1.46 (((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451))) <=> (c3_1(a460) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1283,plain,
% 1.82/1.46 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c3_1(a460) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a460)) | (~c1_1(a460))))),
% 1.82/1.46 inference(monotonicity,[status(thm)],[1282])).
% 1.82/1.46 tff(1284,plain,
% 1.82/1.46 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c3_1(a460) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.82/1.46 inference(transitivity,[status(thm)],[1283, 1281])).
% 1.82/1.46 tff(1285,plain,
% 1.82/1.46 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))),
% 1.82/1.46 inference(quant_inst,[status(thm)],[])).
% 1.82/1.46 tff(1286,plain,
% 1.82/1.46 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c3_1(a460) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a460)) | (~c1_1(a460))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1285, 1284])).
% 1.82/1.46 tff(1287,plain,
% 1.82/1.46 (~c0_1(a460)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1286, 150, 242, 1266, 225, 1265, 886, 1280])).
% 1.82/1.46 tff(1288,plain,
% 1.82/1.46 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c0_1(a460))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp0 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c0_1(a460))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1289,plain,
% 1.82/1.46 ((hskp27 | hskp0 | (~ndr1_0) | c2_1(a460) | c0_1(a460) | c3_1(a460)) <=> (hskp27 | hskp0 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c0_1(a460))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1290,plain,
% 1.82/1.46 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | (~ndr1_0) | c2_1(a460) | c0_1(a460) | c3_1(a460))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c0_1(a460)))),
% 1.82/1.46 inference(monotonicity,[status(thm)],[1289])).
% 1.82/1.46 tff(1291,plain,
% 1.82/1.46 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | (~ndr1_0) | c2_1(a460) | c0_1(a460) | c3_1(a460))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp0 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c0_1(a460))),
% 1.82/1.46 inference(transitivity,[status(thm)],[1290, 1288])).
% 1.82/1.46 tff(1292,plain,
% 1.82/1.46 ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | (~ndr1_0) | c2_1(a460) | c0_1(a460) | c3_1(a460))),
% 1.82/1.46 inference(quant_inst,[status(thm)],[])).
% 1.82/1.46 tff(1293,plain,
% 1.82/1.46 ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp0 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c0_1(a460)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 1.82/1.46 tff(1294,plain,
% 1.82/1.46 (hskp0 | c0_1(a460)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1293, 150, 201, 231, 225, 356])).
% 1.82/1.46 tff(1295,plain,
% 1.82/1.46 (hskp0),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1294, 1287])).
% 1.82/1.46 tff(1296,plain,
% 1.82/1.46 (~c3_1(a400)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[405, 1295])).
% 1.82/1.46 tff(1297,plain,
% 1.82/1.46 (c1_1(a400)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[385, 1295])).
% 1.82/1.46 tff(1298,plain,
% 1.82/1.46 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a451) | c3_1(a400) | (~ndr1_0) | (~c1_1(a400)) | (~c0_1(a400)) | (~c2_1(a451)) | c3_1(a451))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a451) | c3_1(a400) | (~ndr1_0) | (~c1_1(a400)) | (~c0_1(a400)) | (~c2_1(a451)) | c3_1(a451))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1299,plain,
% 1.82/1.46 (((~ndr1_0) | c3_1(a400) | (~c1_1(a400)) | (~c0_1(a400)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451))) <=> (c1_1(a451) | c3_1(a400) | (~ndr1_0) | (~c1_1(a400)) | (~c0_1(a400)) | (~c2_1(a451)) | c3_1(a451))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1300,plain,
% 1.82/1.46 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a400) | (~c1_1(a400)) | (~c0_1(a400)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a451) | c3_1(a400) | (~ndr1_0) | (~c1_1(a400)) | (~c0_1(a400)) | (~c2_1(a451)) | c3_1(a451)))),
% 1.82/1.46 inference(monotonicity,[status(thm)],[1299])).
% 1.82/1.46 tff(1301,plain,
% 1.82/1.46 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a400) | (~c1_1(a400)) | (~c0_1(a400)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a451) | c3_1(a400) | (~ndr1_0) | (~c1_1(a400)) | (~c0_1(a400)) | (~c2_1(a451)) | c3_1(a451))),
% 1.82/1.46 inference(transitivity,[status(thm)],[1300, 1298])).
% 1.82/1.46 tff(1302,plain,
% 1.82/1.46 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a400) | (~c1_1(a400)) | (~c0_1(a400)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))),
% 1.82/1.46 inference(quant_inst,[status(thm)],[])).
% 1.82/1.46 tff(1303,plain,
% 1.82/1.46 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a451) | c3_1(a400) | (~ndr1_0) | (~c1_1(a400)) | (~c0_1(a400)) | (~c2_1(a451)) | c3_1(a451)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 1.82/1.46 tff(1304,plain,
% 1.82/1.46 (~c0_1(a400)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1303, 150, 1266, 1297, 1265, 1296, 886, 1280])).
% 1.82/1.46 tff(1305,plain,
% 1.82/1.46 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c3_1(a460) | c1_1(a451) | (~ndr1_0) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c3_1(a460) | c1_1(a451) | (~ndr1_0) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | (~c1_1(a460)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1306,plain,
% 1.82/1.46 ((hskp9 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | c3_1(a460) | (~c1_1(a460))) <=> (hskp9 | c3_1(a460) | c1_1(a451) | (~ndr1_0) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | (~c1_1(a460)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1307,plain,
% 1.82/1.46 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | c3_1(a460) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c3_1(a460) | c1_1(a451) | (~ndr1_0) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | (~c1_1(a460))))),
% 1.82/1.46 inference(monotonicity,[status(thm)],[1306])).
% 1.82/1.46 tff(1308,plain,
% 1.82/1.46 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | c3_1(a460) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c3_1(a460) | c1_1(a451) | (~ndr1_0) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | (~c1_1(a460)))),
% 1.82/1.46 inference(transitivity,[status(thm)],[1307, 1305])).
% 1.82/1.46 tff(1309,plain,
% 1.82/1.46 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | c3_1(a460) | (~c1_1(a460)))),
% 1.82/1.46 inference(quant_inst,[status(thm)],[])).
% 1.82/1.46 tff(1310,plain,
% 1.82/1.46 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c3_1(a460) | c1_1(a451) | (~ndr1_0) | c3_1(a451) | (~c0_1(a451)) | c0_1(a460) | (~c1_1(a460))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1309, 1308])).
% 1.82/1.46 tff(1311,plain,
% 1.82/1.46 (hskp9),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1310, 150, 242, 1267, 225, 1265, 640, 1287, 1280])).
% 1.82/1.46 tff(1312,plain,
% 1.82/1.46 (~c1_1(a416)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[663, 1311])).
% 1.82/1.46 tff(1313,plain,
% 1.82/1.46 (c2_1(a400)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[374, 1295])).
% 1.82/1.46 tff(1314,plain,
% 1.82/1.46 (c3_1(a416)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[727, 1311])).
% 1.82/1.46 tff(1315,plain,
% 1.82/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a416) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a451)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a416) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a451)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1316,plain,
% 1.82/1.46 (((~ndr1_0) | c3_1(a451) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400))) <=> (c1_1(a416) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a451)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1317,plain,
% 1.82/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a451) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a416) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a451))))),
% 1.82/1.46 inference(monotonicity,[status(thm)],[1316])).
% 1.82/1.46 tff(1318,plain,
% 1.82/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a451) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a416) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a451)))),
% 1.82/1.46 inference(transitivity,[status(thm)],[1317, 1315])).
% 1.82/1.46 tff(1319,plain,
% 1.82/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a451) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))),
% 1.82/1.46 inference(quant_inst,[status(thm)],[])).
% 1.82/1.46 tff(1320,plain,
% 1.82/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a416) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451) | (~c0_1(a451))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1319, 1318])).
% 1.82/1.46 tff(1321,plain,
% 1.82/1.46 (~c2_1(a416)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1320, 150, 1267, 1266, 1314, 1297, 1313, 1312, 704, 1304, 1280])).
% 1.82/1.46 tff(1322,plain,
% 1.82/1.46 (~c0_1(a416)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[669, 1311])).
% 1.82/1.46 tff(1323,plain,
% 1.82/1.46 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1324,plain,
% 1.82/1.46 ((hskp5 | hskp3 | (~ndr1_0) | c2_1(a416) | c0_1(a416) | (~c3_1(a416))) <=> (hskp5 | hskp3 | c0_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1325,plain,
% 1.82/1.46 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a416) | c0_1(a416) | (~c3_1(a416)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416))))),
% 1.82/1.46 inference(monotonicity,[status(thm)],[1324])).
% 1.82/1.46 tff(1326,plain,
% 1.82/1.46 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a416) | c0_1(a416) | (~c3_1(a416)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)))),
% 1.82/1.46 inference(transitivity,[status(thm)],[1325, 1323])).
% 1.82/1.46 tff(1327,plain,
% 1.82/1.46 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a416) | c0_1(a416) | (~c3_1(a416)))),
% 1.82/1.46 inference(quant_inst,[status(thm)],[])).
% 1.82/1.46 tff(1328,plain,
% 1.82/1.46 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 1.82/1.46 tff(1329,plain,
% 1.82/1.46 (hskp5),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1328, 150, 1273, 1314, 1322, 54, 1321])).
% 1.82/1.46 tff(1330,plain,
% 1.82/1.46 (((~hskp5) | (~c0_1(a408))) <=> ((~hskp5) | (~c0_1(a408)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1331,plain,
% 1.82/1.46 (((~c0_1(a408)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a408)))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1332,axiom,((~c0_1(a408)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 1.82/1.46 tff(1333,plain,
% 1.82/1.46 ((~hskp5) | (~c0_1(a408))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 1.82/1.46 tff(1334,plain,
% 1.82/1.46 ((~hskp5) | (~c0_1(a408))),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1333, 1330])).
% 1.82/1.46 tff(1335,plain,
% 1.82/1.46 (~c0_1(a408)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1334, 1329])).
% 1.82/1.46 tff(1336,plain,
% 1.82/1.46 (((~hskp5) | c3_1(a408)) <=> ((~hskp5) | c3_1(a408))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1337,axiom,((~hskp5) | c3_1(a408)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 1.82/1.46 tff(1338,plain,
% 1.82/1.46 ((~hskp5) | c3_1(a408)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1337, 1336])).
% 1.82/1.46 tff(1339,plain,
% 1.82/1.46 ((~hskp5) | c3_1(a408)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1338, 1336])).
% 1.82/1.46 tff(1340,plain,
% 1.82/1.46 ((~hskp5) | c3_1(a408)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1339, 1336])).
% 1.82/1.46 tff(1341,plain,
% 1.82/1.46 ((~hskp5) | c3_1(a408)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1340, 1336])).
% 1.82/1.46 tff(1342,plain,
% 1.82/1.46 ((~hskp5) | c3_1(a408)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1341, 1336])).
% 1.82/1.46 tff(1343,plain,
% 1.82/1.46 ((~hskp5) | c3_1(a408)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1342, 1336])).
% 1.82/1.46 tff(1344,plain,
% 1.82/1.46 ((~hskp5) | c3_1(a408)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1343, 1336])).
% 1.82/1.46 tff(1345,plain,
% 1.82/1.46 ((~hskp5) | c3_1(a408)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1344, 1336])).
% 1.82/1.46 tff(1346,plain,
% 1.82/1.46 (c3_1(a408)),
% 1.82/1.46 inference(unit_resolution,[status(thm)],[1345, 1329])).
% 1.82/1.46 tff(1347,plain,
% 1.82/1.46 (((~hskp5) | c2_1(a408)) <=> ((~hskp5) | c2_1(a408))),
% 1.82/1.46 inference(rewrite,[status(thm)],[])).
% 1.82/1.46 tff(1348,axiom,((~hskp5) | c2_1(a408)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 1.82/1.46 tff(1349,plain,
% 1.82/1.46 ((~hskp5) | c2_1(a408)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1348, 1347])).
% 1.82/1.46 tff(1350,plain,
% 1.82/1.46 ((~hskp5) | c2_1(a408)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1349, 1347])).
% 1.82/1.46 tff(1351,plain,
% 1.82/1.46 ((~hskp5) | c2_1(a408)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1350, 1347])).
% 1.82/1.46 tff(1352,plain,
% 1.82/1.46 ((~hskp5) | c2_1(a408)),
% 1.82/1.46 inference(modus_ponens,[status(thm)],[1351, 1347])).
% 1.82/1.46 tff(1353,plain,
% 1.82/1.46 ((~hskp5) | c2_1(a408)),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1352, 1347])).
% 1.82/1.47 tff(1354,plain,
% 1.82/1.47 ((~hskp5) | c2_1(a408)),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1353, 1347])).
% 1.82/1.47 tff(1355,plain,
% 1.82/1.47 ((~hskp5) | c2_1(a408)),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1354, 1347])).
% 1.82/1.47 tff(1356,plain,
% 1.82/1.47 ((~hskp5) | c2_1(a408)),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1355, 1347])).
% 1.82/1.47 tff(1357,plain,
% 1.82/1.47 (c2_1(a408)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1356, 1329])).
% 1.82/1.47 tff(1358,plain,
% 1.82/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a460) | c1_1(a416) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a416) | (~c3_1(a416)) | c0_1(a460) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a460) | c1_1(a416) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a416) | (~c3_1(a416)) | c0_1(a460) | (~c1_1(a460)))),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1359,plain,
% 1.82/1.47 (((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a460) | c2_1(a460) | (~c1_1(a460))) <=> (c2_1(a460) | c1_1(a416) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a416) | (~c3_1(a416)) | c0_1(a460) | (~c1_1(a460)))),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1360,plain,
% 1.82/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a460) | c2_1(a460) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a460) | c1_1(a416) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a416) | (~c3_1(a416)) | c0_1(a460) | (~c1_1(a460))))),
% 1.82/1.47 inference(monotonicity,[status(thm)],[1359])).
% 1.82/1.47 tff(1361,plain,
% 1.82/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a460) | c2_1(a460) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a460) | c1_1(a416) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a416) | (~c3_1(a416)) | c0_1(a460) | (~c1_1(a460)))),
% 1.82/1.47 inference(transitivity,[status(thm)],[1360, 1358])).
% 1.82/1.47 tff(1362,plain,
% 1.82/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a460) | c2_1(a460) | (~c1_1(a460)))),
% 1.82/1.47 inference(quant_inst,[status(thm)],[])).
% 1.82/1.47 tff(1363,plain,
% 1.82/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a460) | c1_1(a416) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a416) | (~c3_1(a416)) | c0_1(a460) | (~c1_1(a460))),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1362, 1361])).
% 1.82/1.47 tff(1364,plain,
% 1.82/1.47 ($false),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1363, 150, 242, 1314, 1357, 1346, 231, 1312, 1335, 43, 1287, 1321])).
% 1.82/1.47 tff(1365,plain,(hskp19 | (~c1_1(a405)) | (~c3_1(a405)) | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~c0_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.82/1.47 tff(1366,plain,
% 1.82/1.47 (hskp19),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1365, 1246, 106, 107, 335, 334, 108, 55])).
% 1.82/1.47 tff(1367,plain,
% 1.82/1.47 (~c0_1(a445)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[332, 1366])).
% 1.82/1.47 tff(1368,plain,
% 1.82/1.47 (c3_1(a445)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[470, 1366])).
% 1.82/1.47 tff(1369,plain,
% 1.82/1.47 (c1_1(a445)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[458, 1366])).
% 1.82/1.47 tff(1370,plain,
% 1.82/1.47 (((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0))) <=> ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp11 | hskp2 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0))),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1371,plain,
% 1.82/1.47 ((hskp11 | hskp2 | (~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c0_1(a403))) <=> (hskp11 | hskp2 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0))),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1372,plain,
% 1.82/1.47 (((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c0_1(a403)))) <=> ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0)))),
% 1.82/1.47 inference(monotonicity,[status(thm)],[1371])).
% 1.82/1.47 tff(1373,plain,
% 1.82/1.47 (((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c0_1(a403)))) <=> ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp11 | hskp2 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0))),
% 1.82/1.47 inference(transitivity,[status(thm)],[1372, 1370])).
% 1.82/1.47 tff(1374,plain,
% 1.82/1.47 ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp11 | hskp2 | (~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c0_1(a403)))),
% 1.82/1.47 inference(quant_inst,[status(thm)],[])).
% 1.82/1.47 tff(1375,plain,
% 1.82/1.47 ((~![U: $i] : (hskp11 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp11 | hskp2 | (~c0_1(a403)) | c2_1(a403) | c3_1(a403) | (~ndr1_0)),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1374, 1373])).
% 1.82/1.47 tff(1376,plain,
% 1.82/1.47 (hskp11 | hskp2 | (~c0_1(a403)) | c2_1(a403)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1375, 150, 334, 687])).
% 1.82/1.47 tff(1377,plain,
% 1.82/1.47 (hskp11),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1376, 23, 1257, 335])).
% 1.82/1.47 tff(1378,plain,
% 1.82/1.47 (~c2_1(a420)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1223, 1377])).
% 1.82/1.47 tff(1379,plain,
% 1.82/1.47 (~c1_1(a420)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1106, 1377])).
% 1.82/1.47 tff(1380,plain,
% 1.82/1.47 (~c0_1(a420)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1100, 1377])).
% 1.82/1.47 tff(1381,plain,
% 1.82/1.47 (hskp1),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1126, 150, 23, 1380, 1379, 1378, 33])).
% 1.82/1.47 tff(1382,plain,
% 1.82/1.47 (~c3_1(a401)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[794, 1381])).
% 1.82/1.47 tff(1383,plain,
% 1.82/1.47 (c1_1(a401)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[805, 1381])).
% 1.82/1.47 tff(1384,plain,
% 1.82/1.47 (c0_1(a401)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[816, 1381])).
% 1.82/1.47 tff(1385,plain,
% 1.82/1.47 (~hskp22),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[897, 1382, 473, 1383, 1384, 484, 472])).
% 1.82/1.47 tff(1386,plain,
% 1.82/1.47 (~hskp7),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[992, 1385, 1384, 1383, 1382])).
% 1.82/1.47 tff(1387,plain,
% 1.82/1.47 (^[U: $i] : refl((hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 1.82/1.47 inference(bind,[status(th)],[])).
% 1.82/1.47 tff(1388,plain,
% 1.82/1.47 (![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/1.47 inference(quant_intro,[status(thm)],[1387])).
% 1.82/1.47 tff(1389,plain,
% 1.82/1.47 (![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1390,plain,
% 1.82/1.47 (^[U: $i] : 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)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp16))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp3) <=> ((hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp3))), rewrite(((hskp16 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp3) <=> (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp3) <=> (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 1.82/1.47 inference(bind,[status(th)],[])).
% 1.82/1.47 tff(1391,plain,
% 1.82/1.47 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp3) <=> ![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/1.47 inference(quant_intro,[status(thm)],[1390])).
% 1.82/1.47 tff(1392,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp16) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 1.82/1.47 tff(1393,plain,
% 1.82/1.47 (![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 1.82/1.47 tff(1394,plain,
% 1.82/1.47 (![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1393, 1389])).
% 1.82/1.47 tff(1395,plain,(
% 1.82/1.47 ![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/1.47 inference(skolemize,[status(sab)],[1394])).
% 1.82/1.47 tff(1396,plain,
% 1.82/1.47 (![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1395, 1388])).
% 1.82/1.47 tff(1397,plain,
% 1.82/1.47 (((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | hskp3 | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)))),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1398,plain,
% 1.82/1.47 ((hskp16 | hskp3 | (~ndr1_0) | c0_1(a445) | (~c1_1(a445)) | (~c3_1(a445))) <=> (hskp16 | hskp3 | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)))),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1399,plain,
% 1.82/1.47 (((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | (~ndr1_0) | c0_1(a445) | (~c1_1(a445)) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445))))),
% 1.82/1.47 inference(monotonicity,[status(thm)],[1398])).
% 1.82/1.47 tff(1400,plain,
% 1.82/1.47 (((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | (~ndr1_0) | c0_1(a445) | (~c1_1(a445)) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | hskp3 | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445)))),
% 1.82/1.47 inference(transitivity,[status(thm)],[1399, 1397])).
% 1.82/1.47 tff(1401,plain,
% 1.82/1.47 ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | (~ndr1_0) | c0_1(a445) | (~c1_1(a445)) | (~c3_1(a445)))),
% 1.82/1.47 inference(quant_inst,[status(thm)],[])).
% 1.82/1.47 tff(1402,plain,
% 1.82/1.47 ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | hskp3 | c0_1(a445) | (~ndr1_0) | (~c1_1(a445)) | (~c3_1(a445))),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 1.82/1.47 tff(1403,plain,
% 1.82/1.47 (hskp16),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1402, 150, 1273, 484, 473, 472, 1396])).
% 1.82/1.47 tff(1404,plain,
% 1.82/1.47 (~c3_1(a434)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1016, 1403])).
% 1.82/1.47 tff(1405,plain,
% 1.82/1.47 (c1_1(a434)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1044, 1403])).
% 1.82/1.47 tff(1406,plain,
% 1.82/1.47 (hskp7 | hskp2 | c2_1(a434)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1032, 150, 1405, 1404, 118])).
% 1.82/1.47 tff(1407,plain,
% 1.82/1.47 (c2_1(a434)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1406, 1386, 23])).
% 1.82/1.47 tff(1408,plain,
% 1.82/1.47 (~c0_1(a434)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1022, 1403])).
% 1.82/1.47 tff(1409,plain,
% 1.82/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a434) | c3_1(a434) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a434) | c3_1(a434) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a434)))),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1410,plain,
% 1.82/1.47 (((~ndr1_0) | c2_1(a420) | c1_1(a420) | (~c3_1(a420)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)) | c1_1(a420) | c0_1(a420) | (~c3_1(a420))) <=> (c0_1(a434) | c3_1(a434) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a434)))),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1411,plain,
% 1.82/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a420) | c1_1(a420) | (~c3_1(a420)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)) | c1_1(a420) | c0_1(a420) | (~c3_1(a420)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a434) | c3_1(a434) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a434))))),
% 1.82/1.47 inference(monotonicity,[status(thm)],[1410])).
% 1.82/1.47 tff(1412,plain,
% 1.82/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a420) | c1_1(a420) | (~c3_1(a420)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)) | c1_1(a420) | c0_1(a420) | (~c3_1(a420)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a434) | c3_1(a434) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a434)))),
% 1.82/1.47 inference(transitivity,[status(thm)],[1411, 1409])).
% 1.82/1.47 tff(1413,plain,
% 1.82/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a420) | c1_1(a420) | (~c3_1(a420)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)) | c1_1(a420) | c0_1(a420) | (~c3_1(a420)))),
% 1.82/1.47 inference(quant_inst,[status(thm)],[])).
% 1.82/1.47 tff(1414,plain,
% 1.82/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a434) | c3_1(a434) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a434))),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 1.82/1.47 tff(1415,plain,
% 1.82/1.47 ((~c3_1(a420)) | (~c2_1(a434))),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1414, 150, 1408, 1404, 1380, 1379, 1378, 778])).
% 1.82/1.47 tff(1416,plain,
% 1.82/1.47 (~c3_1(a420)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1415, 1407])).
% 1.82/1.47 tff(1417,plain,
% 1.82/1.47 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 1.82/1.47 inference(bind,[status(th)],[])).
% 1.82/1.47 tff(1418,plain,
% 1.82/1.47 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.82/1.47 inference(quant_intro,[status(thm)],[1417])).
% 1.82/1.47 tff(1419,plain,
% 1.82/1.47 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1420,plain,
% 1.82/1.47 (^[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) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 1.82/1.47 inference(bind,[status(th)],[])).
% 1.82/1.47 tff(1421,plain,
% 1.82/1.47 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.82/1.47 inference(quant_intro,[status(thm)],[1420])).
% 1.82/1.47 tff(1422,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause151')).
% 1.82/1.47 tff(1423,plain,
% 1.82/1.47 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1422, 1421])).
% 1.82/1.47 tff(1424,plain,
% 1.82/1.47 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1423, 1419])).
% 1.82/1.47 tff(1425,plain,(
% 1.82/1.47 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.82/1.47 inference(skolemize,[status(sab)],[1424])).
% 1.82/1.47 tff(1426,plain,
% 1.82/1.47 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1425, 1418])).
% 1.82/1.47 tff(1427,plain,
% 1.82/1.47 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c3_1(a434) | c0_1(a420) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c3_1(a434) | c0_1(a420) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1428,plain,
% 1.82/1.47 ((hskp3 | (~ndr1_0) | c3_1(a434) | (~c2_1(a434)) | (~c1_1(a434)) | c1_1(a420) | c0_1(a420) | c3_1(a420)) <=> (hskp3 | c3_1(a434) | c0_1(a420) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1429,plain,
% 1.82/1.47 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a434) | (~c2_1(a434)) | (~c1_1(a434)) | c1_1(a420) | c0_1(a420) | c3_1(a420))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c3_1(a434) | c0_1(a420) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434))))),
% 1.82/1.47 inference(monotonicity,[status(thm)],[1428])).
% 1.82/1.47 tff(1430,plain,
% 1.82/1.47 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a434) | (~c2_1(a434)) | (~c1_1(a434)) | c1_1(a420) | c0_1(a420) | c3_1(a420))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c3_1(a434) | c0_1(a420) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.82/1.47 inference(transitivity,[status(thm)],[1429, 1427])).
% 1.82/1.47 tff(1431,plain,
% 1.82/1.47 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a434) | (~c2_1(a434)) | (~c1_1(a434)) | c1_1(a420) | c0_1(a420) | c3_1(a420))),
% 1.82/1.47 inference(quant_inst,[status(thm)],[])).
% 1.82/1.47 tff(1432,plain,
% 1.82/1.47 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c3_1(a434) | c0_1(a420) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434))),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1431, 1430])).
% 1.82/1.47 tff(1433,plain,
% 1.82/1.47 (c3_1(a420) | (~c2_1(a434))),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1432, 150, 1273, 1405, 1404, 1380, 1379, 1426])).
% 1.82/1.47 tff(1434,plain,
% 1.82/1.47 ($false),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1433, 1416, 1407])).
% 1.82/1.47 tff(1435,plain,(hskp2 | (~c3_1(a445)) | (~c1_1(a445)) | c0_1(a445) | (~c0_1(a403)) | c2_1(a403) | c3_1(a403)), inference(lemma,lemma(discharge,[]))).
% 1.82/1.47 tff(1436,plain,
% 1.82/1.47 (hskp2),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1435, 1368, 1369, 1367, 1246, 335, 334])).
% 1.82/1.47 tff(1437,plain,
% 1.82/1.47 (c0_1(a402)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[520, 1436])).
% 1.82/1.47 tff(1438,plain,
% 1.82/1.47 (~hskp3),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1272, 1246])).
% 1.82/1.47 tff(1439,assumption,(c0_1(a402)), introduced(assumption)).
% 1.82/1.47 tff(1440,plain,
% 1.82/1.47 (~c3_1(a402)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[538, 1439])).
% 1.82/1.47 tff(1441,plain,
% 1.82/1.47 (~c2_1(a445)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[570, 12, 1440, 1439])).
% 1.82/1.47 tff(1442,plain,
% 1.82/1.47 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445)))),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1443,plain,
% 1.82/1.47 ((hskp5 | hskp3 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c3_1(a445))) <=> (hskp5 | hskp3 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445)))),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1444,plain,
% 1.82/1.47 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445))))),
% 1.82/1.47 inference(monotonicity,[status(thm)],[1443])).
% 1.82/1.47 tff(1445,plain,
% 1.82/1.47 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c3_1(a445)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445)))),
% 1.82/1.47 inference(transitivity,[status(thm)],[1444, 1442])).
% 1.82/1.47 tff(1446,plain,
% 1.82/1.47 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a445) | c0_1(a445) | (~c3_1(a445)))),
% 1.82/1.47 inference(quant_inst,[status(thm)],[])).
% 1.82/1.47 tff(1447,plain,
% 1.82/1.47 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a445) | (~ndr1_0) | c2_1(a445) | (~c3_1(a445))),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1446, 1445])).
% 1.82/1.47 tff(1448,plain,
% 1.82/1.47 (hskp5 | c2_1(a445)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1447, 150, 44, 473, 472, 54])).
% 1.82/1.47 tff(1449,plain,
% 1.82/1.47 (hskp5),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1448, 1441])).
% 1.82/1.47 tff(1450,plain,
% 1.82/1.47 (~c0_1(a408)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1334, 1449])).
% 1.82/1.47 tff(1451,plain,
% 1.82/1.47 (c2_1(a408)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1356, 1449])).
% 1.82/1.47 tff(1452,plain,
% 1.82/1.47 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a408) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a408)) | (~c1_1(a408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a408) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a408)) | (~c1_1(a408)))),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1453,plain,
% 1.82/1.47 ((hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a408) | (~c2_1(a408)) | (~c1_1(a408))) <=> (hskp1 | c0_1(a408) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a408)) | (~c1_1(a408)))),
% 1.82/1.47 inference(rewrite,[status(thm)],[])).
% 1.82/1.47 tff(1454,plain,
% 1.82/1.47 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a408) | (~c2_1(a408)) | (~c1_1(a408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a408) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a408)) | (~c1_1(a408))))),
% 1.82/1.47 inference(monotonicity,[status(thm)],[1453])).
% 1.82/1.47 tff(1455,plain,
% 1.82/1.47 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a408) | (~c2_1(a408)) | (~c1_1(a408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a408) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a408)) | (~c1_1(a408)))),
% 1.82/1.47 inference(transitivity,[status(thm)],[1454, 1452])).
% 1.82/1.47 tff(1456,plain,
% 1.82/1.47 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a408) | (~c2_1(a408)) | (~c1_1(a408)))),
% 1.82/1.47 inference(quant_inst,[status(thm)],[])).
% 1.82/1.47 tff(1457,plain,
% 1.82/1.47 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a408) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a408)) | (~c1_1(a408))),
% 1.82/1.47 inference(modus_ponens,[status(thm)],[1456, 1455])).
% 1.82/1.47 tff(1458,plain,
% 1.82/1.47 (~c1_1(a408)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1457, 150, 12, 1451, 1439, 1450, 105, 22, 1440])).
% 1.82/1.47 tff(1459,plain,
% 1.82/1.47 (hskp16),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1402, 150, 44, 484, 473, 472, 1396])).
% 1.82/1.47 tff(1460,plain,
% 1.82/1.47 (~c0_1(a434)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1022, 1459])).
% 1.82/1.47 tff(1461,plain,
% 1.82/1.47 (c1_1(a434)),
% 1.82/1.47 inference(unit_resolution,[status(thm)],[1044, 1459])).
% 1.82/1.47 tff(1462,plain,
% 1.82/1.47 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.82/1.48 inference(rewrite,[status(thm)],[])).
% 1.82/1.48 tff(1463,plain,
% 1.82/1.48 ((hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434))) <=> (hskp1 | c0_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.82/1.48 inference(rewrite,[status(thm)],[])).
% 1.82/1.48 tff(1464,plain,
% 1.82/1.48 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a434)) | (~c1_1(a434))))),
% 1.82/1.48 inference(monotonicity,[status(thm)],[1463])).
% 1.82/1.48 tff(1465,plain,
% 1.82/1.48 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.82/1.48 inference(transitivity,[status(thm)],[1464, 1462])).
% 1.82/1.48 tff(1466,plain,
% 1.82/1.48 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.82/1.48 inference(quant_inst,[status(thm)],[])).
% 1.82/1.48 tff(1467,plain,
% 1.82/1.48 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a434)) | (~c1_1(a434))),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1466, 1465])).
% 1.82/1.48 tff(1468,plain,
% 1.82/1.48 (hskp1 | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a434))),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[1467, 150, 1461, 1460, 105, 22])).
% 1.82/1.48 tff(1469,plain,
% 1.82/1.48 (~c2_1(a434)),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[1468, 12, 1440, 1439])).
% 1.82/1.48 tff(1470,plain,
% 1.82/1.48 (~c3_1(a434)),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[1016, 1459])).
% 1.82/1.48 tff(1471,plain,
% 1.82/1.48 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a434)))),
% 1.82/1.48 inference(rewrite,[status(thm)],[])).
% 1.82/1.48 tff(1472,plain,
% 1.82/1.48 ((hskp9 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434))) <=> (hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a434)))),
% 1.82/1.48 inference(rewrite,[status(thm)],[])).
% 1.82/1.48 tff(1473,plain,
% 1.82/1.48 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a434))))),
% 1.82/1.48 inference(monotonicity,[status(thm)],[1472])).
% 1.82/1.48 tff(1474,plain,
% 1.82/1.48 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a434)))),
% 1.82/1.48 inference(transitivity,[status(thm)],[1473, 1471])).
% 1.82/1.48 tff(1475,plain,
% 1.82/1.48 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434)))),
% 1.82/1.48 inference(quant_inst,[status(thm)],[])).
% 1.82/1.48 tff(1476,plain,
% 1.82/1.48 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a434))),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1475, 1474])).
% 1.82/1.48 tff(1477,plain,
% 1.82/1.48 (hskp9 | c3_1(a402) | (~c0_1(a402))),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[1476, 150, 1461, 1460, 1470, 105, 640])).
% 1.82/1.48 tff(1478,plain,
% 1.82/1.48 (hskp9),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[1477, 1439, 1440])).
% 1.82/1.48 tff(1479,plain,
% 1.82/1.48 (~c1_1(a416)),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[663, 1478])).
% 1.82/1.48 tff(1480,plain,
% 1.82/1.48 (~c0_1(a416)),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[669, 1478])).
% 1.82/1.48 tff(1481,plain,
% 1.82/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a434)))),
% 1.82/1.48 inference(rewrite,[status(thm)],[])).
% 1.82/1.48 tff(1482,plain,
% 1.82/1.48 (((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a434) | c0_1(a434) | c2_1(a434)) <=> (c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a434)))),
% 1.82/1.48 inference(rewrite,[status(thm)],[])).
% 1.82/1.48 tff(1483,plain,
% 1.82/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a434))))),
% 1.82/1.48 inference(monotonicity,[status(thm)],[1482])).
% 1.82/1.48 tff(1484,plain,
% 1.82/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a434)))),
% 1.82/1.48 inference(transitivity,[status(thm)],[1483, 1481])).
% 1.82/1.48 tff(1485,plain,
% 1.82/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a434) | c0_1(a434) | c2_1(a434))),
% 1.82/1.48 inference(quant_inst,[status(thm)],[])).
% 1.82/1.48 tff(1486,plain,
% 1.82/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a434))),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1485, 1484])).
% 1.82/1.48 tff(1487,plain,
% 1.82/1.48 (~c2_1(a416)),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[1486, 150, 1461, 1460, 1470, 1480, 1479, 346, 1469])).
% 1.82/1.48 tff(1488,plain,
% 1.82/1.48 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))))),
% 1.82/1.48 inference(bind,[status(th)],[])).
% 1.82/1.48 tff(1489,plain,
% 1.82/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/1.48 inference(quant_intro,[status(thm)],[1488])).
% 1.82/1.48 tff(1490,plain,
% 1.82/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/1.48 inference(rewrite,[status(thm)],[])).
% 1.82/1.48 tff(1491,plain,
% 1.82/1.48 (^[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)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))))),
% 1.82/1.48 inference(bind,[status(th)],[])).
% 1.82/1.48 tff(1492,plain,
% 1.82/1.48 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/1.48 inference(quant_intro,[status(thm)],[1491])).
% 1.82/1.48 tff(1493,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 1.82/1.48 tff(1494,plain,
% 1.82/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1493, 1492])).
% 1.82/1.48 tff(1495,plain,
% 1.82/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1494, 1490])).
% 1.82/1.48 tff(1496,plain,(
% 1.82/1.48 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/1.48 inference(skolemize,[status(sab)],[1495])).
% 1.82/1.48 tff(1497,plain,
% 1.82/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1496, 1489])).
% 1.82/1.48 tff(1498,plain,
% 1.82/1.48 (^[U: $i] : refl((hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 1.82/1.48 inference(bind,[status(th)],[])).
% 1.82/1.48 tff(1499,plain,
% 1.82/1.48 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.82/1.48 inference(quant_intro,[status(thm)],[1498])).
% 1.82/1.48 tff(1500,plain,
% 1.82/1.48 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.82/1.48 inference(rewrite,[status(thm)],[])).
% 1.82/1.48 tff(1501,plain,
% 1.82/1.48 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp3) <=> ((hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp3))), rewrite(((hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp3) <=> (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp3) <=> (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 1.82/1.48 inference(bind,[status(th)],[])).
% 1.82/1.48 tff(1502,plain,
% 1.82/1.48 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp3) <=> ![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.82/1.48 inference(quant_intro,[status(thm)],[1501])).
% 1.82/1.48 tff(1503,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp18) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 1.82/1.48 tff(1504,plain,
% 1.82/1.48 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1503, 1502])).
% 1.82/1.48 tff(1505,plain,
% 1.82/1.48 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1504, 1500])).
% 1.82/1.48 tff(1506,plain,(
% 1.82/1.48 ![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.82/1.48 inference(skolemize,[status(sab)],[1505])).
% 1.82/1.48 tff(1507,plain,
% 1.82/1.48 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1506, 1499])).
% 1.82/1.48 tff(1508,plain,
% 1.82/1.48 (c3_1(a416)),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[727, 1478])).
% 1.82/1.48 tff(1509,plain,
% 1.82/1.48 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp18 | hskp3 | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)))),
% 1.82/1.48 inference(rewrite,[status(thm)],[])).
% 1.82/1.48 tff(1510,plain,
% 1.82/1.48 ((hskp18 | hskp3 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416))) <=> (hskp18 | hskp3 | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)))),
% 1.82/1.48 inference(rewrite,[status(thm)],[])).
% 1.82/1.48 tff(1511,plain,
% 1.82/1.48 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416))))),
% 1.82/1.48 inference(monotonicity,[status(thm)],[1510])).
% 1.82/1.48 tff(1512,plain,
% 1.82/1.48 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp18 | hskp3 | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)))),
% 1.82/1.48 inference(transitivity,[status(thm)],[1511, 1509])).
% 1.82/1.48 tff(1513,plain,
% 1.82/1.48 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)))),
% 1.82/1.48 inference(quant_inst,[status(thm)],[])).
% 1.82/1.48 tff(1514,plain,
% 1.82/1.48 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp18 | hskp3 | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416))),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1513, 1512])).
% 1.82/1.48 tff(1515,plain,
% 1.82/1.48 (hskp18 | c2_1(a416)),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[1514, 150, 44, 1508, 1479, 1507])).
% 1.82/1.48 tff(1516,plain,
% 1.82/1.48 (hskp18),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[1515, 1487])).
% 1.82/1.48 tff(1517,plain,
% 1.82/1.48 (((~hskp18) | (~c3_1(a440))) <=> ((~hskp18) | (~c3_1(a440)))),
% 1.82/1.48 inference(rewrite,[status(thm)],[])).
% 1.82/1.48 tff(1518,plain,
% 1.82/1.48 (((~c3_1(a440)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a440)))),
% 1.82/1.48 inference(rewrite,[status(thm)],[])).
% 1.82/1.48 tff(1519,axiom,((~c3_1(a440)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 1.82/1.48 tff(1520,plain,
% 1.82/1.48 ((~hskp18) | (~c3_1(a440))),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1519, 1518])).
% 1.82/1.48 tff(1521,plain,
% 1.82/1.48 ((~hskp18) | (~c3_1(a440))),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1520, 1517])).
% 1.82/1.48 tff(1522,plain,
% 1.82/1.48 (~c3_1(a440)),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[1521, 1516])).
% 1.82/1.48 tff(1523,plain,
% 1.82/1.48 (((~hskp18) | (~c2_1(a440))) <=> ((~hskp18) | (~c2_1(a440)))),
% 1.82/1.48 inference(rewrite,[status(thm)],[])).
% 1.82/1.48 tff(1524,plain,
% 1.82/1.48 (((~c2_1(a440)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a440)))),
% 1.82/1.48 inference(rewrite,[status(thm)],[])).
% 1.82/1.48 tff(1525,axiom,((~c2_1(a440)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 1.82/1.48 tff(1526,plain,
% 1.82/1.48 ((~hskp18) | (~c2_1(a440))),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1525, 1524])).
% 1.82/1.48 tff(1527,plain,
% 1.82/1.48 ((~hskp18) | (~c2_1(a440))),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1526, 1523])).
% 1.82/1.48 tff(1528,plain,
% 1.82/1.48 (~c2_1(a440)),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[1527, 1516])).
% 1.82/1.48 tff(1529,plain,
% 1.82/1.48 (c3_1(a408)),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[1345, 1449])).
% 1.82/1.48 tff(1530,plain,
% 1.82/1.48 (((~hskp18) | c0_1(a440)) <=> ((~hskp18) | c0_1(a440))),
% 1.82/1.48 inference(rewrite,[status(thm)],[])).
% 1.82/1.48 tff(1531,axiom,((~hskp18) | c0_1(a440)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 1.82/1.48 tff(1532,plain,
% 1.82/1.48 ((~hskp18) | c0_1(a440)),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1531, 1530])).
% 1.82/1.48 tff(1533,plain,
% 1.82/1.48 ((~hskp18) | c0_1(a440)),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1532, 1530])).
% 1.82/1.48 tff(1534,plain,
% 1.82/1.48 ((~hskp18) | c0_1(a440)),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1533, 1530])).
% 1.82/1.48 tff(1535,plain,
% 1.82/1.48 ((~hskp18) | c0_1(a440)),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1534, 1530])).
% 1.82/1.48 tff(1536,plain,
% 1.82/1.48 ((~hskp18) | c0_1(a440)),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1535, 1530])).
% 1.82/1.48 tff(1537,plain,
% 1.82/1.48 ((~hskp18) | c0_1(a440)),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1536, 1530])).
% 1.82/1.48 tff(1538,plain,
% 1.82/1.48 ((~hskp18) | c0_1(a440)),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1537, 1530])).
% 1.82/1.48 tff(1539,plain,
% 1.82/1.48 ((~hskp18) | c0_1(a440)),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1538, 1530])).
% 1.82/1.48 tff(1540,plain,
% 1.82/1.48 (c0_1(a440)),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[1539, 1516])).
% 1.82/1.48 tff(1541,plain,
% 1.82/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a440) | c3_1(a440) | c1_1(a416) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | c2_1(a416) | (~c3_1(a416)) | (~c0_1(a440)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a440) | c3_1(a440) | c1_1(a416) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | c2_1(a416) | (~c3_1(a416)) | (~c0_1(a440)))),
% 1.82/1.48 inference(rewrite,[status(thm)],[])).
% 1.82/1.48 tff(1542,plain,
% 1.82/1.48 (((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a416) | c2_1(a416) | (~c3_1(a416))) <=> (c2_1(a440) | c3_1(a440) | c1_1(a416) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | c2_1(a416) | (~c3_1(a416)) | (~c0_1(a440)))),
% 1.82/1.48 inference(rewrite,[status(thm)],[])).
% 1.82/1.48 tff(1543,plain,
% 1.82/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a416) | c2_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a440) | c3_1(a440) | c1_1(a416) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | c2_1(a416) | (~c3_1(a416)) | (~c0_1(a440))))),
% 1.82/1.48 inference(monotonicity,[status(thm)],[1542])).
% 1.82/1.48 tff(1544,plain,
% 1.82/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a416) | c2_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a440) | c3_1(a440) | c1_1(a416) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | c2_1(a416) | (~c3_1(a416)) | (~c0_1(a440)))),
% 1.82/1.48 inference(transitivity,[status(thm)],[1543, 1541])).
% 1.82/1.48 tff(1545,plain,
% 1.82/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a416) | c2_1(a416) | (~c3_1(a416)))),
% 1.82/1.48 inference(quant_inst,[status(thm)],[])).
% 1.82/1.48 tff(1546,plain,
% 1.82/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a440) | c3_1(a440) | c1_1(a416) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | c2_1(a416) | (~c3_1(a416)) | (~c0_1(a440))),
% 1.82/1.48 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 1.82/1.48 tff(1547,plain,
% 1.82/1.48 ($false),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[1546, 150, 1540, 1508, 1451, 1529, 1528, 1522, 1479, 1497, 1487, 1458])).
% 1.82/1.48 tff(1548,plain,(hskp1 | hskp3 | (~c0_1(a402)) | c1_1(a402) | (~c3_1(a445)) | c0_1(a445) | (~c1_1(a445))), inference(lemma,lemma(discharge,[]))).
% 1.82/1.48 tff(1549,plain,
% 1.82/1.48 (hskp1),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[1548, 1438, 1437, 105, 1368, 1367, 1369])).
% 1.82/1.48 tff(1550,plain,
% 1.82/1.48 (~c3_1(a401)),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[794, 1549])).
% 1.82/1.48 tff(1551,plain,
% 1.82/1.48 (c1_1(a401)),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[805, 1549])).
% 1.82/1.48 tff(1552,plain,
% 1.82/1.48 (c0_1(a401)),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[816, 1549])).
% 1.82/1.48 tff(1553,plain,
% 1.82/1.48 (hskp20),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[823, 150, 1552, 1551, 1550, 483])).
% 1.82/1.48 tff(1554,plain,
% 1.82/1.48 (c1_1(a449)),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[834, 1553])).
% 1.82/1.48 tff(1555,plain,
% 1.82/1.48 (~hskp22),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[897, 1550, 1368, 1551, 1552, 1369, 1367])).
% 1.82/1.48 tff(1556,plain,
% 1.82/1.48 (c3_1(a449)),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[908, 1553])).
% 1.82/1.48 tff(1557,plain,
% 1.82/1.48 (~c2_1(a449)),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[914, 1553])).
% 1.82/1.48 tff(1558,plain,
% 1.82/1.48 ($false),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[942, 1557, 1556, 1369, 1436, 1555, 1554, 1368, 1367, 105])).
% 1.82/1.48 tff(1559,plain,(c2_1(a403) | c1_1(a402) | c3_1(a403) | (~c3_1(a405)) | (~c1_1(a405)) | (~c0_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.82/1.48 tff(1560,plain,
% 1.82/1.48 (c2_1(a403)),
% 1.82/1.48 inference(unit_resolution,[status(thm)],[1559, 334, 105, 106, 107, 108, 55])).
% 1.82/1.48 tff(1561,assumption,(c2_1(a403)), introduced(assumption)).
% 1.82/1.48 tff(1562,plain,
% 1.82/1.48 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 1.82/1.48 inference(rewrite,[status(thm)],[])).
% 1.82/1.48 tff(1563,plain,
% 1.82/1.48 ((hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403))) <=> (hskp14 | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1564,plain,
% 1.82/1.49 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405))))),
% 1.82/1.49 inference(monotonicity,[status(thm)],[1563])).
% 1.82/1.49 tff(1565,plain,
% 1.82/1.49 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 1.82/1.49 inference(transitivity,[status(thm)],[1564, 1562])).
% 1.82/1.49 tff(1566,plain,
% 1.82/1.49 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))),
% 1.82/1.49 inference(quant_inst,[status(thm)],[])).
% 1.82/1.49 tff(1567,plain,
% 1.82/1.49 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405))),
% 1.82/1.49 inference(modus_ponens,[status(thm)],[1566, 1565])).
% 1.82/1.49 tff(1568,plain,
% 1.82/1.49 (hskp14),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[1567, 150, 107, 106, 336, 1561, 334, 400, 158])).
% 1.82/1.49 tff(1569,plain,
% 1.82/1.49 (~c1_1(a428)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[421, 1568])).
% 1.82/1.49 tff(1570,plain,
% 1.82/1.49 (~c0_1(a428)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[427, 1568])).
% 1.82/1.49 tff(1571,plain,
% 1.82/1.49 (c2_1(a428)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[438, 1568])).
% 1.82/1.49 tff(1572,plain,
% 1.82/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c0_1(a460) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c0_1(a460) | (~c1_1(a460)))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1573,plain,
% 1.82/1.49 (((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a428) | c0_1(a428) | (~c2_1(a428)) | c3_1(a460) | c0_1(a460) | c2_1(a460)) <=> (c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c0_1(a460) | (~c1_1(a460)))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1574,plain,
% 1.82/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a428) | c0_1(a428) | (~c2_1(a428)) | c3_1(a460) | c0_1(a460) | c2_1(a460))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c0_1(a460) | (~c1_1(a460))))),
% 1.82/1.49 inference(monotonicity,[status(thm)],[1573])).
% 1.82/1.49 tff(1575,plain,
% 1.82/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a428) | c0_1(a428) | (~c2_1(a428)) | c3_1(a460) | c0_1(a460) | c2_1(a460))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c0_1(a460) | (~c1_1(a460)))),
% 1.82/1.49 inference(transitivity,[status(thm)],[1574, 1572])).
% 1.82/1.49 tff(1576,plain,
% 1.82/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a428) | c0_1(a428) | (~c2_1(a428)) | c3_1(a460) | c0_1(a460) | c2_1(a460))),
% 1.82/1.49 inference(quant_inst,[status(thm)],[])).
% 1.82/1.49 tff(1577,plain,
% 1.82/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c0_1(a460) | (~c1_1(a460))),
% 1.82/1.49 inference(modus_ponens,[status(thm)],[1576, 1575])).
% 1.82/1.49 tff(1578,plain,
% 1.82/1.49 (c0_1(a460)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[1577, 150, 242, 1571, 231, 225, 1570, 1569, 346])).
% 1.82/1.49 tff(1579,plain,
% 1.82/1.49 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c3_1(a460) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c3_1(a428) | (~c0_1(a460)) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c3_1(a460) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c3_1(a428) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1580,plain,
% 1.82/1.49 (((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a428) | c3_1(a428) | (~c2_1(a428))) <=> (c3_1(a460) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c3_1(a428) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1581,plain,
% 1.82/1.49 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a428) | c3_1(a428) | (~c2_1(a428)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c3_1(a460) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c3_1(a428) | (~c0_1(a460)) | (~c1_1(a460))))),
% 1.82/1.49 inference(monotonicity,[status(thm)],[1580])).
% 1.82/1.49 tff(1582,plain,
% 1.82/1.49 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a428) | c3_1(a428) | (~c2_1(a428)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c3_1(a460) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c3_1(a428) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.82/1.49 inference(transitivity,[status(thm)],[1581, 1579])).
% 1.82/1.49 tff(1583,plain,
% 1.82/1.49 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a428) | c3_1(a428) | (~c2_1(a428)))),
% 1.82/1.49 inference(quant_inst,[status(thm)],[])).
% 1.82/1.49 tff(1584,plain,
% 1.82/1.49 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c3_1(a460) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | c3_1(a428) | (~c0_1(a460)) | (~c1_1(a460))),
% 1.82/1.49 inference(modus_ponens,[status(thm)],[1583, 1582])).
% 1.82/1.49 tff(1585,plain,
% 1.82/1.49 (c3_1(a428)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[1584, 150, 242, 1571, 225, 1569, 886, 1578])).
% 1.82/1.49 tff(1586,plain,
% 1.82/1.49 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.82/1.49 inference(bind,[status(th)],[])).
% 1.82/1.49 tff(1587,plain,
% 1.82/1.49 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.49 inference(quant_intro,[status(thm)],[1586])).
% 1.82/1.49 tff(1588,plain,
% 1.82/1.49 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1589,plain,
% 1.82/1.49 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp1))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.82/1.49 inference(bind,[status(th)],[])).
% 1.82/1.49 tff(1590,plain,
% 1.82/1.49 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.49 inference(quant_intro,[status(thm)],[1589])).
% 1.82/1.49 tff(1591,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 1.82/1.49 tff(1592,plain,
% 1.82/1.49 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.49 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 1.82/1.49 tff(1593,plain,
% 1.82/1.49 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.49 inference(modus_ponens,[status(thm)],[1592, 1588])).
% 1.82/1.49 tff(1594,plain,(
% 1.82/1.49 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.49 inference(skolemize,[status(sab)],[1593])).
% 1.82/1.49 tff(1595,plain,
% 1.82/1.49 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.82/1.49 inference(modus_ponens,[status(thm)],[1594, 1587])).
% 1.82/1.49 tff(1596,plain,
% 1.82/1.49 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a428) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a428) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1597,plain,
% 1.82/1.49 ((hskp1 | (~ndr1_0) | c0_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403))) <=> (hskp1 | c0_1(a428) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1598,plain,
% 1.82/1.49 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a428) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428))))),
% 1.82/1.49 inference(monotonicity,[status(thm)],[1597])).
% 1.82/1.49 tff(1599,plain,
% 1.82/1.49 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a428) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)))),
% 1.82/1.49 inference(transitivity,[status(thm)],[1598, 1596])).
% 1.82/1.49 tff(1600,plain,
% 1.82/1.49 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))),
% 1.82/1.49 inference(quant_inst,[status(thm)],[])).
% 1.82/1.49 tff(1601,plain,
% 1.82/1.49 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a428) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428))),
% 1.82/1.49 inference(modus_ponens,[status(thm)],[1600, 1599])).
% 1.82/1.49 tff(1602,plain,
% 1.82/1.49 (hskp1),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[1601, 150, 1571, 1570, 336, 1561, 334, 1595, 1585])).
% 1.82/1.49 tff(1603,plain,
% 1.82/1.49 (~c3_1(a401)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[794, 1602])).
% 1.82/1.49 tff(1604,plain,
% 1.82/1.49 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c3_1(a460) | c0_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c0_1(a460)) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c3_1(a460) | c0_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1605,plain,
% 1.82/1.49 ((hskp11 | (~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c0_1(a428) | (~c2_1(a428)) | (~c3_1(a428))) <=> (hskp11 | c3_1(a460) | c0_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1606,plain,
% 1.82/1.49 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c0_1(a428) | (~c2_1(a428)) | (~c3_1(a428)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c3_1(a460) | c0_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c0_1(a460)) | (~c1_1(a460))))),
% 1.82/1.49 inference(monotonicity,[status(thm)],[1605])).
% 1.82/1.49 tff(1607,plain,
% 1.82/1.49 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c0_1(a428) | (~c2_1(a428)) | (~c3_1(a428)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c3_1(a460) | c0_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.82/1.49 inference(transitivity,[status(thm)],[1606, 1604])).
% 1.82/1.49 tff(1608,plain,
% 1.82/1.49 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c0_1(a428) | (~c2_1(a428)) | (~c3_1(a428)))),
% 1.82/1.49 inference(quant_inst,[status(thm)],[])).
% 1.82/1.49 tff(1609,plain,
% 1.82/1.49 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c3_1(a460) | c0_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c0_1(a460)) | (~c1_1(a460))),
% 1.82/1.49 inference(modus_ponens,[status(thm)],[1608, 1607])).
% 1.82/1.49 tff(1610,plain,
% 1.82/1.49 (hskp11),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[1609, 150, 242, 1571, 225, 1570, 1117, 1578, 1585])).
% 1.82/1.49 tff(1611,plain,
% 1.82/1.49 (~c2_1(a420)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[1223, 1610])).
% 1.82/1.49 tff(1612,plain,
% 1.82/1.49 (~c1_1(a420)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[1106, 1610])).
% 1.82/1.49 tff(1613,plain,
% 1.82/1.49 (~c0_1(a420)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[1100, 1610])).
% 1.82/1.49 tff(1614,plain,
% 1.82/1.49 (c1_1(a401)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[805, 1602])).
% 1.82/1.49 tff(1615,plain,
% 1.82/1.49 (c0_1(a401)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[816, 1602])).
% 1.82/1.49 tff(1616,plain,
% 1.82/1.49 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | (~c0_1(a460)))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1617,plain,
% 1.82/1.49 ((hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a460) | c3_1(a460) | (~c0_1(a460))) <=> (hskp22 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | (~c0_1(a460)))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1618,plain,
% 1.82/1.49 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | (~c0_1(a460))))),
% 1.82/1.49 inference(monotonicity,[status(thm)],[1617])).
% 1.82/1.49 tff(1619,plain,
% 1.82/1.49 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | (~c0_1(a460)))),
% 1.82/1.49 inference(transitivity,[status(thm)],[1618, 1616])).
% 1.82/1.49 tff(1620,plain,
% 1.82/1.49 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a460) | c3_1(a460) | (~c0_1(a460)))),
% 1.82/1.49 inference(quant_inst,[status(thm)],[])).
% 1.82/1.49 tff(1621,plain,
% 1.82/1.49 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a460) | c3_1(a460) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | (~c0_1(a460))),
% 1.82/1.49 inference(modus_ponens,[status(thm)],[1620, 1619])).
% 1.82/1.49 tff(1622,plain,
% 1.82/1.49 (hskp22 | (~c0_1(a460))),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[1621, 150, 107, 106, 231, 225, 929, 158])).
% 1.82/1.49 tff(1623,plain,
% 1.82/1.49 (hskp22),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[1622, 1578])).
% 1.82/1.49 tff(1624,plain,
% 1.82/1.49 (c2_1(a451)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[855, 1623])).
% 1.82/1.49 tff(1625,plain,
% 1.82/1.49 (c0_1(a451)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[866, 1623])).
% 1.82/1.49 tff(1626,plain,
% 1.82/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1627,plain,
% 1.82/1.49 (((~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420)) <=> (c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1628,plain,
% 1.82/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451))))),
% 1.82/1.49 inference(monotonicity,[status(thm)],[1627])).
% 1.82/1.49 tff(1629,plain,
% 1.82/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.82/1.49 inference(transitivity,[status(thm)],[1628, 1626])).
% 1.82/1.49 tff(1630,plain,
% 1.82/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420))),
% 1.82/1.49 inference(quant_inst,[status(thm)],[])).
% 1.82/1.49 tff(1631,plain,
% 1.82/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | c2_1(a420) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451))),
% 1.82/1.49 inference(modus_ponens,[status(thm)],[1630, 1629])).
% 1.82/1.49 tff(1632,plain,
% 1.82/1.49 (~c3_1(a451)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[1631, 150, 1625, 1624, 1615, 1614, 1613, 1612, 1611, 1603, 11])).
% 1.82/1.49 tff(1633,plain,
% 1.82/1.49 (~c1_1(a451)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[844, 1623])).
% 1.82/1.49 tff(1634,plain,
% 1.82/1.49 ($false),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[892, 150, 1624, 1615, 1614, 1633, 1603, 886, 1632])).
% 1.82/1.49 tff(1635,plain,(hskp19 | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~c0_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.82/1.49 tff(1636,plain,
% 1.82/1.49 (hskp19),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[1635, 336, 106, 107, 1560, 334, 108, 55])).
% 1.82/1.49 tff(1637,plain,
% 1.82/1.49 (c1_1(a445)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[458, 1636])).
% 1.82/1.49 tff(1638,plain,
% 1.82/1.49 (~c0_1(a445)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[332, 1636])).
% 1.82/1.49 tff(1639,plain,
% 1.82/1.49 (c3_1(a445)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[470, 1636])).
% 1.82/1.49 tff(1640,plain,
% 1.82/1.49 (((~hskp3) | (~c2_1(a403))) <=> ((~hskp3) | (~c2_1(a403)))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1641,plain,
% 1.82/1.49 (((~c2_1(a403)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a403)))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1642,axiom,((~c2_1(a403)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 1.82/1.49 tff(1643,plain,
% 1.82/1.49 ((~hskp3) | (~c2_1(a403))),
% 1.82/1.49 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 1.82/1.49 tff(1644,plain,
% 1.82/1.49 ((~hskp3) | (~c2_1(a403))),
% 1.82/1.49 inference(modus_ponens,[status(thm)],[1643, 1640])).
% 1.82/1.49 tff(1645,plain,
% 1.82/1.49 (~hskp3),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[1644, 1561])).
% 1.82/1.49 tff(1646,plain,
% 1.82/1.49 (~c0_1(a402)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[1548, 12, 1645, 105, 473, 472, 484])).
% 1.82/1.49 tff(1647,plain,
% 1.82/1.49 (~hskp2),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[520, 1646])).
% 1.82/1.49 tff(1648,plain,
% 1.82/1.49 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a402) | c1_1(a402) | c2_1(a402) | (~ndr1_0))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a402) | c1_1(a402) | c2_1(a402) | (~ndr1_0))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1649,plain,
% 1.82/1.49 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | c0_1(a402)) <=> (hskp2 | hskp1 | c0_1(a402) | c1_1(a402) | c2_1(a402) | (~ndr1_0))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1650,plain,
% 1.82/1.49 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | c0_1(a402))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a402) | c1_1(a402) | c2_1(a402) | (~ndr1_0)))),
% 1.82/1.49 inference(monotonicity,[status(thm)],[1649])).
% 1.82/1.49 tff(1651,plain,
% 1.82/1.49 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | c0_1(a402))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a402) | c1_1(a402) | c2_1(a402) | (~ndr1_0))),
% 1.82/1.49 inference(transitivity,[status(thm)],[1650, 1648])).
% 1.82/1.49 tff(1652,plain,
% 1.82/1.49 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | c0_1(a402))),
% 1.82/1.49 inference(quant_inst,[status(thm)],[])).
% 1.82/1.49 tff(1653,plain,
% 1.82/1.49 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a402) | c1_1(a402) | c2_1(a402) | (~ndr1_0)),
% 1.82/1.49 inference(modus_ponens,[status(thm)],[1652, 1651])).
% 1.82/1.49 tff(1654,plain,
% 1.82/1.49 (hskp2 | hskp1 | c0_1(a402) | c2_1(a402)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[1653, 150, 105, 33])).
% 1.82/1.49 tff(1655,plain,
% 1.82/1.49 (c2_1(a402)),
% 1.82/1.49 inference(unit_resolution,[status(thm)],[1654, 1646, 12, 1647])).
% 1.82/1.49 tff(1656,plain,
% 1.82/1.49 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a445) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a445)) | (~c3_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a445) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a445)) | (~c3_1(a445)))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1657,plain,
% 1.82/1.49 ((hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403))) <=> (hskp1 | c0_1(a445) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a445)) | (~c3_1(a445)))),
% 1.82/1.49 inference(rewrite,[status(thm)],[])).
% 1.82/1.49 tff(1658,plain,
% 1.82/1.49 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a445) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a445)) | (~c3_1(a445))))),
% 1.82/1.50 inference(monotonicity,[status(thm)],[1657])).
% 1.82/1.50 tff(1659,plain,
% 1.82/1.50 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a445) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a445)) | (~c3_1(a445)))),
% 1.82/1.50 inference(transitivity,[status(thm)],[1658, 1656])).
% 1.82/1.50 tff(1660,plain,
% 1.82/1.50 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))),
% 1.82/1.50 inference(quant_inst,[status(thm)],[])).
% 1.82/1.50 tff(1661,plain,
% 1.82/1.50 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a445) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a445)) | (~c3_1(a445))),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1660, 1659])).
% 1.82/1.50 tff(1662,plain,
% 1.82/1.50 (hskp1 | (~c2_1(a445))),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1661, 150, 473, 472, 336, 1561, 334, 1595])).
% 1.82/1.50 tff(1663,plain,
% 1.82/1.50 (~c2_1(a445)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1662, 12])).
% 1.82/1.50 tff(1664,plain,
% 1.82/1.50 (hskp5 | c2_1(a445)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1447, 150, 1645, 473, 472, 54])).
% 1.82/1.50 tff(1665,plain,
% 1.82/1.50 (hskp5),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1664, 1663])).
% 1.82/1.50 tff(1666,plain,
% 1.82/1.50 (~c0_1(a408)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1334, 1665])).
% 1.82/1.50 tff(1667,plain,
% 1.82/1.50 (c3_1(a408)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1345, 1665])).
% 1.82/1.50 tff(1668,plain,
% 1.82/1.50 (c2_1(a408)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1356, 1665])).
% 1.82/1.50 tff(1669,plain,
% 1.82/1.50 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a408) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a408)) | (~c3_1(a408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a408) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1670,plain,
% 1.82/1.50 ((hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402))) <=> (hskp1 | c0_1(a402) | c0_1(a408) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1671,plain,
% 1.82/1.50 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a408) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a408)) | (~c3_1(a408))))),
% 1.82/1.50 inference(monotonicity,[status(thm)],[1670])).
% 1.82/1.50 tff(1672,plain,
% 1.82/1.50 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a408) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.82/1.50 inference(transitivity,[status(thm)],[1671, 1669])).
% 1.82/1.50 tff(1673,plain,
% 1.82/1.50 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))),
% 1.82/1.50 inference(quant_inst,[status(thm)],[])).
% 1.82/1.50 tff(1674,plain,
% 1.82/1.50 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a408) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a408)) | (~c3_1(a408))),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 1.82/1.50 tff(1675,plain,
% 1.82/1.50 (c3_1(a402)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1674, 150, 12, 1668, 1667, 1646, 1666, 1655, 1595])).
% 1.82/1.50 tff(1676,plain,
% 1.82/1.50 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1677,plain,
% 1.82/1.50 ((hskp1 | (~ndr1_0) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403))) <=> (hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1678,plain,
% 1.82/1.50 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402))))),
% 1.82/1.50 inference(monotonicity,[status(thm)],[1677])).
% 1.82/1.50 tff(1679,plain,
% 1.82/1.50 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)))),
% 1.82/1.50 inference(transitivity,[status(thm)],[1678, 1676])).
% 1.82/1.50 tff(1680,plain,
% 1.82/1.50 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a403) | c3_1(a403) | (~c2_1(a403)))),
% 1.82/1.50 inference(quant_inst,[status(thm)],[])).
% 1.82/1.50 tff(1681,plain,
% 1.82/1.50 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402))),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1680, 1679])).
% 1.82/1.50 tff(1682,plain,
% 1.82/1.50 ($false),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1681, 150, 12, 1646, 336, 1561, 334, 1655, 1595, 1675])).
% 1.82/1.50 tff(1683,plain,(hskp1 | c0_1(a403) | (~c2_1(a403)) | c3_1(a403) | (~c3_1(a445)) | c0_1(a445) | c1_1(a402) | (~c1_1(a445))), inference(lemma,lemma(discharge,[]))).
% 1.82/1.50 tff(1684,plain,
% 1.82/1.50 (hskp1),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1683, 336, 1560, 334, 1639, 1638, 105, 1637])).
% 1.82/1.50 tff(1685,plain,
% 1.82/1.50 (~c3_1(a401)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[794, 1684])).
% 1.82/1.50 tff(1686,plain,
% 1.82/1.50 (c1_1(a401)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[805, 1684])).
% 1.82/1.50 tff(1687,plain,
% 1.82/1.50 (c0_1(a401)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[816, 1684])).
% 1.82/1.50 tff(1688,plain,
% 1.82/1.50 (~hskp22),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[897, 1685, 1639, 1686, 1687, 1637, 1638])).
% 1.82/1.50 tff(1689,plain,
% 1.82/1.50 (~hskp7),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[992, 1688, 1687, 1686, 1685])).
% 1.82/1.50 tff(1690,plain,
% 1.82/1.50 (hskp20),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[823, 150, 1687, 1686, 1685, 483])).
% 1.82/1.50 tff(1691,plain,
% 1.82/1.50 (c1_1(a449)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[834, 1690])).
% 1.82/1.50 tff(1692,plain,
% 1.82/1.50 (~c2_1(a449)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[914, 1690])).
% 1.82/1.50 tff(1693,plain,
% 1.82/1.50 (c3_1(a449)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[908, 1690])).
% 1.82/1.50 tff(1694,plain,
% 1.82/1.50 (~hskp2),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[942, 1693, 1637, 1692, 1688, 1691, 1639, 1638, 105])).
% 1.82/1.50 tff(1695,plain,
% 1.82/1.50 (~hskp3),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1644, 1560])).
% 1.82/1.50 tff(1696,plain,
% 1.82/1.50 (hskp16),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1402, 150, 1695, 1637, 1639, 1638, 1396])).
% 1.82/1.50 tff(1697,plain,
% 1.82/1.50 (~c3_1(a434)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1016, 1696])).
% 1.82/1.50 tff(1698,plain,
% 1.82/1.50 (c1_1(a434)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1044, 1696])).
% 1.82/1.50 tff(1699,plain,
% 1.82/1.50 (hskp7 | hskp2 | c2_1(a434)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1032, 150, 1698, 1697, 118])).
% 1.82/1.50 tff(1700,plain,
% 1.82/1.50 (c2_1(a434)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1699, 1694, 1689])).
% 1.82/1.50 tff(1701,plain,
% 1.82/1.50 (hskp14),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1072, 1694, 106, 1689, 1686, 1685, 1687, 1696, 108])).
% 1.82/1.50 tff(1702,plain,
% 1.82/1.50 (~c1_1(a428)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[421, 1701])).
% 1.82/1.50 tff(1703,plain,
% 1.82/1.50 ((hskp15 | hskp7 | hskp3) <=> (hskp15 | hskp7 | hskp3)),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1704,plain,
% 1.82/1.50 (((hskp15 | hskp7) | hskp3) <=> (hskp15 | hskp7 | hskp3)),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1705,axiom,((hskp15 | hskp7) | hskp3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause31')).
% 1.82/1.50 tff(1706,plain,
% 1.82/1.50 (hskp15 | hskp7 | hskp3),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1705, 1704])).
% 1.82/1.50 tff(1707,plain,
% 1.82/1.50 (hskp15 | hskp7 | hskp3),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1706, 1703])).
% 1.82/1.50 tff(1708,plain,
% 1.82/1.50 (hskp15 | hskp7 | hskp3),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1707, 1703])).
% 1.82/1.50 tff(1709,plain,
% 1.82/1.50 (hskp15 | hskp7 | hskp3),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1708, 1703])).
% 1.82/1.50 tff(1710,plain,
% 1.82/1.50 (hskp15 | hskp7 | hskp3),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1709, 1703])).
% 1.82/1.50 tff(1711,plain,
% 1.82/1.50 (hskp15 | hskp7 | hskp3),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1710, 1703])).
% 1.82/1.50 tff(1712,plain,
% 1.82/1.50 (hskp15 | hskp7 | hskp3),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1711, 1703])).
% 1.82/1.50 tff(1713,plain,
% 1.82/1.50 (hskp15 | hskp7 | hskp3),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1712, 1703])).
% 1.82/1.50 tff(1714,plain,
% 1.82/1.50 (hskp15),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1713, 1689, 1695])).
% 1.82/1.50 tff(1715,plain,
% 1.82/1.50 (((~hskp15) | (~c3_1(a430))) <=> ((~hskp15) | (~c3_1(a430)))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1716,plain,
% 1.82/1.50 (((~c3_1(a430)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a430)))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1717,axiom,((~c3_1(a430)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 1.82/1.50 tff(1718,plain,
% 1.82/1.50 ((~hskp15) | (~c3_1(a430))),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1717, 1716])).
% 1.82/1.50 tff(1719,plain,
% 1.82/1.50 ((~hskp15) | (~c3_1(a430))),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1718, 1715])).
% 1.82/1.50 tff(1720,plain,
% 1.82/1.50 (~c3_1(a430)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1719, 1714])).
% 1.82/1.50 tff(1721,plain,
% 1.82/1.50 (~c0_1(a434)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1022, 1696])).
% 1.82/1.50 tff(1722,plain,
% 1.82/1.50 (c2_1(a428)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[438, 1701])).
% 1.82/1.50 tff(1723,plain,
% 1.82/1.50 (((~hskp15) | c2_1(a430)) <=> ((~hskp15) | c2_1(a430))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1724,axiom,((~hskp15) | c2_1(a430)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 1.82/1.50 tff(1725,plain,
% 1.82/1.50 ((~hskp15) | c2_1(a430)),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1724, 1723])).
% 1.82/1.50 tff(1726,plain,
% 1.82/1.50 ((~hskp15) | c2_1(a430)),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1725, 1723])).
% 1.82/1.50 tff(1727,plain,
% 1.82/1.50 ((~hskp15) | c2_1(a430)),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1726, 1723])).
% 1.82/1.50 tff(1728,plain,
% 1.82/1.50 ((~hskp15) | c2_1(a430)),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1727, 1723])).
% 1.82/1.50 tff(1729,plain,
% 1.82/1.50 ((~hskp15) | c2_1(a430)),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1728, 1723])).
% 1.82/1.50 tff(1730,plain,
% 1.82/1.50 ((~hskp15) | c2_1(a430)),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1729, 1723])).
% 1.82/1.50 tff(1731,plain,
% 1.82/1.50 ((~hskp15) | c2_1(a430)),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1730, 1723])).
% 1.82/1.50 tff(1732,plain,
% 1.82/1.50 ((~hskp15) | c2_1(a430)),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1731, 1723])).
% 1.82/1.50 tff(1733,plain,
% 1.82/1.50 (c2_1(a430)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1732, 1714])).
% 1.82/1.50 tff(1734,plain,
% 1.82/1.50 (((~hskp15) | c0_1(a430)) <=> ((~hskp15) | c0_1(a430))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1735,axiom,((~hskp15) | c0_1(a430)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 1.82/1.50 tff(1736,plain,
% 1.82/1.50 ((~hskp15) | c0_1(a430)),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1735, 1734])).
% 1.82/1.50 tff(1737,plain,
% 1.82/1.50 ((~hskp15) | c0_1(a430)),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1736, 1734])).
% 1.82/1.50 tff(1738,plain,
% 1.82/1.50 ((~hskp15) | c0_1(a430)),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1737, 1734])).
% 1.82/1.50 tff(1739,plain,
% 1.82/1.50 ((~hskp15) | c0_1(a430)),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1738, 1734])).
% 1.82/1.50 tff(1740,plain,
% 1.82/1.50 ((~hskp15) | c0_1(a430)),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1739, 1734])).
% 1.82/1.50 tff(1741,plain,
% 1.82/1.50 ((~hskp15) | c0_1(a430)),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1740, 1734])).
% 1.82/1.50 tff(1742,plain,
% 1.82/1.50 ((~hskp15) | c0_1(a430)),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1741, 1734])).
% 1.82/1.50 tff(1743,plain,
% 1.82/1.50 ((~hskp15) | c0_1(a430)),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1742, 1734])).
% 1.82/1.50 tff(1744,plain,
% 1.82/1.50 (c0_1(a430)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1743, 1714])).
% 1.82/1.50 tff(1745,plain,
% 1.82/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a434) | c3_1(a430) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a430)) | (~c0_1(a430)) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a434) | c3_1(a430) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a430)) | (~c0_1(a430)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1746,plain,
% 1.82/1.50 (((~ndr1_0) | c3_1(a430) | (~c2_1(a430)) | (~c0_1(a430)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434))) <=> (c0_1(a434) | c3_1(a430) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a430)) | (~c0_1(a430)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1747,plain,
% 1.82/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a430) | (~c2_1(a430)) | (~c0_1(a430)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a434) | c3_1(a430) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a430)) | (~c0_1(a430)) | (~c2_1(a434)) | (~c1_1(a434))))),
% 1.82/1.50 inference(monotonicity,[status(thm)],[1746])).
% 1.82/1.50 tff(1748,plain,
% 1.82/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a430) | (~c2_1(a430)) | (~c0_1(a430)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a434) | c3_1(a430) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a430)) | (~c0_1(a430)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.82/1.50 inference(transitivity,[status(thm)],[1747, 1745])).
% 1.82/1.50 tff(1749,plain,
% 1.82/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a430) | (~c2_1(a430)) | (~c0_1(a430)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.82/1.50 inference(quant_inst,[status(thm)],[])).
% 1.82/1.50 tff(1750,plain,
% 1.82/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a434) | c3_1(a430) | c1_1(a428) | (~ndr1_0) | (~c2_1(a428)) | (~c3_1(a428)) | (~c2_1(a430)) | (~c0_1(a430)) | (~c2_1(a434)) | (~c1_1(a434))),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1749, 1748])).
% 1.82/1.50 tff(1751,plain,
% 1.82/1.50 (~c3_1(a428)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1750, 150, 1698, 1744, 1733, 1722, 1721, 1720, 1702, 704, 1700])).
% 1.82/1.50 tff(1752,plain,
% 1.82/1.50 ($false),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1092, 150, 1722, 1687, 1686, 1702, 1685, 886, 1751])).
% 1.82/1.50 tff(1753,plain,(c0_1(a403) | (~c3_1(a405)) | (~c0_1(a405)) | c1_1(a402) | c3_1(a403) | (~c1_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.82/1.50 tff(1754,plain,
% 1.82/1.50 (c0_1(a403)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1753, 334, 108, 105, 106, 107, 55])).
% 1.82/1.50 tff(1755,plain,
% 1.82/1.50 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~c0_1(a403)) | (~c2_1(a403)) | (~ndr1_0) | (~c1_1(a403)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~c0_1(a403)) | (~c2_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1756,plain,
% 1.82/1.50 ((hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a403)) | (~c1_1(a403)) | (~c0_1(a403))) <=> (hskp24 | hskp19 | (~c0_1(a403)) | (~c2_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1757,plain,
% 1.82/1.50 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a403)) | (~c1_1(a403)) | (~c0_1(a403)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~c0_1(a403)) | (~c2_1(a403)) | (~ndr1_0) | (~c1_1(a403))))),
% 1.82/1.50 inference(monotonicity,[status(thm)],[1756])).
% 1.82/1.50 tff(1758,plain,
% 1.82/1.50 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a403)) | (~c1_1(a403)) | (~c0_1(a403)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~c0_1(a403)) | (~c2_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.82/1.50 inference(transitivity,[status(thm)],[1757, 1755])).
% 1.82/1.50 tff(1759,plain,
% 1.82/1.50 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a403)) | (~c1_1(a403)) | (~c0_1(a403)))),
% 1.82/1.50 inference(quant_inst,[status(thm)],[])).
% 1.82/1.50 tff(1760,plain,
% 1.82/1.50 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~c0_1(a403)) | (~c2_1(a403)) | (~ndr1_0) | (~c1_1(a403))),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1759, 1758])).
% 1.82/1.50 tff(1761,plain,
% 1.82/1.50 (hskp19 | (~c0_1(a403)) | (~c1_1(a403))),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1760, 150, 55, 1561, 129])).
% 1.82/1.50 tff(1762,plain,
% 1.82/1.50 (~c1_1(a403)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1761, 119, 1257])).
% 1.82/1.50 tff(1763,plain,
% 1.82/1.50 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c3_1(a460) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c0_1(a460)) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c3_1(a460) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1764,plain,
% 1.82/1.50 (((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a403) | c3_1(a403) | (~c2_1(a403))) <=> (c3_1(a460) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1765,plain,
% 1.82/1.50 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c3_1(a460) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c0_1(a460)) | (~c1_1(a460))))),
% 1.82/1.50 inference(monotonicity,[status(thm)],[1764])).
% 1.82/1.50 tff(1766,plain,
% 1.82/1.50 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a403) | c3_1(a403) | (~c2_1(a403)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c3_1(a460) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.82/1.50 inference(transitivity,[status(thm)],[1765, 1763])).
% 1.82/1.50 tff(1767,plain,
% 1.82/1.50 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a403) | c3_1(a403) | (~c2_1(a403)))),
% 1.82/1.50 inference(quant_inst,[status(thm)],[])).
% 1.82/1.50 tff(1768,plain,
% 1.82/1.50 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c3_1(a460) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c0_1(a460)) | (~c1_1(a460))),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1767, 1766])).
% 1.82/1.50 tff(1769,plain,
% 1.82/1.50 (~c0_1(a460)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1768, 150, 242, 225, 1561, 334, 886, 1762])).
% 1.82/1.50 tff(1770,plain,
% 1.82/1.50 (hskp0),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1293, 150, 201, 231, 225, 356, 1769])).
% 1.82/1.50 tff(1771,plain,
% 1.82/1.50 (c2_1(a400)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[374, 1770])).
% 1.82/1.50 tff(1772,plain,
% 1.82/1.50 (c1_1(a400)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[385, 1770])).
% 1.82/1.50 tff(1773,plain,
% 1.82/1.50 (~c0_1(a400)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[389, 150, 55, 119, 1772, 1771, 129])).
% 1.82/1.50 tff(1774,plain,
% 1.82/1.50 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c3_1(a460) | (~c0_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c3_1(a460) | (~c0_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460)))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1775,plain,
% 1.82/1.50 ((hskp9 | (~ndr1_0) | c1_1(a403) | c3_1(a403) | (~c0_1(a403)) | c0_1(a460) | c3_1(a460) | (~c1_1(a460))) <=> (hskp9 | c3_1(a460) | (~c0_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460)))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1776,plain,
% 1.82/1.50 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a403) | c3_1(a403) | (~c0_1(a403)) | c0_1(a460) | c3_1(a460) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c3_1(a460) | (~c0_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460))))),
% 1.82/1.50 inference(monotonicity,[status(thm)],[1775])).
% 1.82/1.50 tff(1777,plain,
% 1.82/1.50 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a403) | c3_1(a403) | (~c0_1(a403)) | c0_1(a460) | c3_1(a460) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c3_1(a460) | (~c0_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460)))),
% 1.82/1.50 inference(transitivity,[status(thm)],[1776, 1774])).
% 1.82/1.50 tff(1778,plain,
% 1.82/1.50 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a403) | c3_1(a403) | (~c0_1(a403)) | c0_1(a460) | c3_1(a460) | (~c1_1(a460)))),
% 1.82/1.50 inference(quant_inst,[status(thm)],[])).
% 1.82/1.50 tff(1779,plain,
% 1.82/1.50 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c3_1(a460) | (~c0_1(a403)) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460))),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1778, 1777])).
% 1.82/1.50 tff(1780,plain,
% 1.82/1.50 (hskp9),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1779, 150, 242, 225, 1257, 334, 640, 1762, 1769])).
% 1.82/1.50 tff(1781,plain,
% 1.82/1.50 (~c1_1(a416)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[663, 1780])).
% 1.82/1.50 tff(1782,plain,
% 1.82/1.50 (c3_1(a416)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[727, 1780])).
% 1.82/1.50 tff(1783,plain,
% 1.82/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a416) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a416) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1784,plain,
% 1.82/1.50 (((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400))) <=> (c1_1(a416) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)))),
% 1.82/1.50 inference(rewrite,[status(thm)],[])).
% 1.82/1.50 tff(1785,plain,
% 1.82/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a416) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416))))),
% 1.82/1.50 inference(monotonicity,[status(thm)],[1784])).
% 1.82/1.50 tff(1786,plain,
% 1.82/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a416) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416)))),
% 1.82/1.50 inference(transitivity,[status(thm)],[1785, 1783])).
% 1.82/1.50 tff(1787,plain,
% 1.82/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))),
% 1.82/1.50 inference(quant_inst,[status(thm)],[])).
% 1.82/1.50 tff(1788,plain,
% 1.82/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a416) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | (~c2_1(a416)) | (~c3_1(a416))),
% 1.82/1.50 inference(modus_ponens,[status(thm)],[1787, 1786])).
% 1.82/1.50 tff(1789,plain,
% 1.82/1.50 (~c2_1(a416)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1788, 150, 1782, 1772, 1771, 1781, 1257, 1561, 334, 704, 1773])).
% 1.82/1.50 tff(1790,plain,
% 1.82/1.50 (~c0_1(a416)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[669, 1780])).
% 1.82/1.50 tff(1791,plain,
% 1.82/1.50 (hskp5),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1328, 150, 1645, 1782, 1790, 54, 1789])).
% 1.82/1.50 tff(1792,plain,
% 1.82/1.50 (~c0_1(a408)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1334, 1791])).
% 1.82/1.50 tff(1793,plain,
% 1.82/1.50 (c3_1(a408)),
% 1.82/1.50 inference(unit_resolution,[status(thm)],[1345, 1791])).
% 1.82/1.51 tff(1794,plain,
% 1.82/1.51 (c2_1(a408)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1356, 1791])).
% 1.82/1.51 tff(1795,plain,
% 1.82/1.51 ($false),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1363, 150, 242, 1782, 1794, 1793, 231, 1781, 1792, 43, 1769, 1789])).
% 1.82/1.51 tff(1796,plain,(hskp19 | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | hskp24 | (~c0_1(a405)) | (~c1_1(a405))), inference(lemma,lemma(discharge,[]))).
% 1.82/1.51 tff(1797,plain,
% 1.82/1.51 (hskp19),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1796, 1754, 1560, 334, 55, 108, 107])).
% 1.82/1.51 tff(1798,plain,
% 1.82/1.51 (~c0_1(a445)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[332, 1797])).
% 1.82/1.51 tff(1799,plain,
% 1.82/1.51 (c3_1(a445)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[470, 1797])).
% 1.82/1.51 tff(1800,plain,
% 1.82/1.51 (c1_1(a445)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[458, 1797])).
% 1.82/1.51 tff(1801,assumption,(~c0_1(a402)), introduced(assumption)).
% 1.82/1.51 tff(1802,plain,
% 1.82/1.51 (~hskp2),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[520, 1801])).
% 1.82/1.51 tff(1803,plain,
% 1.82/1.51 (c2_1(a402)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1654, 1801, 12, 1802])).
% 1.82/1.51 tff(1804,plain,
% 1.82/1.51 (hskp13),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[278, 1057, 1802])).
% 1.82/1.51 tff(1805,plain,
% 1.82/1.51 (~c0_1(a427)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[284, 1804])).
% 1.82/1.51 tff(1806,plain,
% 1.82/1.51 (c2_1(a427)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[306, 1804])).
% 1.82/1.51 tff(1807,plain,
% 1.82/1.51 (c1_1(a427)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[317, 1804])).
% 1.82/1.51 tff(1808,plain,
% 1.82/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(1809,plain,
% 1.82/1.51 (((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427))) <=> (c0_1(a427) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(1810,plain,
% 1.82/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a427)) | (~c1_1(a427))))),
% 1.82/1.51 inference(monotonicity,[status(thm)],[1809])).
% 1.82/1.51 tff(1811,plain,
% 1.82/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.82/1.51 inference(transitivity,[status(thm)],[1810, 1808])).
% 1.82/1.51 tff(1812,plain,
% 1.82/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.82/1.51 inference(quant_inst,[status(thm)],[])).
% 1.82/1.51 tff(1813,plain,
% 1.82/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a427)) | (~c1_1(a427))),
% 1.82/1.51 inference(modus_ponens,[status(thm)],[1812, 1811])).
% 1.82/1.51 tff(1814,plain,
% 1.82/1.51 (~c3_1(a402)),
% 1.82/1.51 inference(unit_resolution,[status(thm)],[1813, 150, 1807, 1806, 1805, 1257, 1561, 334, 105, 1803, 704])).
% 1.82/1.51 tff(1815,plain,
% 1.82/1.51 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.82/1.51 inference(bind,[status(th)],[])).
% 1.82/1.51 tff(1816,plain,
% 1.82/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.82/1.51 inference(quant_intro,[status(thm)],[1815])).
% 1.82/1.51 tff(1817,plain,
% 1.82/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(1818,plain,
% 1.82/1.51 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.82/1.51 inference(bind,[status(th)],[])).
% 1.82/1.51 tff(1819,plain,
% 1.82/1.51 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_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)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.82/1.51 inference(quant_intro,[status(thm)],[1818])).
% 1.82/1.51 tff(1820,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 1.82/1.51 tff(1821,plain,
% 1.82/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.82/1.51 inference(modus_ponens,[status(thm)],[1820, 1819])).
% 1.82/1.51 tff(1822,plain,
% 1.82/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.82/1.51 inference(modus_ponens,[status(thm)],[1821, 1817])).
% 1.82/1.51 tff(1823,plain,(
% 1.82/1.51 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.82/1.51 inference(skolemize,[status(sab)],[1822])).
% 1.82/1.51 tff(1824,plain,
% 1.82/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.82/1.51 inference(modus_ponens,[status(thm)],[1823, 1816])).
% 1.82/1.51 tff(1825,plain,
% 1.82/1.51 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(1826,plain,
% 1.82/1.51 ((hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402))) <=> (hskp14 | c0_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402))),
% 1.82/1.51 inference(rewrite,[status(thm)],[])).
% 1.82/1.51 tff(1827,plain,
% 1.82/1.51 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402)))),
% 1.90/1.51 inference(monotonicity,[status(thm)],[1826])).
% 1.90/1.51 tff(1828,plain,
% 1.90/1.51 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402))),
% 1.90/1.51 inference(transitivity,[status(thm)],[1827, 1825])).
% 1.90/1.51 tff(1829,plain,
% 1.90/1.51 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))),
% 1.90/1.51 inference(quant_inst,[status(thm)],[])).
% 1.90/1.51 tff(1830,plain,
% 1.90/1.51 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402)),
% 1.90/1.51 inference(modus_ponens,[status(thm)],[1829, 1828])).
% 1.90/1.51 tff(1831,plain,
% 1.90/1.51 (hskp14 | c3_1(a402)),
% 1.90/1.51 inference(unit_resolution,[status(thm)],[1830, 150, 107, 106, 1801, 1803, 400, 1057])).
% 1.90/1.51 tff(1832,plain,
% 1.90/1.51 (hskp14),
% 1.90/1.51 inference(unit_resolution,[status(thm)],[1831, 1814])).
% 1.90/1.51 tff(1833,plain,
% 1.90/1.51 (~c1_1(a428)),
% 1.90/1.51 inference(unit_resolution,[status(thm)],[421, 1832])).
% 1.90/1.51 tff(1834,plain,
% 1.90/1.51 (~c0_1(a428)),
% 1.90/1.51 inference(unit_resolution,[status(thm)],[427, 1832])).
% 1.90/1.51 tff(1835,plain,
% 1.90/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a402) | c0_1(a428) | c1_1(a428) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c3_1(a428)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a402) | c0_1(a428) | c1_1(a428) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c3_1(a428)))),
% 1.90/1.51 inference(rewrite,[status(thm)],[])).
% 1.90/1.51 tff(1836,plain,
% 1.90/1.51 (((~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c2_1(a402)) | c1_1(a428) | c0_1(a428) | (~c3_1(a428)) | c3_1(a402) | c1_1(a402) | c0_1(a402)) <=> (c0_1(a402) | c0_1(a428) | c1_1(a428) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c3_1(a428)))),
% 1.90/1.51 inference(rewrite,[status(thm)],[])).
% 1.90/1.51 tff(1837,plain,
% 1.90/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c2_1(a402)) | c1_1(a428) | c0_1(a428) | (~c3_1(a428)) | c3_1(a402) | c1_1(a402) | c0_1(a402))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a402) | c0_1(a428) | c1_1(a428) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c3_1(a428))))),
% 1.90/1.51 inference(monotonicity,[status(thm)],[1836])).
% 1.90/1.51 tff(1838,plain,
% 1.90/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c2_1(a402)) | c1_1(a428) | c0_1(a428) | (~c3_1(a428)) | c3_1(a402) | c1_1(a402) | c0_1(a402))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a402) | c0_1(a428) | c1_1(a428) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c3_1(a428)))),
% 1.90/1.51 inference(transitivity,[status(thm)],[1837, 1835])).
% 1.90/1.51 tff(1839,plain,
% 1.90/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c2_1(a402)) | c1_1(a428) | c0_1(a428) | (~c3_1(a428)) | c3_1(a402) | c1_1(a402) | c0_1(a402))),
% 1.90/1.51 inference(quant_inst,[status(thm)],[])).
% 1.90/1.51 tff(1840,plain,
% 1.90/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a402) | c0_1(a428) | c1_1(a428) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c3_1(a428))),
% 1.90/1.51 inference(modus_ponens,[status(thm)],[1839, 1838])).
% 1.90/1.51 tff(1841,plain,
% 1.90/1.51 (~c3_1(a428)),
% 1.90/1.51 inference(unit_resolution,[status(thm)],[1840, 150, 1801, 1834, 1833, 105, 1803, 1824, 1814])).
% 1.90/1.51 tff(1842,plain,
% 1.90/1.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a427) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a427)) | (~c3_1(a427)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a427) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a427)) | (~c3_1(a427)))),
% 1.90/1.51 inference(rewrite,[status(thm)],[])).
% 1.90/1.51 tff(1843,plain,
% 1.90/1.51 ((hskp1 | (~ndr1_0) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402))) <=> (hskp1 | c0_1(a402) | c0_1(a427) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a427)) | (~c3_1(a427)))),
% 1.90/1.51 inference(rewrite,[status(thm)],[])).
% 1.90/1.51 tff(1844,plain,
% 1.90/1.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a427) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a427)) | (~c3_1(a427))))),
% 1.90/1.51 inference(monotonicity,[status(thm)],[1843])).
% 1.90/1.51 tff(1845,plain,
% 1.90/1.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a427) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a427)) | (~c3_1(a427)))),
% 1.90/1.51 inference(transitivity,[status(thm)],[1844, 1842])).
% 1.90/1.51 tff(1846,plain,
% 1.90/1.51 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))),
% 1.90/1.51 inference(quant_inst,[status(thm)],[])).
% 1.90/1.51 tff(1847,plain,
% 1.90/1.51 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a427) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a427)) | (~c3_1(a427))),
% 1.90/1.51 inference(modus_ponens,[status(thm)],[1846, 1845])).
% 1.90/1.51 tff(1848,plain,
% 1.90/1.51 (~c3_1(a427)),
% 1.90/1.51 inference(unit_resolution,[status(thm)],[1847, 150, 12, 1806, 1801, 1805, 1803, 1595, 1814])).
% 1.90/1.51 tff(1849,plain,
% 1.90/1.51 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a427)) | (~c1_1(a427)) | c3_1(a427) | c3_1(a428))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a427)) | (~c1_1(a427)) | c3_1(a427) | c3_1(a428))),
% 1.90/1.51 inference(rewrite,[status(thm)],[])).
% 1.90/1.51 tff(1850,plain,
% 1.90/1.51 ((hskp3 | (~ndr1_0) | c3_1(a427) | (~c2_1(a427)) | (~c1_1(a427)) | c1_1(a428) | c0_1(a428) | c3_1(a428)) <=> (hskp3 | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a427)) | (~c1_1(a427)) | c3_1(a427) | c3_1(a428))),
% 1.90/1.51 inference(rewrite,[status(thm)],[])).
% 1.90/1.51 tff(1851,plain,
% 1.90/1.51 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a427) | (~c2_1(a427)) | (~c1_1(a427)) | c1_1(a428) | c0_1(a428) | c3_1(a428))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a427)) | (~c1_1(a427)) | c3_1(a427) | c3_1(a428)))),
% 1.90/1.51 inference(monotonicity,[status(thm)],[1850])).
% 1.90/1.51 tff(1852,plain,
% 1.90/1.51 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a427) | (~c2_1(a427)) | (~c1_1(a427)) | c1_1(a428) | c0_1(a428) | c3_1(a428))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a427)) | (~c1_1(a427)) | c3_1(a427) | c3_1(a428))),
% 1.90/1.51 inference(transitivity,[status(thm)],[1851, 1849])).
% 1.90/1.51 tff(1853,plain,
% 1.90/1.51 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a427) | (~c2_1(a427)) | (~c1_1(a427)) | c1_1(a428) | c0_1(a428) | c3_1(a428))),
% 1.90/1.51 inference(quant_inst,[status(thm)],[])).
% 1.90/1.51 tff(1854,plain,
% 1.90/1.51 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a428) | c1_1(a428) | (~ndr1_0) | (~c2_1(a427)) | (~c1_1(a427)) | c3_1(a427) | c3_1(a428)),
% 1.90/1.51 inference(modus_ponens,[status(thm)],[1853, 1852])).
% 1.90/1.51 tff(1855,plain,
% 1.90/1.51 ($false),
% 1.90/1.51 inference(unit_resolution,[status(thm)],[1854, 150, 1645, 1807, 1806, 1834, 1833, 1426, 1848, 1841])).
% 1.90/1.51 tff(1856,plain,(c2_1(a405) | c0_1(a402) | c1_1(a402) | (~c1_1(a405)) | (~c3_1(a405)) | hskp1 | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403)), inference(lemma,lemma(discharge,[]))).
% 1.90/1.51 tff(1857,plain,
% 1.90/1.51 (c2_1(a405)),
% 1.90/1.51 inference(unit_resolution,[status(thm)],[1856, 1646, 105, 107, 106, 12, 1257, 1561, 334])).
% 1.90/1.51 tff(1858,plain,
% 1.90/1.51 (c0_1(a420) | c2_1(a420)),
% 1.90/1.51 inference(unit_resolution,[status(thm)],[1126, 150, 1802, 12, 1119, 33])).
% 1.90/1.51 tff(1859,plain,
% 1.90/1.51 (c2_1(a420)),
% 1.90/1.51 inference(unit_resolution,[status(thm)],[1858, 1118])).
% 1.90/1.51 tff(1860,plain,
% 1.90/1.51 (~hskp11),
% 1.90/1.51 inference(unit_resolution,[status(thm)],[1223, 1859])).
% 1.90/1.51 tff(1861,plain,
% 1.90/1.51 (~c2_1(a405)),
% 1.90/1.51 inference(unit_resolution,[status(thm)],[968, 1860, 934])).
% 1.90/1.51 tff(1862,plain,
% 1.90/1.51 (hskp13),
% 1.90/1.51 inference(unit_resolution,[status(thm)],[278, 1861, 1802])).
% 1.90/1.51 tff(1863,plain,
% 1.90/1.51 (~c0_1(a427)),
% 1.90/1.51 inference(unit_resolution,[status(thm)],[284, 1862])).
% 1.90/1.51 tff(1864,plain,
% 1.90/1.51 (c2_1(a427)),
% 1.90/1.51 inference(unit_resolution,[status(thm)],[306, 1862])).
% 1.90/1.51 tff(1865,plain,
% 1.90/1.51 (c1_1(a427)),
% 1.90/1.51 inference(unit_resolution,[status(thm)],[317, 1862])).
% 1.90/1.51 tff(1866,plain,
% 1.90/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | c1_1(a420) | (~c2_1(a420)) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a420) | (~c2_1(a420)) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.90/1.51 inference(rewrite,[status(thm)],[])).
% 1.90/1.51 tff(1867,plain,
% 1.90/1.51 (((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a420) | (~c2_1(a420)) | (~c3_1(a420)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427))) <=> (c0_1(a427) | c1_1(a420) | (~c2_1(a420)) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.90/1.51 inference(rewrite,[status(thm)],[])).
% 1.90/1.51 tff(1868,plain,
% 1.90/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a420) | (~c2_1(a420)) | (~c3_1(a420)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | c1_1(a420) | (~c2_1(a420)) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a427)) | (~c1_1(a427))))),
% 1.90/1.51 inference(monotonicity,[status(thm)],[1867])).
% 1.90/1.51 tff(1869,plain,
% 1.90/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a420) | (~c2_1(a420)) | (~c3_1(a420)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a420) | (~c2_1(a420)) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.90/1.51 inference(transitivity,[status(thm)],[1868, 1866])).
% 1.90/1.51 tff(1870,plain,
% 1.90/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a403) | (~c2_1(a403)) | (~c0_1(a403)) | c1_1(a420) | (~c2_1(a420)) | (~c3_1(a420)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.90/1.51 inference(quant_inst,[status(thm)],[])).
% 1.90/1.51 tff(1871,plain,
% 1.90/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a420) | (~c2_1(a420)) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | (~ndr1_0) | (~c3_1(a420)) | (~c2_1(a427)) | (~c1_1(a427))),
% 1.90/1.51 inference(modus_ponens,[status(thm)],[1870, 1869])).
% 1.90/1.51 tff(1872,plain,
% 1.90/1.51 (~c3_1(a420)),
% 1.90/1.51 inference(unit_resolution,[status(thm)],[1871, 150, 1865, 1864, 1863, 1119, 1859, 1257, 1561, 334, 704])).
% 1.90/1.51 tff(1873,plain,
% 1.90/1.51 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a420))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a420))),
% 1.90/1.51 inference(rewrite,[status(thm)],[])).
% 1.90/1.51 tff(1874,plain,
% 1.90/1.51 ((hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a420) | c3_1(a420) | (~c2_1(a420))) <=> (hskp14 | c0_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a420))),
% 1.90/1.51 inference(rewrite,[status(thm)],[])).
% 1.90/1.51 tff(1875,plain,
% 1.90/1.51 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a420) | c3_1(a420) | (~c2_1(a420)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a420)))),
% 1.90/1.51 inference(monotonicity,[status(thm)],[1874])).
% 1.90/1.51 tff(1876,plain,
% 1.90/1.51 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a420) | c3_1(a420) | (~c2_1(a420)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a420))),
% 1.90/1.51 inference(transitivity,[status(thm)],[1875, 1873])).
% 1.90/1.51 tff(1877,plain,
% 1.90/1.51 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c0_1(a420) | c3_1(a420) | (~c2_1(a420)))),
% 1.90/1.51 inference(quant_inst,[status(thm)],[])).
% 1.90/1.51 tff(1878,plain,
% 1.90/1.51 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a420)),
% 1.90/1.52 inference(modus_ponens,[status(thm)],[1877, 1876])).
% 1.90/1.52 tff(1879,plain,
% 1.90/1.52 (hskp14 | c3_1(a420)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1878, 150, 107, 106, 1118, 1859, 400, 1861])).
% 1.90/1.52 tff(1880,plain,
% 1.90/1.52 (hskp14),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1879, 1872])).
% 1.90/1.52 tff(1881,plain,
% 1.90/1.52 (~c1_1(a428)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[421, 1880])).
% 1.90/1.52 tff(1882,plain,
% 1.90/1.52 (~c0_1(a428)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[427, 1880])).
% 1.90/1.52 tff(1883,plain,
% 1.90/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a428) | c1_1(a428) | c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c3_1(a420) | (~c3_1(a428)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a428) | c1_1(a428) | c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c3_1(a420) | (~c3_1(a428)))),
% 1.90/1.52 inference(rewrite,[status(thm)],[])).
% 1.90/1.52 tff(1884,plain,
% 1.90/1.52 (((~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c2_1(a420)) | c1_1(a428) | c0_1(a428) | (~c3_1(a428)) | c3_1(a420) | c1_1(a420) | c0_1(a420)) <=> (c0_1(a428) | c1_1(a428) | c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c3_1(a420) | (~c3_1(a428)))),
% 1.90/1.52 inference(rewrite,[status(thm)],[])).
% 1.90/1.52 tff(1885,plain,
% 1.90/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c2_1(a420)) | c1_1(a428) | c0_1(a428) | (~c3_1(a428)) | c3_1(a420) | c1_1(a420) | c0_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a428) | c1_1(a428) | c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c3_1(a420) | (~c3_1(a428))))),
% 1.90/1.52 inference(monotonicity,[status(thm)],[1884])).
% 1.90/1.52 tff(1886,plain,
% 1.90/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c2_1(a420)) | c1_1(a428) | c0_1(a428) | (~c3_1(a428)) | c3_1(a420) | c1_1(a420) | c0_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a428) | c1_1(a428) | c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c3_1(a420) | (~c3_1(a428)))),
% 1.90/1.52 inference(transitivity,[status(thm)],[1885, 1883])).
% 1.90/1.52 tff(1887,plain,
% 1.90/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c2_1(a420)) | c1_1(a428) | c0_1(a428) | (~c3_1(a428)) | c3_1(a420) | c1_1(a420) | c0_1(a420))),
% 1.90/1.52 inference(quant_inst,[status(thm)],[])).
% 1.90/1.52 tff(1888,plain,
% 1.90/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a428) | c1_1(a428) | c0_1(a420) | c1_1(a420) | (~c2_1(a420)) | (~ndr1_0) | c3_1(a420) | (~c3_1(a428))),
% 1.90/1.52 inference(modus_ponens,[status(thm)],[1887, 1886])).
% 1.90/1.52 tff(1889,plain,
% 1.90/1.52 (~c3_1(a428)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1888, 150, 1882, 1881, 1118, 1119, 1859, 1824, 1872])).
% 1.90/1.52 tff(1890,plain,
% 1.90/1.52 (~c3_1(a402)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1813, 150, 1865, 1864, 1863, 1257, 1561, 334, 105, 1803, 704])).
% 1.90/1.52 tff(1891,plain,
% 1.90/1.52 (~c3_1(a427)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1847, 150, 12, 1864, 1801, 1863, 1803, 1595, 1890])).
% 1.90/1.52 tff(1892,plain,
% 1.90/1.52 ($false),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1854, 150, 1645, 1865, 1864, 1882, 1881, 1426, 1891, 1889])).
% 1.90/1.52 tff(1893,plain,(c0_1(a420) | c1_1(a420) | (~c1_1(a405)) | (~c3_1(a405)) | hskp1 | c0_1(a402) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402) | hskp22 | (~c0_1(a405))), inference(lemma,lemma(discharge,[]))).
% 1.90/1.52 tff(1894,plain,
% 1.90/1.52 (c0_1(a420)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1893, 1119, 107, 106, 12, 1646, 1257, 1561, 334, 105, 934, 108])).
% 1.90/1.52 tff(1895,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c1_1(a445)) | (~c3_1(a445)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c1_1(a445)) | (~c3_1(a445)))),
% 1.90/1.52 inference(rewrite,[status(thm)],[])).
% 1.90/1.52 tff(1896,plain,
% 1.90/1.52 (((~ndr1_0) | c1_1(a420) | (~c3_1(a420)) | (~c0_1(a420)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445))) <=> (c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c1_1(a445)) | (~c3_1(a445)))),
% 1.90/1.52 inference(rewrite,[status(thm)],[])).
% 1.90/1.52 tff(1897,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a420) | (~c3_1(a420)) | (~c0_1(a420)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c1_1(a445)) | (~c3_1(a445))))),
% 1.90/1.52 inference(monotonicity,[status(thm)],[1896])).
% 1.90/1.52 tff(1898,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a420) | (~c3_1(a420)) | (~c0_1(a420)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c1_1(a445)) | (~c3_1(a445)))),
% 1.90/1.52 inference(transitivity,[status(thm)],[1897, 1895])).
% 1.90/1.52 tff(1899,plain,
% 1.90/1.52 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a420) | (~c3_1(a420)) | (~c0_1(a420)) | c0_1(a445) | (~c3_1(a445)) | (~c1_1(a445)))),
% 1.90/1.52 inference(quant_inst,[status(thm)],[])).
% 1.90/1.52 tff(1900,plain,
% 1.90/1.52 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c1_1(a445)) | (~c3_1(a445))),
% 1.90/1.52 inference(modus_ponens,[status(thm)],[1899, 1898])).
% 1.90/1.52 tff(1901,plain,
% 1.90/1.52 ((~c0_1(a420)) | (~c3_1(a420))),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1900, 150, 484, 473, 472, 1119, 531])).
% 1.90/1.52 tff(1902,plain,
% 1.90/1.52 (~c3_1(a420)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1901, 1894])).
% 1.90/1.52 tff(1903,plain,
% 1.90/1.52 (hskp16),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1402, 150, 1645, 484, 473, 472, 1396])).
% 1.90/1.52 tff(1904,plain,
% 1.90/1.52 (~c3_1(a434)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1016, 1903])).
% 1.90/1.52 tff(1905,plain,
% 1.90/1.52 (~c0_1(a434)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1022, 1903])).
% 1.90/1.52 tff(1906,plain,
% 1.90/1.52 (c1_1(a434)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1044, 1903])).
% 1.90/1.52 tff(1907,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a434) | c3_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a434) | c3_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c1_1(a434)))),
% 1.90/1.52 inference(rewrite,[status(thm)],[])).
% 1.90/1.52 tff(1908,plain,
% 1.90/1.52 ((hskp9 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434))) <=> (hskp9 | c0_1(a434) | c3_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c1_1(a434)))),
% 1.90/1.52 inference(rewrite,[status(thm)],[])).
% 1.90/1.52 tff(1909,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a434) | c3_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c1_1(a434))))),
% 1.90/1.52 inference(monotonicity,[status(thm)],[1908])).
% 1.90/1.52 tff(1910,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a434) | c3_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c1_1(a434)))),
% 1.90/1.52 inference(transitivity,[status(thm)],[1909, 1907])).
% 1.90/1.52 tff(1911,plain,
% 1.90/1.52 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434)))),
% 1.90/1.52 inference(quant_inst,[status(thm)],[])).
% 1.90/1.52 tff(1912,plain,
% 1.90/1.52 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a434) | c3_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c1_1(a434))),
% 1.90/1.52 inference(modus_ponens,[status(thm)],[1911, 1910])).
% 1.90/1.52 tff(1913,plain,
% 1.90/1.52 (hskp9 | (~c0_1(a420)) | c3_1(a420)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1912, 150, 1906, 1905, 1904, 1119, 640])).
% 1.90/1.52 tff(1914,plain,
% 1.90/1.52 (hskp9),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1913, 1894, 1902])).
% 1.90/1.52 tff(1915,plain,
% 1.90/1.52 (~c1_1(a416)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[663, 1914])).
% 1.90/1.52 tff(1916,plain,
% 1.90/1.52 (~c0_1(a416)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[669, 1914])).
% 1.90/1.52 tff(1917,plain,
% 1.90/1.52 (c2_1(a416)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[676, 150, 1647, 12, 1916, 1915, 33])).
% 1.90/1.52 tff(1918,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.90/1.52 inference(rewrite,[status(thm)],[])).
% 1.90/1.52 tff(1919,plain,
% 1.90/1.52 ((hskp1 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434))) <=> (hskp1 | c0_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.90/1.52 inference(rewrite,[status(thm)],[])).
% 1.90/1.52 tff(1920,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434))))),
% 1.90/1.52 inference(monotonicity,[status(thm)],[1919])).
% 1.90/1.52 tff(1921,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.90/1.52 inference(transitivity,[status(thm)],[1920, 1918])).
% 1.90/1.52 tff(1922,plain,
% 1.90/1.52 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.90/1.52 inference(quant_inst,[status(thm)],[])).
% 1.90/1.52 tff(1923,plain,
% 1.90/1.52 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a434) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a434)) | (~c1_1(a434))),
% 1.90/1.52 inference(modus_ponens,[status(thm)],[1922, 1921])).
% 1.90/1.52 tff(1924,plain,
% 1.90/1.52 ((~c0_1(a420)) | c3_1(a420) | (~c2_1(a434))),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1923, 150, 12, 1906, 1905, 1119, 22])).
% 1.90/1.52 tff(1925,plain,
% 1.90/1.52 (~c2_1(a434)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1924, 1894, 1902])).
% 1.90/1.52 tff(1926,plain,
% 1.90/1.52 (hskp7 | hskp2 | c2_1(a434)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1032, 150, 1906, 1904, 118])).
% 1.90/1.52 tff(1927,plain,
% 1.90/1.52 (hskp7),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1926, 1925, 1647])).
% 1.90/1.52 tff(1928,plain,
% 1.90/1.52 (~c3_1(a410)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[254, 1927])).
% 1.90/1.52 tff(1929,plain,
% 1.90/1.52 (c0_1(a410)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[295, 1927])).
% 1.90/1.52 tff(1930,plain,
% 1.90/1.52 (~hskp11),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1100, 1894])).
% 1.90/1.52 tff(1931,plain,
% 1.90/1.52 (c2_1(a410)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[693, 150, 1930, 1647, 1929, 1928, 687])).
% 1.90/1.52 tff(1932,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a445)) | (~c1_1(a445)))),
% 1.90/1.52 inference(rewrite,[status(thm)],[])).
% 1.90/1.52 tff(1933,plain,
% 1.90/1.52 ((hskp1 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445))) <=> (hskp1 | c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a445)) | (~c1_1(a445)))),
% 1.90/1.52 inference(rewrite,[status(thm)],[])).
% 1.90/1.52 tff(1934,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a445)) | (~c1_1(a445))))),
% 1.90/1.52 inference(monotonicity,[status(thm)],[1933])).
% 1.90/1.52 tff(1935,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a445)) | (~c1_1(a445)))),
% 1.90/1.52 inference(transitivity,[status(thm)],[1934, 1932])).
% 1.90/1.52 tff(1936,plain,
% 1.90/1.52 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a420) | c3_1(a420) | (~c0_1(a420)) | c0_1(a445) | (~c2_1(a445)) | (~c1_1(a445)))),
% 1.90/1.52 inference(quant_inst,[status(thm)],[])).
% 1.90/1.52 tff(1937,plain,
% 1.90/1.52 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a445) | (~c0_1(a420)) | c1_1(a420) | (~ndr1_0) | c3_1(a420) | (~c2_1(a445)) | (~c1_1(a445))),
% 1.90/1.52 inference(modus_ponens,[status(thm)],[1936, 1935])).
% 1.90/1.52 tff(1938,plain,
% 1.90/1.52 ((~c0_1(a420)) | c3_1(a420) | (~c2_1(a445))),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1937, 150, 12, 484, 472, 1119, 22])).
% 1.90/1.52 tff(1939,plain,
% 1.90/1.52 (~c2_1(a445)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1938, 1894, 1902])).
% 1.90/1.52 tff(1940,plain,
% 1.90/1.52 (hskp13),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[715, 1939, 1647])).
% 1.90/1.52 tff(1941,plain,
% 1.90/1.52 (~c0_1(a427)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[284, 1940])).
% 1.90/1.52 tff(1942,plain,
% 1.90/1.52 (c3_1(a416)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[727, 1914])).
% 1.90/1.52 tff(1943,plain,
% 1.90/1.52 (c2_1(a427)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[306, 1940])).
% 1.90/1.52 tff(1944,plain,
% 1.90/1.52 (c1_1(a427)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[317, 1940])).
% 1.90/1.52 tff(1945,plain,
% 1.90/1.52 ($false),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[736, 150, 1944, 1943, 1942, 1929, 1941, 1915, 1928, 704, 1931, 1917])).
% 1.90/1.52 tff(1946,plain,(c1_1(a420) | hskp1 | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | (~c1_1(a405)) | (~c3_1(a405)) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402) | hskp22 | (~c0_1(a405))), inference(lemma,lemma(discharge,[]))).
% 1.90/1.52 tff(1947,plain,
% 1.90/1.52 (c1_1(a420)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1946, 934, 484, 473, 472, 107, 106, 1257, 1561, 334, 105, 12, 108])).
% 1.90/1.52 tff(1948,plain,
% 1.90/1.52 (hskp11),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[968, 934, 1857])).
% 1.90/1.52 tff(1949,plain,
% 1.90/1.52 ($false),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1106, 1948, 1947])).
% 1.90/1.52 tff(1950,plain,(hskp22 | (~c0_1(a405)) | (~c3_1(a405)) | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | (~c1_1(a405)) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.90/1.52 tff(1951,plain,
% 1.90/1.52 (hskp22),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1950, 12, 106, 484, 473, 472, 107, 1257, 1561, 334, 105, 108])).
% 1.90/1.52 tff(1952,plain,
% 1.90/1.52 (~c1_1(a451)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[844, 1951])).
% 1.90/1.52 tff(1953,plain,
% 1.90/1.52 (c2_1(a451)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[855, 1951])).
% 1.90/1.52 tff(1954,plain,
% 1.90/1.52 (c0_1(a451)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[866, 1951])).
% 1.90/1.52 tff(1955,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | c1_1(a451) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c2_1(a451)) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c1_1(a451) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c2_1(a451)) | (~c0_1(a451)))),
% 1.90/1.52 inference(rewrite,[status(thm)],[])).
% 1.90/1.52 tff(1956,plain,
% 1.90/1.52 ((hskp3 | (~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451))) <=> (hskp3 | c1_1(a451) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c2_1(a451)) | (~c0_1(a451)))),
% 1.90/1.52 inference(rewrite,[status(thm)],[])).
% 1.90/1.52 tff(1957,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | c1_1(a451) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c2_1(a451)) | (~c0_1(a451))))),
% 1.90/1.52 inference(monotonicity,[status(thm)],[1956])).
% 1.90/1.52 tff(1958,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c1_1(a451) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c2_1(a451)) | (~c0_1(a451)))),
% 1.90/1.52 inference(transitivity,[status(thm)],[1957, 1955])).
% 1.90/1.52 tff(1959,plain,
% 1.90/1.52 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)))),
% 1.90/1.52 inference(quant_inst,[status(thm)],[])).
% 1.90/1.52 tff(1960,plain,
% 1.90/1.52 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c1_1(a451) | (~ndr1_0) | (~c0_1(a405)) | (~c2_1(a405)) | (~c3_1(a405)) | (~c2_1(a451)) | (~c0_1(a451))),
% 1.90/1.52 inference(modus_ponens,[status(thm)],[1959, 1958])).
% 1.90/1.52 tff(1961,plain,
% 1.90/1.52 ($false),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1960, 150, 1645, 108, 106, 1954, 1953, 1952, 1256, 1857])).
% 1.90/1.52 tff(1962,plain,(hskp1 | (~c0_1(a405)) | (~c3_1(a405)) | (~c1_1(a445)) | (~c3_1(a445)) | c0_1(a445) | (~c1_1(a405)) | (~c0_1(a403)) | (~c2_1(a403)) | c3_1(a403) | c1_1(a402)), inference(lemma,lemma(discharge,[]))).
% 1.90/1.52 tff(1963,plain,
% 1.90/1.52 (hskp1),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1962, 1800, 106, 108, 1799, 1798, 107, 1754, 1560, 334, 105])).
% 1.90/1.52 tff(1964,plain,
% 1.90/1.52 (~c3_1(a401)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[794, 1963])).
% 1.90/1.52 tff(1965,plain,
% 1.90/1.52 (c1_1(a401)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[805, 1963])).
% 1.90/1.52 tff(1966,plain,
% 1.90/1.52 (c0_1(a401)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[816, 1963])).
% 1.90/1.52 tff(1967,plain,
% 1.90/1.52 (~hskp22),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[897, 1964, 1799, 1965, 1966, 1800, 1798])).
% 1.90/1.52 tff(1968,plain,
% 1.90/1.52 (~hskp7),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[992, 1967, 1966, 1965, 1964])).
% 1.90/1.52 tff(1969,plain,
% 1.90/1.52 (hskp16),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1402, 150, 1695, 1800, 1799, 1798, 1396])).
% 1.90/1.52 tff(1970,plain,
% 1.90/1.52 (~c0_1(a434)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1022, 1969])).
% 1.90/1.52 tff(1971,plain,
% 1.90/1.52 (~c3_1(a434)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1016, 1969])).
% 1.90/1.52 tff(1972,plain,
% 1.90/1.52 (hskp20),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[823, 150, 1966, 1965, 1964, 483])).
% 1.90/1.52 tff(1973,plain,
% 1.90/1.52 (c1_1(a449)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[834, 1972])).
% 1.90/1.52 tff(1974,plain,
% 1.90/1.52 (~c2_1(a449)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[914, 1972])).
% 1.90/1.52 tff(1975,plain,
% 1.90/1.52 (c3_1(a449)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[908, 1972])).
% 1.90/1.52 tff(1976,plain,
% 1.90/1.52 (~hskp2),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[942, 1975, 1800, 1974, 1967, 1973, 1799, 1798, 105])).
% 1.90/1.52 tff(1977,plain,
% 1.90/1.52 (c2_1(a434)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1055, 1976, 106, 1971, 1965, 1970, 1964, 1966, 1968, 108])).
% 1.90/1.52 tff(1978,plain,
% 1.90/1.52 (hskp14),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1072, 1976, 106, 1968, 1965, 1964, 1966, 1969, 108])).
% 1.90/1.52 tff(1979,plain,
% 1.90/1.52 (~c1_1(a428)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[421, 1978])).
% 1.90/1.52 tff(1980,plain,
% 1.90/1.52 (hskp15),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1713, 1968, 1695])).
% 1.90/1.52 tff(1981,plain,
% 1.90/1.52 (~c3_1(a430)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1719, 1980])).
% 1.90/1.52 tff(1982,plain,
% 1.90/1.52 (c2_1(a428)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[438, 1978])).
% 1.90/1.52 tff(1983,plain,
% 1.90/1.52 (c2_1(a430)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1732, 1980])).
% 1.90/1.52 tff(1984,plain,
% 1.90/1.52 (c0_1(a430)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1743, 1980])).
% 1.90/1.52 tff(1985,plain,
% 1.90/1.52 (c1_1(a434)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1044, 1969])).
% 1.90/1.52 tff(1986,plain,
% 1.90/1.52 (~c3_1(a428)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1750, 150, 1985, 1984, 1983, 1982, 1970, 1981, 1979, 704, 1977])).
% 1.90/1.52 tff(1987,plain,
% 1.90/1.52 ($false),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1092, 150, 1982, 1966, 1965, 1979, 1964, 886, 1986])).
% 1.90/1.52 tff(1988,plain,(c3_1(a403) | (~c3_1(a405)) | (~c0_1(a405)) | c1_1(a402) | (~c1_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.90/1.52 tff(1989,plain,
% 1.90/1.52 (c3_1(a403)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1988, 105, 108, 106, 107, 55])).
% 1.90/1.52 tff(1990,plain,
% 1.90/1.52 (((~hskp3) | (~c3_1(a403))) <=> ((~hskp3) | (~c3_1(a403)))),
% 1.90/1.52 inference(rewrite,[status(thm)],[])).
% 1.90/1.52 tff(1991,plain,
% 1.90/1.52 (((~c3_1(a403)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a403)))),
% 1.90/1.52 inference(rewrite,[status(thm)],[])).
% 1.90/1.52 tff(1992,axiom,((~c3_1(a403)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 1.90/1.52 tff(1993,plain,
% 1.90/1.52 ((~hskp3) | (~c3_1(a403))),
% 1.90/1.52 inference(modus_ponens,[status(thm)],[1992, 1991])).
% 1.90/1.52 tff(1994,plain,
% 1.90/1.52 ((~hskp3) | (~c3_1(a403))),
% 1.90/1.52 inference(modus_ponens,[status(thm)],[1993, 1990])).
% 1.90/1.52 tff(1995,plain,
% 1.90/1.52 (~hskp3),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1994, 1989])).
% 1.90/1.52 tff(1996,plain,
% 1.90/1.52 (c3_1(a445)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[470, 327])).
% 1.90/1.52 tff(1997,plain,
% 1.90/1.52 (c1_1(a445)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[458, 327])).
% 1.90/1.52 tff(1998,assumption,(~c3_1(a402)), introduced(assumption)).
% 1.90/1.52 tff(1999,plain,
% 1.90/1.52 (~c0_1(a402)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1548, 472, 44, 105, 12, 473, 484])).
% 1.90/1.52 tff(2000,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a402) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a402) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.90/1.52 inference(rewrite,[status(thm)],[])).
% 1.90/1.52 tff(2001,plain,
% 1.90/1.52 ((hskp3 | (~ndr1_0) | c3_1(a434) | (~c2_1(a434)) | (~c1_1(a434)) | c1_1(a402) | c0_1(a402) | c3_1(a402)) <=> (hskp3 | c0_1(a402) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.90/1.52 inference(rewrite,[status(thm)],[])).
% 1.90/1.52 tff(2002,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a434) | (~c2_1(a434)) | (~c1_1(a434)) | c1_1(a402) | c0_1(a402) | c3_1(a402))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a402) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c2_1(a434)) | (~c1_1(a434))))),
% 1.90/1.52 inference(monotonicity,[status(thm)],[2001])).
% 1.90/1.52 tff(2003,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a434) | (~c2_1(a434)) | (~c1_1(a434)) | c1_1(a402) | c0_1(a402) | c3_1(a402))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a402) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.90/1.52 inference(transitivity,[status(thm)],[2002, 2000])).
% 1.90/1.52 tff(2004,plain,
% 1.90/1.52 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a434) | (~c2_1(a434)) | (~c1_1(a434)) | c1_1(a402) | c0_1(a402) | c3_1(a402))),
% 1.90/1.52 inference(quant_inst,[status(thm)],[])).
% 1.90/1.52 tff(2005,plain,
% 1.90/1.52 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a402) | c3_1(a434) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c2_1(a434)) | (~c1_1(a434))),
% 1.90/1.52 inference(modus_ponens,[status(thm)],[2004, 2003])).
% 1.90/1.52 tff(2006,plain,
% 1.90/1.52 (c3_1(a402) | (~c2_1(a434))),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[2005, 150, 44, 1461, 1999, 1470, 105, 1426])).
% 1.90/1.52 tff(2007,plain,
% 1.90/1.52 (~c2_1(a434)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[2006, 1998])).
% 1.90/1.52 tff(2008,plain,
% 1.90/1.52 (hskp7 | c2_1(a434)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1032, 150, 23, 1461, 1470, 118])).
% 1.90/1.52 tff(2009,plain,
% 1.90/1.52 (hskp7),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[2008, 2007])).
% 1.90/1.52 tff(2010,plain,
% 1.90/1.52 (~c3_1(a410)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[254, 2009])).
% 1.90/1.52 tff(2011,plain,
% 1.90/1.52 (~c1_1(a410)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[260, 2009])).
% 1.90/1.52 tff(2012,plain,
% 1.90/1.52 (c2_1(a402)),
% 1.90/1.52 inference(unit_resolution,[status(thm)],[1654, 1999, 12, 23])).
% 1.90/1.52 tff(2013,plain,
% 1.90/1.52 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a445) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a445)) | (~c3_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a445) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a445)) | (~c3_1(a445)))),
% 1.90/1.52 inference(rewrite,[status(thm)],[])).
% 1.90/1.52 tff(2014,plain,
% 1.90/1.52 ((hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402))) <=> (hskp1 | c0_1(a402) | c0_1(a445) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a445)) | (~c3_1(a445)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(2015,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a445) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a445)) | (~c3_1(a445))))),
% 1.90/1.53 inference(monotonicity,[status(thm)],[2014])).
% 1.90/1.53 tff(2016,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a445) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a445)) | (~c3_1(a445)))),
% 1.90/1.53 inference(transitivity,[status(thm)],[2015, 2013])).
% 1.90/1.53 tff(2017,plain,
% 1.90/1.53 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))),
% 1.90/1.53 inference(quant_inst,[status(thm)],[])).
% 1.90/1.53 tff(2018,plain,
% 1.90/1.53 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a445) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402) | (~c2_1(a445)) | (~c3_1(a445))),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[2017, 2016])).
% 1.90/1.53 tff(2019,plain,
% 1.90/1.53 (c3_1(a402) | (~c2_1(a445))),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2018, 150, 12, 473, 1999, 472, 2012, 1595])).
% 1.90/1.53 tff(2020,plain,
% 1.90/1.53 (~c2_1(a445)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2019, 1998])).
% 1.90/1.53 tff(2021,plain,
% 1.90/1.53 (hskp13 | c2_1(a445)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[714, 150, 23, 484, 473, 271])).
% 1.90/1.53 tff(2022,plain,
% 1.90/1.53 (hskp13),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2021, 2020])).
% 1.90/1.53 tff(2023,plain,
% 1.90/1.53 (~c0_1(a427)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[284, 2022])).
% 1.90/1.53 tff(2024,plain,
% 1.90/1.53 (c0_1(a410)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[295, 2009])).
% 1.90/1.53 tff(2025,plain,
% 1.90/1.53 (c2_1(a427)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[306, 2022])).
% 1.90/1.53 tff(2026,plain,
% 1.90/1.53 (c1_1(a427)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[317, 2022])).
% 1.90/1.53 tff(2027,plain,
% 1.90/1.53 ($false),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[324, 150, 12, 2026, 2025, 2024, 2023, 2011, 2010, 22])).
% 1.90/1.53 tff(2028,plain,(c3_1(a402) | hskp1 | hskp2 | (~c1_1(a445)) | (~c3_1(a445)) | hskp3 | c1_1(a402) | c0_1(a445)), inference(lemma,lemma(discharge,[]))).
% 1.90/1.53 tff(2029,plain,
% 1.90/1.53 (c3_1(a402)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2028, 1997, 12, 23, 1996, 1995, 105, 333])).
% 1.90/1.53 tff(2030,plain,
% 1.90/1.53 (~c0_1(a402)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1548, 333, 1995, 105, 12, 1996, 1997])).
% 1.90/1.53 tff(2031,plain,
% 1.90/1.53 (c2_1(a402)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1654, 2030, 12, 23])).
% 1.90/1.53 tff(2032,plain,
% 1.90/1.53 (hskp16),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1402, 150, 1995, 1997, 1996, 333, 1396])).
% 1.90/1.53 tff(2033,plain,
% 1.90/1.53 (~c3_1(a434)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1016, 2032])).
% 1.90/1.53 tff(2034,plain,
% 1.90/1.53 (~c0_1(a434)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1022, 2032])).
% 1.90/1.53 tff(2035,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a434) | c3_1(a434) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a434) | c3_1(a434) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a434)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(2036,plain,
% 1.90/1.53 ((hskp1 | (~ndr1_0) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434))) <=> (hskp1 | c0_1(a402) | c0_1(a434) | c3_1(a434) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a434)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(2037,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a434) | c3_1(a434) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a434))))),
% 1.90/1.53 inference(monotonicity,[status(thm)],[2036])).
% 1.90/1.53 tff(2038,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a434) | c3_1(a434) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a434)))),
% 1.90/1.53 inference(transitivity,[status(thm)],[2037, 2035])).
% 1.90/1.53 tff(2039,plain,
% 1.90/1.53 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))),
% 1.90/1.53 inference(quant_inst,[status(thm)],[])).
% 1.90/1.53 tff(2040,plain,
% 1.90/1.53 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a434) | c3_1(a434) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | (~c2_1(a434))),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[2039, 2038])).
% 1.90/1.53 tff(2041,plain,
% 1.90/1.53 (~c2_1(a434)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2040, 150, 12, 2030, 2034, 2033, 2031, 1595, 2029])).
% 1.90/1.53 tff(2042,plain,
% 1.90/1.53 (c1_1(a434)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1044, 2032])).
% 1.90/1.53 tff(2043,plain,
% 1.90/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a402) | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a402) | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(2044,plain,
% 1.90/1.53 (((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a402) | c0_1(a402) | (~c2_1(a402)) | c3_1(a434) | c0_1(a434) | c2_1(a434)) <=> (c0_1(a402) | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(2045,plain,
% 1.90/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a402) | c0_1(a402) | (~c2_1(a402)) | c3_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a402) | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434))))),
% 1.90/1.53 inference(monotonicity,[status(thm)],[2044])).
% 1.90/1.53 tff(2046,plain,
% 1.90/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a402) | c0_1(a402) | (~c2_1(a402)) | c3_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a402) | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)))),
% 1.90/1.53 inference(transitivity,[status(thm)],[2045, 2043])).
% 1.90/1.53 tff(2047,plain,
% 1.90/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a402) | c0_1(a402) | (~c2_1(a402)) | c3_1(a434) | c0_1(a434) | c2_1(a434))),
% 1.90/1.53 inference(quant_inst,[status(thm)],[])).
% 1.90/1.53 tff(2048,plain,
% 1.90/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a402) | c0_1(a434) | c3_1(a434) | c1_1(a402) | (~c2_1(a402)) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434))),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[2047, 2046])).
% 1.90/1.53 tff(2049,plain,
% 1.90/1.53 ($false),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2048, 150, 2042, 2030, 2034, 2033, 105, 2031, 346, 2041])).
% 1.90/1.53 tff(2050,plain,(hskp2 | c1_1(a402) | hskp1 | (~c0_1(a405)) | (~c1_1(a405)) | (~c3_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.90/1.53 tff(2051,plain,
% 1.90/1.53 (hskp2),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2050, 12, 105, 104, 93, 82, 55])).
% 1.90/1.53 tff(2052,plain,
% 1.90/1.53 (~c2_1(a402)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[509, 2051])).
% 1.90/1.53 tff(2053,plain,
% 1.90/1.53 (c0_1(a402)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[520, 2051])).
% 1.90/1.53 tff(2054,assumption,(~c2_1(a402)), introduced(assumption)).
% 1.90/1.53 tff(2055,plain,
% 1.90/1.53 (c3_1(a403)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1988, 105, 104, 82, 93, 55])).
% 1.90/1.53 tff(2056,plain,
% 1.90/1.53 (~hskp3),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1994, 2055])).
% 1.90/1.53 tff(2057,plain,
% 1.90/1.53 (hskp19 | (~c2_1(a405))),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[156, 150, 55, 104, 93, 129])).
% 1.90/1.53 tff(2058,plain,
% 1.90/1.53 (~c2_1(a405)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2057, 119])).
% 1.90/1.53 tff(2059,plain,
% 1.90/1.53 (hskp27 | hskp23 | c2_1(a405)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[217, 150, 104, 93, 211])).
% 1.90/1.53 tff(2060,plain,
% 1.90/1.53 (hskp23),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2059, 201, 2058])).
% 1.90/1.53 tff(2061,plain,
% 1.90/1.53 (c1_1(a460)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[241, 2060])).
% 1.90/1.53 tff(2062,plain,
% 1.90/1.53 (~c3_1(a460)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[224, 2060])).
% 1.90/1.53 tff(2063,plain,
% 1.90/1.53 (~c2_1(a460)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[230, 2060])).
% 1.90/1.53 tff(2064,plain,
% 1.90/1.53 (~c3_1(a451)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1279, 150, 44, 867, 856, 845, 1256])).
% 1.90/1.53 tff(2065,assumption,(~c3_1(a460)), introduced(assumption)).
% 1.90/1.53 tff(2066,assumption,(c1_1(a460)), introduced(assumption)).
% 1.90/1.53 tff(2067,plain,
% 1.90/1.53 (~c0_1(a460)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1286, 150, 2066, 856, 2065, 845, 886, 2064])).
% 1.90/1.53 tff(2068,assumption,(~c2_1(a460)), introduced(assumption)).
% 1.90/1.53 tff(2069,assumption,(~hskp27), introduced(assumption)).
% 1.90/1.53 tff(2070,plain,
% 1.90/1.53 (hskp0 | c0_1(a460)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1293, 150, 2069, 2068, 2065, 356])).
% 1.90/1.53 tff(2071,plain,
% 1.90/1.53 (hskp0),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2070, 2067])).
% 1.90/1.53 tff(2072,plain,
% 1.90/1.53 (~c3_1(a400)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[405, 2071])).
% 1.90/1.53 tff(2073,plain,
% 1.90/1.53 (c1_1(a400)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[385, 2071])).
% 1.90/1.53 tff(2074,plain,
% 1.90/1.53 (~c0_1(a400)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1303, 150, 856, 2073, 845, 2072, 886, 2064])).
% 1.90/1.53 tff(2075,plain,
% 1.90/1.53 (c2_1(a400)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[374, 2071])).
% 1.90/1.53 tff(2076,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c1_1(a451) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a451) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c1_1(a451) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a451) | (~c0_1(a451)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(2077,plain,
% 1.90/1.53 ((hskp1 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400))) <=> (hskp1 | c1_1(a451) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a451) | (~c0_1(a451)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(2078,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c1_1(a451) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a451) | (~c0_1(a451))))),
% 1.90/1.53 inference(monotonicity,[status(thm)],[2077])).
% 1.90/1.53 tff(2079,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c1_1(a451) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a451) | (~c0_1(a451)))),
% 1.90/1.53 inference(transitivity,[status(thm)],[2078, 2076])).
% 1.90/1.53 tff(2080,plain,
% 1.90/1.53 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a400) | (~c2_1(a400)) | (~c1_1(a400)))),
% 1.90/1.53 inference(quant_inst,[status(thm)],[])).
% 1.90/1.53 tff(2081,plain,
% 1.90/1.53 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c1_1(a451) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c0_1(a400) | c3_1(a451) | (~c0_1(a451))),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[2080, 2079])).
% 1.90/1.53 tff(2082,plain,
% 1.90/1.53 ($false),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2081, 150, 12, 867, 2073, 2075, 845, 22, 2074, 2064])).
% 1.90/1.53 tff(2083,plain,((~hskp22) | hskp1 | hskp27 | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.90/1.53 tff(2084,plain,
% 1.90/1.53 (~hskp22),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2083, 201, 12, 2063, 2062, 2061, 2056])).
% 1.90/1.53 tff(2085,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a402) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a402) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402) | (~c0_1(a402)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(2086,plain,
% 1.90/1.53 ((hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402))) <=> (hskp22 | c2_1(a402) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402) | (~c0_1(a402)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(2087,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a402) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402) | (~c0_1(a402))))),
% 1.90/1.53 inference(monotonicity,[status(thm)],[2086])).
% 1.90/1.53 tff(2088,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a402) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402) | (~c0_1(a402)))),
% 1.90/1.53 inference(transitivity,[status(thm)],[2087, 2085])).
% 1.90/1.53 tff(2089,plain,
% 1.90/1.53 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))),
% 1.90/1.53 inference(quant_inst,[status(thm)],[])).
% 1.90/1.53 tff(2090,plain,
% 1.90/1.53 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a402) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)) | c3_1(a402) | (~c0_1(a402))),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[2089, 2088])).
% 1.90/1.53 tff(2091,plain,
% 1.90/1.53 (hskp22 | c3_1(a402)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2090, 150, 93, 82, 1439, 2054, 929, 2058])).
% 1.90/1.53 tff(2092,plain,
% 1.90/1.53 (c3_1(a402)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2091, 2084])).
% 1.90/1.53 tff(2093,plain,
% 1.90/1.53 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp18 | hskp3 | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(2094,plain,
% 1.90/1.53 ((hskp18 | hskp3 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c3_1(a402))) <=> (hskp18 | hskp3 | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(2095,plain,
% 1.90/1.53 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c3_1(a402)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402))))),
% 1.90/1.53 inference(monotonicity,[status(thm)],[2094])).
% 1.90/1.53 tff(2096,plain,
% 1.90/1.53 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c3_1(a402)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp18 | hskp3 | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)))),
% 1.90/1.53 inference(transitivity,[status(thm)],[2095, 2093])).
% 1.90/1.53 tff(2097,plain,
% 1.90/1.53 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c3_1(a402)))),
% 1.90/1.53 inference(quant_inst,[status(thm)],[])).
% 1.90/1.53 tff(2098,plain,
% 1.90/1.53 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp18 | hskp3 | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402))),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[2097, 2096])).
% 1.90/1.53 tff(2099,plain,
% 1.90/1.53 (hskp18 | hskp3 | c2_1(a402) | (~c3_1(a402))),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2098, 150, 105, 1507])).
% 1.90/1.53 tff(2100,plain,
% 1.90/1.53 (hskp18),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2099, 2092, 2056, 2054])).
% 1.90/1.53 tff(2101,plain,
% 1.90/1.53 (~c3_1(a440)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1521, 2100])).
% 1.90/1.53 tff(2102,plain,
% 1.90/1.53 (~c2_1(a440)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1527, 2100])).
% 1.90/1.53 tff(2103,plain,
% 1.90/1.53 (^[U: $i] : refl((hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.90/1.53 inference(bind,[status(th)],[])).
% 1.90/1.53 tff(2104,plain,
% 1.90/1.53 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.90/1.53 inference(quant_intro,[status(thm)],[2103])).
% 1.90/1.53 tff(2105,plain,
% 1.90/1.53 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(2106,plain,
% 1.90/1.53 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp21) <=> ((hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21))), rewrite(((hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21) <=> (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp21) <=> (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.90/1.53 inference(bind,[status(th)],[])).
% 1.90/1.53 tff(2107,plain,
% 1.90/1.53 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp21) <=> ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.90/1.53 inference(quant_intro,[status(thm)],[2106])).
% 1.90/1.53 tff(2108,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 1.90/1.53 tff(2109,plain,
% 1.90/1.53 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[2108, 2107])).
% 1.90/1.53 tff(2110,plain,
% 1.90/1.53 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[2109, 2105])).
% 1.90/1.53 tff(2111,plain,(
% 1.90/1.53 ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.90/1.53 inference(skolemize,[status(sab)],[2110])).
% 1.90/1.53 tff(2112,plain,
% 1.90/1.53 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[2111, 2104])).
% 1.90/1.53 tff(2113,plain,
% 1.90/1.53 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp20 | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(2114,plain,
% 1.90/1.53 ((hskp21 | hskp20 | (~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402))) <=> (hskp21 | hskp20 | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(2115,plain,
% 1.90/1.53 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | (~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402))))),
% 1.90/1.53 inference(monotonicity,[status(thm)],[2114])).
% 1.90/1.53 tff(2116,plain,
% 1.90/1.53 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | (~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp20 | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)))),
% 1.90/1.53 inference(transitivity,[status(thm)],[2115, 2113])).
% 1.90/1.53 tff(2117,plain,
% 1.90/1.53 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp20 | (~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)))),
% 1.90/1.53 inference(quant_inst,[status(thm)],[])).
% 1.90/1.53 tff(2118,plain,
% 1.90/1.53 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp20 | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402))),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[2117, 2116])).
% 1.90/1.53 tff(2119,plain,
% 1.90/1.53 (hskp20 | (~c3_1(a402)) | (~c0_1(a402))),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2118, 150, 56, 105, 2112])).
% 1.90/1.53 tff(2120,plain,
% 1.90/1.53 (hskp20),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2119, 2092, 1439])).
% 1.90/1.53 tff(2121,plain,
% 1.90/1.53 (~c2_1(a449)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[914, 2120])).
% 1.90/1.53 tff(2122,plain,
% 1.90/1.53 (c0_1(a440)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1539, 2100])).
% 1.90/1.53 tff(2123,plain,
% 1.90/1.53 (c3_1(a449)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[908, 2120])).
% 1.90/1.53 tff(2124,plain,
% 1.90/1.53 (c1_1(a449)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[834, 2120])).
% 1.90/1.53 tff(2125,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a449) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c0_1(a440)) | (~c3_1(a449)) | (~c1_1(a449)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c0_1(a440)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(2126,plain,
% 1.90/1.53 ((hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a440) | c3_1(a440) | (~c0_1(a440))) <=> (hskp22 | c2_1(a449) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c0_1(a440)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.90/1.53 inference(rewrite,[status(thm)],[])).
% 1.90/1.53 tff(2127,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a449) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c0_1(a440)) | (~c3_1(a449)) | (~c1_1(a449))))),
% 1.90/1.53 inference(monotonicity,[status(thm)],[2126])).
% 1.90/1.53 tff(2128,plain,
% 1.90/1.53 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c0_1(a440)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.90/1.53 inference(transitivity,[status(thm)],[2127, 2125])).
% 1.90/1.53 tff(2129,plain,
% 1.90/1.53 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)))),
% 1.90/1.53 inference(quant_inst,[status(thm)],[])).
% 1.90/1.53 tff(2130,plain,
% 1.90/1.53 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c0_1(a440)) | (~c3_1(a449)) | (~c1_1(a449))),
% 1.90/1.53 inference(modus_ponens,[status(thm)],[2129, 2128])).
% 1.90/1.53 tff(2131,plain,
% 1.90/1.53 ($false),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2130, 150, 2084, 2124, 2123, 2122, 2121, 2102, 2101, 929])).
% 1.90/1.53 tff(2132,plain,(hskp19 | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | hskp21 | hskp1 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.90/1.53 tff(2133,plain,
% 1.90/1.53 (hskp19),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2132, 2053, 105, 12, 56, 2052, 55])).
% 1.90/1.53 tff(2134,plain,
% 1.90/1.53 (c1_1(a445)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[458, 2133])).
% 1.90/1.53 tff(2135,plain,
% 1.90/1.53 (c3_1(a445)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[470, 2133])).
% 1.90/1.53 tff(2136,plain,
% 1.90/1.53 (~c0_1(a445)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[332, 2133])).
% 1.90/1.53 tff(2137,plain,
% 1.90/1.53 ($false),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[1548, 2136, 2135, 2056, 105, 12, 2053, 2134])).
% 1.90/1.53 tff(2138,plain,(hskp1 | c1_1(a402) | hskp21 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.90/1.53 tff(2139,plain,
% 1.90/1.53 (hskp1),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[2138, 105, 56, 55])).
% 1.90/1.53 tff(2140,plain,
% 1.90/1.53 (~c3_1(a401)),
% 1.90/1.53 inference(unit_resolution,[status(thm)],[794, 2139])).
% 1.90/1.53 tff(2141,plain,
% 1.90/1.53 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.90/1.53 inference(bind,[status(th)],[])).
% 1.90/1.53 tff(2142,plain,
% 1.90/1.53 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.90/1.54 inference(quant_intro,[status(thm)],[2141])).
% 1.90/1.54 tff(2143,plain,
% 1.90/1.54 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2144,plain,
% 1.90/1.54 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.90/1.54 inference(bind,[status(th)],[])).
% 1.90/1.54 tff(2145,plain,
% 1.90/1.54 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.90/1.54 inference(quant_intro,[status(thm)],[2144])).
% 1.90/1.54 tff(2146,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause150')).
% 1.90/1.54 tff(2147,plain,
% 1.90/1.54 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2146, 2145])).
% 1.90/1.54 tff(2148,plain,
% 1.90/1.54 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2147, 2143])).
% 1.90/1.54 tff(2149,plain,(
% 1.90/1.54 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.90/1.54 inference(skolemize,[status(sab)],[2148])).
% 1.90/1.54 tff(2150,plain,
% 1.90/1.54 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2149, 2142])).
% 1.90/1.54 tff(2151,plain,
% 1.90/1.54 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2152,plain,
% 1.90/1.54 ((hskp5 | hskp3 | (~ndr1_0) | c2_1(a403) | c0_1(a403) | (~c3_1(a403))) <=> (hskp5 | hskp3 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2153,plain,
% 1.90/1.54 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a403) | c0_1(a403) | (~c3_1(a403)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0)))),
% 1.90/1.54 inference(monotonicity,[status(thm)],[2152])).
% 1.90/1.54 tff(2154,plain,
% 1.90/1.54 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a403) | c0_1(a403) | (~c3_1(a403)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0))),
% 1.90/1.54 inference(transitivity,[status(thm)],[2153, 2151])).
% 1.90/1.54 tff(2155,plain,
% 1.90/1.54 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a403) | c0_1(a403) | (~c3_1(a403)))),
% 1.90/1.54 inference(quant_inst,[status(thm)],[])).
% 1.90/1.54 tff(2156,plain,
% 1.90/1.54 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2155, 2154])).
% 1.90/1.54 tff(2157,plain,
% 1.90/1.54 (hskp5 | c0_1(a403) | c2_1(a403)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[2156, 150, 1995, 1989, 54])).
% 1.90/1.54 tff(2158,plain,
% 1.90/1.54 (hskp5),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[2157, 335, 336])).
% 1.90/1.54 tff(2159,plain,
% 1.90/1.54 (~c0_1(a408)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[1334, 2158])).
% 1.90/1.54 tff(2160,plain,
% 1.90/1.54 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.90/1.54 inference(bind,[status(th)],[])).
% 1.90/1.54 tff(2161,plain,
% 1.90/1.54 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.90/1.54 inference(quant_intro,[status(thm)],[2160])).
% 1.90/1.54 tff(2162,plain,
% 1.90/1.54 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2163,plain,
% 1.90/1.54 (^[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)) | c2_1(V) | 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)) | c2_1(V) | 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)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | 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)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.90/1.54 inference(bind,[status(th)],[])).
% 1.90/1.54 tff(2164,plain,
% 1.90/1.54 (![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)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.90/1.54 inference(quant_intro,[status(thm)],[2163])).
% 1.90/1.54 tff(2165,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/sandbox2/benchmark/theBenchmark.p','clause163')).
% 1.90/1.54 tff(2166,plain,
% 1.90/1.54 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2165, 2164])).
% 1.90/1.54 tff(2167,plain,
% 1.90/1.54 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2166, 2162])).
% 1.90/1.54 tff(2168,plain,(
% 1.90/1.54 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.90/1.54 inference(skolemize,[status(sab)],[2167])).
% 1.90/1.54 tff(2169,plain,
% 1.90/1.54 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2168, 2161])).
% 1.90/1.54 tff(2170,plain,
% 1.90/1.54 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2171,plain,
% 1.90/1.54 ((hskp10 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a403) | c0_1(a403) | (~c3_1(a403))) <=> (hskp10 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2172,plain,
% 1.90/1.54 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a403) | c0_1(a403) | (~c3_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405))))),
% 1.90/1.54 inference(monotonicity,[status(thm)],[2171])).
% 1.90/1.54 tff(2173,plain,
% 1.90/1.54 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a403) | c0_1(a403) | (~c3_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405)))),
% 1.90/1.54 inference(transitivity,[status(thm)],[2172, 2170])).
% 1.90/1.54 tff(2174,plain,
% 1.90/1.54 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a405) | (~c1_1(a405)) | (~c3_1(a405)) | c2_1(a403) | c0_1(a403) | (~c3_1(a403)))),
% 1.90/1.54 inference(quant_inst,[status(thm)],[])).
% 1.90/1.54 tff(2175,plain,
% 1.90/1.54 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c2_1(a405) | (~c3_1(a405)) | (~c1_1(a405))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2174, 2173])).
% 1.90/1.54 tff(2176,plain,
% 1.90/1.54 (hskp10),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[2175, 150, 107, 106, 336, 335, 1989, 2169, 158])).
% 1.90/1.54 tff(2177,plain,
% 1.90/1.54 (((~hskp10) | (~c2_1(a418))) <=> ((~hskp10) | (~c2_1(a418)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2178,plain,
% 1.90/1.54 (((~c2_1(a418)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a418)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2179,axiom,((~c2_1(a418)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 1.90/1.54 tff(2180,plain,
% 1.90/1.54 ((~hskp10) | (~c2_1(a418))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2179, 2178])).
% 1.90/1.54 tff(2181,plain,
% 1.90/1.54 ((~hskp10) | (~c2_1(a418))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2180, 2177])).
% 1.90/1.54 tff(2182,plain,
% 1.90/1.54 (~c2_1(a418)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[2181, 2176])).
% 1.90/1.54 tff(2183,plain,
% 1.90/1.54 (((~hskp10) | (~c0_1(a418))) <=> ((~hskp10) | (~c0_1(a418)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2184,plain,
% 1.90/1.54 (((~c0_1(a418)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a418)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2185,axiom,((~c0_1(a418)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 1.90/1.54 tff(2186,plain,
% 1.90/1.54 ((~hskp10) | (~c0_1(a418))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2185, 2184])).
% 1.90/1.54 tff(2187,plain,
% 1.90/1.54 ((~hskp10) | (~c0_1(a418))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2186, 2183])).
% 1.90/1.54 tff(2188,plain,
% 1.90/1.54 (~c0_1(a418)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[2187, 2176])).
% 1.90/1.54 tff(2189,plain,
% 1.90/1.54 (c3_1(a408)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[1345, 2158])).
% 1.90/1.54 tff(2190,plain,
% 1.90/1.54 (c2_1(a408)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[1356, 2158])).
% 1.90/1.54 tff(2191,plain,
% 1.90/1.54 (((~hskp10) | c1_1(a418)) <=> ((~hskp10) | c1_1(a418))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2192,axiom,((~hskp10) | c1_1(a418)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 1.90/1.54 tff(2193,plain,
% 1.90/1.54 ((~hskp10) | c1_1(a418)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2192, 2191])).
% 1.90/1.54 tff(2194,plain,
% 1.90/1.54 ((~hskp10) | c1_1(a418)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2193, 2191])).
% 1.90/1.54 tff(2195,plain,
% 1.90/1.54 ((~hskp10) | c1_1(a418)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2194, 2191])).
% 1.90/1.54 tff(2196,plain,
% 1.90/1.54 ((~hskp10) | c1_1(a418)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2195, 2191])).
% 1.90/1.54 tff(2197,plain,
% 1.90/1.54 ((~hskp10) | c1_1(a418)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2196, 2191])).
% 1.90/1.54 tff(2198,plain,
% 1.90/1.54 ((~hskp10) | c1_1(a418)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2197, 2191])).
% 1.90/1.54 tff(2199,plain,
% 1.90/1.54 ((~hskp10) | c1_1(a418)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2198, 2191])).
% 1.90/1.54 tff(2200,plain,
% 1.90/1.54 ((~hskp10) | c1_1(a418)),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2199, 2191])).
% 1.90/1.54 tff(2201,plain,
% 1.90/1.54 (c1_1(a418)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[2200, 2176])).
% 1.90/1.54 tff(2202,plain,
% 1.90/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a418) | c2_1(a418) | c0_1(a408) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c1_1(a403) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a418) | c2_1(a418) | c0_1(a408) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c1_1(a403) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2203,plain,
% 1.90/1.54 (((~ndr1_0) | c2_1(a403) | c1_1(a403) | (~c3_1(a403)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a418) | c2_1(a418) | (~c1_1(a418))) <=> (c0_1(a418) | c2_1(a418) | c0_1(a408) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c1_1(a403) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2204,plain,
% 1.90/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a403) | c1_1(a403) | (~c3_1(a403)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a418) | c2_1(a418) | (~c1_1(a418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a418) | c2_1(a418) | c0_1(a408) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c1_1(a403) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418))))),
% 1.90/1.54 inference(monotonicity,[status(thm)],[2203])).
% 1.90/1.54 tff(2205,plain,
% 1.90/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a403) | c1_1(a403) | (~c3_1(a403)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a418) | c2_1(a418) | (~c1_1(a418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a418) | c2_1(a418) | c0_1(a408) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c1_1(a403) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)))),
% 1.90/1.54 inference(transitivity,[status(thm)],[2204, 2202])).
% 1.90/1.54 tff(2206,plain,
% 1.90/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a403) | c1_1(a403) | (~c3_1(a403)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a418) | c2_1(a418) | (~c1_1(a418)))),
% 1.90/1.54 inference(quant_inst,[status(thm)],[])).
% 1.90/1.54 tff(2207,plain,
% 1.90/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a418) | c2_1(a418) | c0_1(a408) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | c1_1(a403) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2206, 2205])).
% 1.90/1.54 tff(2208,plain,
% 1.90/1.54 (c1_1(a403)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[2207, 150, 2201, 2190, 2189, 2188, 2182, 2159, 335, 1989, 43])).
% 1.90/1.54 tff(2209,plain,
% 1.90/1.54 (((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))) <=> ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | hskp3 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2210,plain,
% 1.90/1.54 ((hskp16 | hskp3 | (~ndr1_0) | c0_1(a403) | (~c1_1(a403)) | (~c3_1(a403))) <=> (hskp16 | hskp3 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2211,plain,
% 1.90/1.54 (((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | (~ndr1_0) | c0_1(a403) | (~c1_1(a403)) | (~c3_1(a403)))) <=> ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403))))),
% 1.90/1.54 inference(monotonicity,[status(thm)],[2210])).
% 1.90/1.54 tff(2212,plain,
% 1.90/1.54 (((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | (~ndr1_0) | c0_1(a403) | (~c1_1(a403)) | (~c3_1(a403)))) <=> ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | hskp3 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.90/1.54 inference(transitivity,[status(thm)],[2211, 2209])).
% 1.90/1.54 tff(2213,plain,
% 1.90/1.54 ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | (~ndr1_0) | c0_1(a403) | (~c1_1(a403)) | (~c3_1(a403)))),
% 1.90/1.54 inference(quant_inst,[status(thm)],[])).
% 1.90/1.54 tff(2214,plain,
% 1.90/1.54 ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | hskp3 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2213, 2212])).
% 1.90/1.54 tff(2215,plain,
% 1.90/1.54 (hskp16 | c0_1(a403) | (~c1_1(a403))),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[2214, 150, 1995, 1989, 1396])).
% 1.90/1.54 tff(2216,plain,
% 1.90/1.54 (hskp16),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[2215, 2208, 336])).
% 1.90/1.54 tff(2217,plain,
% 1.90/1.54 (~c3_1(a434)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[1016, 2216])).
% 1.90/1.54 tff(2218,plain,
% 1.90/1.54 (~c0_1(a434)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[1022, 2216])).
% 1.90/1.54 tff(2219,plain,
% 1.90/1.54 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a434)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2220,plain,
% 1.90/1.54 ((hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434))) <=> (hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a434)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2221,plain,
% 1.90/1.54 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a434))))),
% 1.90/1.54 inference(monotonicity,[status(thm)],[2220])).
% 1.90/1.54 tff(2222,plain,
% 1.90/1.54 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a434)))),
% 1.90/1.54 inference(transitivity,[status(thm)],[2221, 2219])).
% 1.90/1.54 tff(2223,plain,
% 1.90/1.54 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))),
% 1.90/1.54 inference(quant_inst,[status(thm)],[])).
% 1.90/1.54 tff(2224,plain,
% 1.90/1.54 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a434))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2223, 2222])).
% 1.90/1.54 tff(2225,plain,
% 1.90/1.54 (~c2_1(a434)),
% 1.90/1.54 inference(unit_resolution,[status(thm)],[2224, 150, 12, 2190, 2189, 2218, 2217, 2159, 1595])).
% 1.90/1.54 tff(2226,plain,
% 1.90/1.54 (^[U: $i] : refl((hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 1.90/1.54 inference(bind,[status(th)],[])).
% 1.90/1.54 tff(2227,plain,
% 1.90/1.54 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.90/1.54 inference(quant_intro,[status(thm)],[2226])).
% 1.90/1.54 tff(2228,plain,
% 1.90/1.54 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2229,plain,
% 1.90/1.54 (^[U: $i] : 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)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp27))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp9) <=> ((hskp27 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp9))), rewrite(((hskp27 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp9) <=> (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp9) <=> (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 1.90/1.54 inference(bind,[status(th)],[])).
% 1.90/1.54 tff(2230,plain,
% 1.90/1.54 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp9) <=> ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.90/1.54 inference(quant_intro,[status(thm)],[2229])).
% 1.90/1.54 tff(2231,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 1.90/1.54 tff(2232,plain,
% 1.90/1.54 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2231, 2230])).
% 1.90/1.54 tff(2233,plain,
% 1.90/1.54 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2232, 2228])).
% 1.90/1.54 tff(2234,plain,(
% 1.90/1.54 ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.90/1.54 inference(skolemize,[status(sab)],[2233])).
% 1.90/1.54 tff(2235,plain,
% 1.90/1.54 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.90/1.54 inference(modus_ponens,[status(thm)],[2234, 2227])).
% 1.90/1.54 tff(2236,plain,
% 1.90/1.54 (((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp27 | hskp9 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))) <=> ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp27 | hskp9 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2237,plain,
% 1.90/1.54 ((hskp27 | hskp9 | (~ndr1_0) | c0_1(a403) | (~c1_1(a403)) | (~c3_1(a403))) <=> (hskp27 | hskp9 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.90/1.54 inference(rewrite,[status(thm)],[])).
% 1.90/1.54 tff(2238,plain,
% 1.90/1.54 (((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp27 | hskp9 | (~ndr1_0) | c0_1(a403) | (~c1_1(a403)) | (~c3_1(a403)))) <=> ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp27 | hskp9 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403))))),
% 1.90/1.54 inference(monotonicity,[status(thm)],[2237])).
% 1.90/1.54 tff(2239,plain,
% 1.90/1.54 (((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp27 | hskp9 | (~ndr1_0) | c0_1(a403) | (~c1_1(a403)) | (~c3_1(a403)))) <=> ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp27 | hskp9 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.90/1.54 inference(transitivity,[status(thm)],[2238, 2236])).
% 1.90/1.55 tff(2240,plain,
% 1.90/1.55 ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp27 | hskp9 | (~ndr1_0) | c0_1(a403) | (~c1_1(a403)) | (~c3_1(a403)))),
% 1.90/1.55 inference(quant_inst,[status(thm)],[])).
% 1.90/1.55 tff(2241,plain,
% 1.90/1.55 ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp27 | hskp9 | c0_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403))),
% 1.90/1.55 inference(modus_ponens,[status(thm)],[2240, 2239])).
% 1.90/1.55 tff(2242,plain,
% 1.90/1.55 (hskp27 | hskp9 | c0_1(a403) | (~c1_1(a403))),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2241, 150, 1989, 2235])).
% 1.90/1.55 tff(2243,plain,
% 1.90/1.55 (hskp9),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2242, 2208, 336, 201])).
% 1.90/1.55 tff(2244,plain,
% 1.90/1.55 (~c1_1(a416)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[663, 2243])).
% 1.90/1.55 tff(2245,plain,
% 1.90/1.55 (~c0_1(a416)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[669, 2243])).
% 1.90/1.55 tff(2246,plain,
% 1.90/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a460) | c3_1(a460) | c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a460)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(2247,plain,
% 1.90/1.55 (((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a434) | c0_1(a434) | c2_1(a434)) <=> (c2_1(a460) | c3_1(a460) | c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a460)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(2248,plain,
% 1.90/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a460) | c3_1(a460) | c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a460))))),
% 1.90/1.55 inference(monotonicity,[status(thm)],[2247])).
% 1.90/1.55 tff(2249,plain,
% 1.90/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a460)))),
% 1.90/1.55 inference(transitivity,[status(thm)],[2248, 2246])).
% 1.90/1.55 tff(2250,plain,
% 1.90/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a434) | c0_1(a434) | c2_1(a434))),
% 1.90/1.55 inference(quant_inst,[status(thm)],[])).
% 1.90/1.55 tff(2251,plain,
% 1.90/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a434) | c3_1(a434) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c2_1(a434) | (~c1_1(a460))),
% 1.90/1.55 inference(modus_ponens,[status(thm)],[2250, 2249])).
% 1.90/1.55 tff(2252,plain,
% 1.90/1.55 ((~c2_1(a416)) | c2_1(a434)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2251, 150, 242, 231, 225, 2218, 2217, 2245, 2244, 346])).
% 1.90/1.55 tff(2253,plain,
% 1.90/1.55 (~c2_1(a416)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2252, 2225])).
% 1.90/1.55 tff(2254,plain,
% 1.90/1.55 (hskp2 | c2_1(a416)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[676, 150, 12, 2245, 2244, 33])).
% 1.90/1.55 tff(2255,plain,
% 1.90/1.55 (hskp2),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2254, 2253])).
% 1.90/1.55 tff(2256,plain,
% 1.90/1.55 (c0_1(a402)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[520, 2255])).
% 1.90/1.55 tff(2257,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a403) | (~c3_1(a403)) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a403) | (~c3_1(a403)) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a403)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(2258,plain,
% 1.90/1.55 (((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a403) | (~c3_1(a403)) | (~c1_1(a403))) <=> (c0_1(a403) | (~c3_1(a403)) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a403)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(2259,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a403) | (~c3_1(a403)) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a403) | (~c3_1(a403)) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a403))))),
% 1.90/1.55 inference(monotonicity,[status(thm)],[2258])).
% 1.90/1.55 tff(2260,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a403) | (~c3_1(a403)) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a403) | (~c3_1(a403)) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a403)))),
% 1.90/1.55 inference(transitivity,[status(thm)],[2259, 2257])).
% 1.90/1.55 tff(2261,plain,
% 1.90/1.55 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a403) | (~c3_1(a403)) | (~c1_1(a403)))),
% 1.90/1.55 inference(quant_inst,[status(thm)],[])).
% 1.90/1.55 tff(2262,plain,
% 1.90/1.55 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a403) | (~c3_1(a403)) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a403))),
% 1.90/1.55 inference(modus_ponens,[status(thm)],[2261, 2260])).
% 1.90/1.55 tff(2263,plain,
% 1.90/1.55 ((~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a403))),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2262, 150, 336, 1989, 105, 531])).
% 1.90/1.55 tff(2264,plain,
% 1.90/1.55 (~c3_1(a402)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2263, 2256, 2208])).
% 1.90/1.55 tff(2265,plain,
% 1.90/1.55 (hskp1 | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a408))),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1457, 150, 2190, 2159, 105, 22])).
% 1.90/1.55 tff(2266,plain,
% 1.90/1.55 (~c1_1(a408)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2265, 2264, 12, 2256])).
% 1.90/1.55 tff(2267,plain,
% 1.90/1.55 (c1_1(a434)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1044, 2216])).
% 1.90/1.55 tff(2268,plain,
% 1.90/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | c1_1(a408) | c2_1(a434) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | c1_1(a408) | c2_1(a434) | (~c1_1(a434)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(2269,plain,
% 1.90/1.55 (((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)) | c3_1(a434) | c0_1(a434) | c2_1(a434)) <=> (c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | c1_1(a408) | c2_1(a434) | (~c1_1(a434)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(2270,plain,
% 1.90/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)) | c3_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | c1_1(a408) | c2_1(a434) | (~c1_1(a434))))),
% 1.90/1.55 inference(monotonicity,[status(thm)],[2269])).
% 1.90/1.55 tff(2271,plain,
% 1.90/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)) | c3_1(a434) | c0_1(a434) | c2_1(a434))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | c1_1(a408) | c2_1(a434) | (~c1_1(a434)))),
% 1.90/1.55 inference(transitivity,[status(thm)],[2270, 2268])).
% 1.90/1.55 tff(2272,plain,
% 1.90/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)) | c3_1(a434) | c0_1(a434) | c2_1(a434))),
% 1.90/1.55 inference(quant_inst,[status(thm)],[])).
% 1.90/1.55 tff(2273,plain,
% 1.90/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a434) | c3_1(a434) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | c1_1(a408) | c2_1(a434) | (~c1_1(a434))),
% 1.90/1.55 inference(modus_ponens,[status(thm)],[2272, 2271])).
% 1.90/1.55 tff(2274,plain,
% 1.90/1.55 ($false),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2273, 150, 2267, 2190, 2218, 2217, 2159, 346, 2225, 2266])).
% 1.90/1.55 tff(2275,plain,(hskp19 | hskp1 | c1_1(a402) | c0_1(a403) | c2_1(a403) | (~c1_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.90/1.55 tff(2276,plain,
% 1.90/1.55 (hskp19),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2275, 12, 105, 336, 335, 107, 106, 108, 55])).
% 1.90/1.55 tff(2277,plain,
% 1.90/1.55 (c1_1(a445)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[458, 2276])).
% 1.90/1.55 tff(2278,plain,
% 1.90/1.55 (~c0_1(a445)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[332, 2276])).
% 1.90/1.55 tff(2279,plain,
% 1.90/1.55 (c3_1(a445)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[470, 2276])).
% 1.90/1.55 tff(2280,plain,
% 1.90/1.55 (~c0_1(a402)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1548, 2279, 1995, 105, 12, 2278, 2277])).
% 1.90/1.55 tff(2281,plain,
% 1.90/1.55 (~hskp2),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[520, 2280])).
% 1.90/1.55 tff(2282,plain,
% 1.90/1.55 (c2_1(a402)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1654, 2280, 12, 2281])).
% 1.90/1.55 tff(2283,plain,
% 1.90/1.55 (c3_1(a402)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1674, 150, 12, 2190, 2189, 2280, 2159, 2282, 1595])).
% 1.90/1.55 tff(2284,plain,
% 1.90/1.55 (hskp2 | hskp1 | c2_1(a403) | c1_1(a403)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[502, 150, 336, 33])).
% 1.90/1.55 tff(2285,plain,
% 1.90/1.55 (c1_1(a403)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2284, 2281, 335, 12])).
% 1.90/1.55 tff(2286,plain,
% 1.90/1.55 (hskp16),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2215, 2285, 336])).
% 1.90/1.55 tff(2287,plain,
% 1.90/1.55 (~c3_1(a434)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1016, 2286])).
% 1.90/1.55 tff(2288,plain,
% 1.90/1.55 (~c0_1(a434)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1022, 2286])).
% 1.90/1.55 tff(2289,plain,
% 1.90/1.55 (~c2_1(a434)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2040, 150, 12, 2280, 2288, 2287, 2282, 1595, 2283])).
% 1.90/1.55 tff(2290,plain,
% 1.90/1.55 (c1_1(a434)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1044, 2286])).
% 1.90/1.55 tff(2291,plain,
% 1.90/1.55 (hskp7 | c2_1(a434)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1032, 150, 2281, 2290, 2287, 118])).
% 1.90/1.55 tff(2292,plain,
% 1.90/1.55 (hskp7),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2291, 2289])).
% 1.90/1.55 tff(2293,plain,
% 1.90/1.55 (~c3_1(a410)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[254, 2292])).
% 1.90/1.55 tff(2294,plain,
% 1.90/1.55 (~c1_1(a410)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[260, 2292])).
% 1.90/1.55 tff(2295,plain,
% 1.90/1.55 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(2296,plain,
% 1.90/1.55 ((hskp13 | hskp2 | (~ndr1_0) | c2_1(a403) | (~c1_1(a403)) | (~c3_1(a403))) <=> (hskp13 | hskp2 | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(2297,plain,
% 1.90/1.55 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a403) | (~c1_1(a403)) | (~c3_1(a403)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403))))),
% 1.90/1.55 inference(monotonicity,[status(thm)],[2296])).
% 1.90/1.55 tff(2298,plain,
% 1.90/1.55 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a403) | (~c1_1(a403)) | (~c3_1(a403)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403)))),
% 1.90/1.55 inference(transitivity,[status(thm)],[2297, 2295])).
% 1.90/1.55 tff(2299,plain,
% 1.90/1.55 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a403) | (~c1_1(a403)) | (~c3_1(a403)))),
% 1.90/1.55 inference(quant_inst,[status(thm)],[])).
% 1.90/1.55 tff(2300,plain,
% 1.90/1.55 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c1_1(a403))),
% 1.90/1.55 inference(modus_ponens,[status(thm)],[2299, 2298])).
% 1.90/1.55 tff(2301,plain,
% 1.90/1.55 (hskp13 | hskp2 | c2_1(a403) | (~c1_1(a403))),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2300, 150, 1989, 271])).
% 1.90/1.55 tff(2302,plain,
% 1.90/1.55 (hskp13),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2301, 2285, 335, 2281])).
% 1.90/1.55 tff(2303,plain,
% 1.90/1.55 (~c0_1(a427)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[284, 2302])).
% 1.90/1.55 tff(2304,plain,
% 1.90/1.55 (c0_1(a410)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[295, 2292])).
% 1.90/1.55 tff(2305,plain,
% 1.90/1.55 (c2_1(a427)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[306, 2302])).
% 1.90/1.55 tff(2306,plain,
% 1.90/1.55 (c1_1(a427)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[317, 2302])).
% 1.90/1.55 tff(2307,plain,
% 1.90/1.55 ($false),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[324, 150, 12, 2306, 2305, 2304, 2303, 2294, 2293, 22])).
% 1.90/1.55 tff(2308,plain,(hskp1 | c2_1(a403) | c0_1(a403) | c1_1(a402) | (~c1_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.90/1.55 tff(2309,plain,
% 1.90/1.55 (hskp1),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2308, 335, 336, 105, 107, 106, 108, 55])).
% 1.90/1.55 tff(2310,plain,
% 1.90/1.55 (~c3_1(a401)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[794, 2309])).
% 1.90/1.55 tff(2311,plain,
% 1.90/1.55 (c1_1(a401)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[805, 2309])).
% 1.90/1.55 tff(2312,plain,
% 1.90/1.55 (c0_1(a401)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[816, 2309])).
% 1.90/1.55 tff(2313,plain,
% 1.90/1.55 (hskp20),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[823, 150, 2312, 2311, 2310, 483])).
% 1.90/1.55 tff(2314,plain,
% 1.90/1.55 (~c2_1(a449)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[914, 2313])).
% 1.90/1.55 tff(2315,plain,
% 1.90/1.55 (c3_1(a449)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[908, 2313])).
% 1.90/1.55 tff(2316,plain,
% 1.90/1.55 (c1_1(a449)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[834, 2313])).
% 1.90/1.55 tff(2317,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a449) | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a449) | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(2318,plain,
% 1.90/1.55 ((hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a403) | c0_1(a403) | (~c3_1(a403))) <=> (hskp10 | c2_1(a449) | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(2319,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a403) | c0_1(a403) | (~c3_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a449) | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449))))),
% 1.90/1.55 inference(monotonicity,[status(thm)],[2318])).
% 1.90/1.55 tff(2320,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a403) | c0_1(a403) | (~c3_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a449) | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.90/1.55 inference(transitivity,[status(thm)],[2319, 2317])).
% 1.90/1.55 tff(2321,plain,
% 1.90/1.55 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a403) | c0_1(a403) | (~c3_1(a403)))),
% 1.90/1.55 inference(quant_inst,[status(thm)],[])).
% 1.90/1.55 tff(2322,plain,
% 1.90/1.55 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a449) | c0_1(a403) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449))),
% 1.90/1.55 inference(modus_ponens,[status(thm)],[2321, 2320])).
% 1.90/1.55 tff(2323,plain,
% 1.90/1.55 (hskp10),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2322, 150, 2316, 2315, 2314, 336, 335, 1989, 2169])).
% 1.90/1.55 tff(2324,plain,
% 1.90/1.55 (~c2_1(a418)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2181, 2323])).
% 1.90/1.55 tff(2325,plain,
% 1.90/1.55 (~c0_1(a418)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2187, 2323])).
% 1.90/1.55 tff(2326,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c0_1(a408) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a408)) | (~c3_1(a408)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a408) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(2327,plain,
% 1.90/1.55 ((hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408))) <=> (hskp11 | c0_1(a408) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(2328,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c0_1(a408) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a408)) | (~c3_1(a408))))),
% 1.90/1.55 inference(monotonicity,[status(thm)],[2327])).
% 1.90/1.55 tff(2329,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a408) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.90/1.55 inference(transitivity,[status(thm)],[2328, 2326])).
% 1.90/1.55 tff(2330,plain,
% 1.90/1.55 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.90/1.55 inference(quant_inst,[status(thm)],[])).
% 1.90/1.55 tff(2331,plain,
% 1.90/1.55 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a408) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a408)) | (~c3_1(a408))),
% 1.90/1.55 inference(modus_ponens,[status(thm)],[2330, 2329])).
% 1.90/1.55 tff(2332,plain,
% 1.90/1.55 (hskp11),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2331, 150, 2190, 2189, 2312, 2311, 2159, 2310, 1117])).
% 1.90/1.55 tff(2333,plain,
% 1.90/1.55 (~c2_1(a420)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1223, 2332])).
% 1.90/1.55 tff(2334,plain,
% 1.90/1.55 (~c1_1(a420)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1106, 2332])).
% 1.90/1.55 tff(2335,plain,
% 1.90/1.55 (c1_1(a418)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2200, 2323])).
% 1.90/1.55 tff(2336,plain,
% 1.90/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c1_1(a420) | c2_1(a420) | c0_1(a418) | c2_1(a418) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)) | (~c3_1(a420)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c1_1(a420) | c2_1(a420) | c0_1(a418) | c2_1(a418) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)) | (~c3_1(a420)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(2337,plain,
% 1.90/1.55 (((~ndr1_0) | c2_1(a420) | c1_1(a420) | (~c3_1(a420)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a418) | c2_1(a418) | (~c1_1(a418))) <=> (c1_1(a420) | c2_1(a420) | c0_1(a418) | c2_1(a418) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)) | (~c3_1(a420)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(2338,plain,
% 1.90/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a420) | c1_1(a420) | (~c3_1(a420)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a418) | c2_1(a418) | (~c1_1(a418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c1_1(a420) | c2_1(a420) | c0_1(a418) | c2_1(a418) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)) | (~c3_1(a420))))),
% 1.90/1.55 inference(monotonicity,[status(thm)],[2337])).
% 1.90/1.55 tff(2339,plain,
% 1.90/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a420) | c1_1(a420) | (~c3_1(a420)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a418) | c2_1(a418) | (~c1_1(a418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c1_1(a420) | c2_1(a420) | c0_1(a418) | c2_1(a418) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)) | (~c3_1(a420)))),
% 1.90/1.55 inference(transitivity,[status(thm)],[2338, 2336])).
% 1.90/1.55 tff(2340,plain,
% 1.90/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a420) | c1_1(a420) | (~c3_1(a420)) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a418) | c2_1(a418) | (~c1_1(a418)))),
% 1.90/1.55 inference(quant_inst,[status(thm)],[])).
% 1.90/1.55 tff(2341,plain,
% 1.90/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c1_1(a420) | c2_1(a420) | c0_1(a418) | c2_1(a418) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c1_1(a418)) | (~c3_1(a420))),
% 1.90/1.55 inference(modus_ponens,[status(thm)],[2340, 2339])).
% 1.90/1.55 tff(2342,plain,
% 1.90/1.55 (~c3_1(a420)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2341, 150, 2335, 2190, 2189, 2334, 2333, 2325, 2324, 2159, 43])).
% 1.90/1.55 tff(2343,plain,
% 1.90/1.55 (~c0_1(a420)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[1100, 2332])).
% 1.90/1.55 tff(2344,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(2345,plain,
% 1.90/1.55 ((hskp0 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a420) | c1_1(a420) | c0_1(a420)) <=> (hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(2346,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a420) | c1_1(a420) | c0_1(a420))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408))))),
% 1.90/1.55 inference(monotonicity,[status(thm)],[2345])).
% 1.90/1.55 tff(2347,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a420) | c1_1(a420) | c0_1(a420))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)))),
% 1.90/1.55 inference(transitivity,[status(thm)],[2346, 2344])).
% 1.90/1.55 tff(2348,plain,
% 1.90/1.55 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c2_1(a420) | c1_1(a420) | c0_1(a420))),
% 1.90/1.55 inference(quant_inst,[status(thm)],[])).
% 1.90/1.55 tff(2349,plain,
% 1.90/1.55 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408))),
% 1.90/1.55 inference(modus_ponens,[status(thm)],[2348, 2347])).
% 1.90/1.55 tff(2350,plain,
% 1.90/1.55 (hskp0),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[2349, 150, 2190, 2189, 2343, 2334, 2333, 2159, 2150])).
% 1.90/1.55 tff(2351,plain,
% 1.90/1.55 (~c3_1(a400)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[405, 2350])).
% 1.90/1.55 tff(2352,plain,
% 1.90/1.55 (c2_1(a400)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[374, 2350])).
% 1.90/1.55 tff(2353,plain,
% 1.90/1.55 (c1_1(a400)),
% 1.90/1.55 inference(unit_resolution,[status(thm)],[385, 2350])).
% 1.90/1.55 tff(2354,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a420) | c1_1(a420) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c3_1(a420))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a420) | c1_1(a420) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c3_1(a420))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(2355,plain,
% 1.90/1.55 ((hskp3 | (~ndr1_0) | c3_1(a400) | (~c2_1(a400)) | (~c1_1(a400)) | c1_1(a420) | c0_1(a420) | c3_1(a420)) <=> (hskp3 | c0_1(a420) | c1_1(a420) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c3_1(a420))),
% 1.90/1.55 inference(rewrite,[status(thm)],[])).
% 1.90/1.55 tff(2356,plain,
% 1.90/1.55 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a400) | (~c2_1(a400)) | (~c1_1(a400)) | c1_1(a420) | c0_1(a420) | c3_1(a420))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a420) | c1_1(a420) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c3_1(a420)))),
% 1.90/1.56 inference(monotonicity,[status(thm)],[2355])).
% 1.90/1.56 tff(2357,plain,
% 1.90/1.56 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a400) | (~c2_1(a400)) | (~c1_1(a400)) | c1_1(a420) | c0_1(a420) | c3_1(a420))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a420) | c1_1(a420) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c3_1(a420))),
% 1.90/1.56 inference(transitivity,[status(thm)],[2356, 2354])).
% 1.90/1.56 tff(2358,plain,
% 1.90/1.56 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a400) | (~c2_1(a400)) | (~c1_1(a400)) | c1_1(a420) | c0_1(a420) | c3_1(a420))),
% 1.90/1.56 inference(quant_inst,[status(thm)],[])).
% 1.90/1.56 tff(2359,plain,
% 1.90/1.56 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a420) | c1_1(a420) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)) | c3_1(a420)),
% 1.90/1.56 inference(modus_ponens,[status(thm)],[2358, 2357])).
% 1.90/1.56 tff(2360,plain,
% 1.90/1.56 ($false),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2359, 150, 1995, 2353, 2352, 2343, 2334, 2351, 1426, 2342])).
% 1.90/1.56 tff(2361,plain,(c2_1(a403) | c0_1(a403) | c1_1(a402) | (~c1_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.90/1.56 tff(2362,plain,
% 1.90/1.56 (c2_1(a403)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2361, 336, 105, 107, 106, 108, 55])).
% 1.90/1.56 tff(2363,plain,
% 1.90/1.56 (~c0_1(a402)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[1548, 1996, 1995, 105, 12, 333, 1997])).
% 1.90/1.56 tff(2364,plain,
% 1.90/1.56 (c2_1(a402)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[1654, 2363, 12, 23])).
% 1.90/1.56 tff(2365,plain,
% 1.90/1.56 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402))),
% 1.90/1.56 inference(rewrite,[status(thm)],[])).
% 1.90/1.56 tff(2366,plain,
% 1.90/1.56 ((hskp1 | (~ndr1_0) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402))) <=> (hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402))),
% 1.90/1.56 inference(rewrite,[status(thm)],[])).
% 1.90/1.56 tff(2367,plain,
% 1.90/1.56 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402)))),
% 1.90/1.56 inference(monotonicity,[status(thm)],[2366])).
% 1.90/1.56 tff(2368,plain,
% 1.90/1.56 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402))),
% 1.90/1.56 inference(transitivity,[status(thm)],[2367, 2365])).
% 1.90/1.56 tff(2369,plain,
% 1.90/1.56 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c0_1(a402) | c3_1(a402) | (~c2_1(a402)))),
% 1.90/1.56 inference(quant_inst,[status(thm)],[])).
% 1.90/1.56 tff(2370,plain,
% 1.90/1.56 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a402) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | c3_1(a402)),
% 1.90/1.56 inference(modus_ponens,[status(thm)],[2369, 2368])).
% 1.90/1.56 tff(2371,plain,
% 1.90/1.56 (c3_1(a402)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2370, 150, 12, 2363, 336, 2362, 1989, 2364, 1595])).
% 1.90/1.56 tff(2372,plain,
% 1.90/1.56 (~c2_1(a434)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2040, 150, 12, 2363, 2034, 2033, 2364, 1595, 2371])).
% 1.90/1.56 tff(2373,plain,
% 1.90/1.56 ($false),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2048, 150, 2042, 2363, 2034, 2033, 105, 2364, 346, 2372])).
% 1.90/1.56 tff(2374,plain,(hskp2 | c1_1(a402) | hskp1 | c0_1(a403) | (~c0_1(a405)) | (~c1_1(a405)) | (~c3_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.90/1.56 tff(2375,plain,
% 1.90/1.56 (hskp2),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2374, 12, 105, 336, 108, 107, 106, 55])).
% 1.90/1.56 tff(2376,plain,
% 1.90/1.56 (c0_1(a402)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[520, 2375])).
% 1.90/1.56 tff(2377,plain,
% 1.90/1.56 (~c2_1(a402)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[509, 2375])).
% 1.90/1.56 tff(2378,assumption,(c3_1(a402)), introduced(assumption)).
% 1.90/1.56 tff(2379,assumption,(c3_1(a403)), introduced(assumption)).
% 1.90/1.56 tff(2380,plain,
% 1.90/1.56 ((~c3_1(a402)) | (~c0_1(a402)) | (~c1_1(a403))),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2262, 150, 336, 2379, 105, 531])).
% 1.90/1.56 tff(2381,plain,
% 1.90/1.56 (~c1_1(a403)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2380, 2378, 1439])).
% 1.90/1.56 tff(2382,plain,
% 1.90/1.56 (~hskp3),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[1994, 2379])).
% 1.90/1.56 tff(2383,plain,
% 1.90/1.56 (hskp18),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2099, 2378, 2382, 2054])).
% 1.90/1.56 tff(2384,plain,
% 1.90/1.56 (~c3_1(a440)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[1521, 2383])).
% 1.90/1.56 tff(2385,plain,
% 1.90/1.56 (~c2_1(a440)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[1527, 2383])).
% 1.90/1.56 tff(2386,plain,
% 1.90/1.56 (c0_1(a440)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[1539, 2383])).
% 1.90/1.56 tff(2387,plain,
% 1.90/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a440) | c3_1(a440) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | (~c0_1(a440)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a440) | c3_1(a440) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | (~c0_1(a440)))),
% 1.90/1.56 inference(rewrite,[status(thm)],[])).
% 1.90/1.56 tff(2388,plain,
% 1.90/1.56 (((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~c3_1(a402))) <=> (c2_1(a440) | c3_1(a440) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | (~c0_1(a440)))),
% 1.90/1.56 inference(rewrite,[status(thm)],[])).
% 1.90/1.56 tff(2389,plain,
% 1.90/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~c3_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a440) | c3_1(a440) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | (~c0_1(a440))))),
% 1.90/1.56 inference(monotonicity,[status(thm)],[2388])).
% 1.90/1.56 tff(2390,plain,
% 1.90/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~c3_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a440) | c3_1(a440) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | (~c0_1(a440)))),
% 1.90/1.56 inference(transitivity,[status(thm)],[2389, 2387])).
% 1.90/1.56 tff(2391,plain,
% 1.90/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~c3_1(a402)))),
% 1.90/1.56 inference(quant_inst,[status(thm)],[])).
% 1.90/1.56 tff(2392,plain,
% 1.90/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a440) | c3_1(a440) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | (~c0_1(a440))),
% 1.90/1.56 inference(modus_ponens,[status(thm)],[2391, 2390])).
% 1.90/1.56 tff(2393,plain,
% 1.90/1.56 ($false),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2392, 150, 2386, 2385, 2384, 1561, 2379, 105, 2054, 1497, 2378, 2381])).
% 1.90/1.56 tff(2394,plain,((~c3_1(a402)) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)) | c0_1(a403)), inference(lemma,lemma(discharge,[]))).
% 1.90/1.56 tff(2395,plain,
% 1.90/1.56 (~c3_1(a402)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2394, 2377, 1989, 105, 2362, 2376, 336])).
% 1.90/1.56 tff(2396,plain,
% 1.90/1.56 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a403) | (~c2_1(a403)) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a403) | (~c2_1(a403)) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403)))),
% 1.90/1.56 inference(rewrite,[status(thm)],[])).
% 1.90/1.56 tff(2397,plain,
% 1.90/1.56 ((hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a403) | (~c2_1(a403)) | (~c1_1(a403))) <=> (hskp1 | c0_1(a403) | (~c2_1(a403)) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403)))),
% 1.90/1.56 inference(rewrite,[status(thm)],[])).
% 1.90/1.56 tff(2398,plain,
% 1.90/1.56 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a403) | (~c2_1(a403)) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a403) | (~c2_1(a403)) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403))))),
% 1.90/1.56 inference(monotonicity,[status(thm)],[2397])).
% 1.90/1.56 tff(2399,plain,
% 1.90/1.56 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a403) | (~c2_1(a403)) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a403) | (~c2_1(a403)) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403)))),
% 1.90/1.56 inference(transitivity,[status(thm)],[2398, 2396])).
% 1.90/1.56 tff(2400,plain,
% 1.90/1.56 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a402) | c3_1(a402) | (~c0_1(a402)) | c0_1(a403) | (~c2_1(a403)) | (~c1_1(a403)))),
% 1.90/1.56 inference(quant_inst,[status(thm)],[])).
% 1.90/1.56 tff(2401,plain,
% 1.90/1.56 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a403) | (~c2_1(a403)) | c1_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403))),
% 1.90/1.56 inference(modus_ponens,[status(thm)],[2400, 2399])).
% 1.90/1.56 tff(2402,plain,
% 1.90/1.56 (hskp1 | (~c2_1(a403)) | c3_1(a402) | (~c0_1(a402)) | (~c1_1(a403))),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2401, 150, 336, 105, 22])).
% 1.90/1.56 tff(2403,plain,
% 1.90/1.56 (~c1_1(a403)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2402, 2395, 2362, 12, 2376])).
% 1.90/1.56 tff(2404,plain,
% 1.90/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a460) | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460)))),
% 1.90/1.56 inference(rewrite,[status(thm)],[])).
% 1.90/1.56 tff(2405,plain,
% 1.90/1.56 (((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a403) | c0_1(a403) | (~c2_1(a403)) | c3_1(a460) | c0_1(a460) | c2_1(a460)) <=> (c2_1(a460) | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460)))),
% 1.90/1.56 inference(rewrite,[status(thm)],[])).
% 1.90/1.56 tff(2406,plain,
% 1.90/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a403) | c0_1(a403) | (~c2_1(a403)) | c3_1(a460) | c0_1(a460) | c2_1(a460))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a460) | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460))))),
% 1.90/1.56 inference(monotonicity,[status(thm)],[2405])).
% 1.90/1.56 tff(2407,plain,
% 1.90/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a403) | c0_1(a403) | (~c2_1(a403)) | c3_1(a460) | c0_1(a460) | c2_1(a460))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460)))),
% 1.90/1.56 inference(transitivity,[status(thm)],[2406, 2404])).
% 1.90/1.56 tff(2408,plain,
% 1.90/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a460) | c3_1(a460) | (~c1_1(a460)) | c1_1(a403) | c0_1(a403) | (~c2_1(a403)) | c3_1(a460) | c0_1(a460) | c2_1(a460))),
% 1.90/1.56 inference(quant_inst,[status(thm)],[])).
% 1.90/1.56 tff(2409,plain,
% 1.90/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a460) | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~ndr1_0) | c1_1(a403) | c0_1(a460) | (~c1_1(a460))),
% 1.90/1.56 inference(modus_ponens,[status(thm)],[2408, 2407])).
% 1.90/1.56 tff(2410,plain,
% 1.90/1.56 (c0_1(a460)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2409, 150, 242, 231, 225, 336, 1561, 346, 496])).
% 1.90/1.56 tff(2411,plain,
% 1.90/1.56 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0) | (~c0_1(a460)) | (~c1_1(a460)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.90/1.56 inference(rewrite,[status(thm)],[])).
% 1.90/1.56 tff(2412,plain,
% 1.90/1.56 ((hskp11 | (~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403))) <=> (hskp11 | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.90/1.56 inference(rewrite,[status(thm)],[])).
% 1.90/1.56 tff(2413,plain,
% 1.90/1.56 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0) | (~c0_1(a460)) | (~c1_1(a460))))),
% 1.90/1.56 inference(monotonicity,[status(thm)],[2412])).
% 1.90/1.56 tff(2414,plain,
% 1.90/1.56 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.90/1.56 inference(transitivity,[status(thm)],[2413, 2411])).
% 1.90/1.56 tff(2415,plain,
% 1.90/1.56 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)))),
% 1.90/1.56 inference(quant_inst,[status(thm)],[])).
% 1.90/1.56 tff(2416,plain,
% 1.90/1.56 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c3_1(a460) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0) | (~c0_1(a460)) | (~c1_1(a460))),
% 1.90/1.56 inference(modus_ponens,[status(thm)],[2415, 2414])).
% 1.90/1.56 tff(2417,plain,
% 1.90/1.56 (hskp11),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2416, 150, 242, 225, 336, 1561, 2379, 1117, 2410])).
% 1.90/1.56 tff(2418,plain,
% 1.90/1.56 (~c2_1(a420)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[1223, 2417])).
% 1.90/1.56 tff(2419,plain,
% 1.90/1.56 (~c1_1(a420)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[1106, 2417])).
% 1.90/1.56 tff(2420,plain,
% 1.90/1.56 (~c0_1(a420)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[1100, 2417])).
% 1.90/1.56 tff(2421,plain,
% 1.90/1.56 (hskp22),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2090, 150, 107, 106, 1439, 2054, 929, 158, 1998])).
% 1.90/1.56 tff(2422,plain,
% 1.90/1.56 (c2_1(a451)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[855, 2421])).
% 1.90/1.56 tff(2423,plain,
% 1.90/1.56 (c0_1(a451)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[866, 2421])).
% 1.90/1.56 tff(2424,plain,
% 1.90/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a460) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | (~c0_1(a460)) | (~c1_1(a460)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a460) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.90/1.56 inference(rewrite,[status(thm)],[])).
% 1.90/1.56 tff(2425,plain,
% 1.90/1.56 (((~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a420) | c0_1(a420) | c2_1(a420)) <=> (c3_1(a460) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.90/1.56 inference(rewrite,[status(thm)],[])).
% 1.90/1.56 tff(2426,plain,
% 1.90/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a420) | c0_1(a420) | c2_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a460) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | (~c0_1(a460)) | (~c1_1(a460))))),
% 1.90/1.56 inference(monotonicity,[status(thm)],[2425])).
% 1.90/1.56 tff(2427,plain,
% 1.90/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a420) | c0_1(a420) | c2_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a460) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | (~c0_1(a460)) | (~c1_1(a460)))),
% 1.90/1.56 inference(transitivity,[status(thm)],[2426, 2424])).
% 1.90/1.56 tff(2428,plain,
% 1.90/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c3_1(a460) | (~c1_1(a460)) | (~c0_1(a460)) | c1_1(a420) | c0_1(a420) | c2_1(a420))),
% 1.90/1.56 inference(quant_inst,[status(thm)],[])).
% 1.90/1.56 tff(2429,plain,
% 1.90/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a460) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | (~c0_1(a460)) | (~c1_1(a460))),
% 1.90/1.56 inference(modus_ponens,[status(thm)],[2428, 2427])).
% 1.90/1.56 tff(2430,plain,
% 1.90/1.56 (~c3_1(a451)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2429, 150, 242, 2423, 2422, 225, 2420, 2419, 2418, 11, 2410])).
% 1.90/1.56 tff(2431,plain,
% 1.90/1.56 (~c1_1(a451)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[844, 2421])).
% 1.90/1.56 tff(2432,plain,
% 1.90/1.56 ($false),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[1286, 150, 242, 2422, 225, 2431, 886, 2410, 2430])).
% 1.90/1.56 tff(2433,plain,(hskp19 | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c1_1(a403) | (~c1_1(a405)) | (~c3_1(a405)) | (~c0_1(a402)) | c2_1(a402) | c3_1(a402) | (~c0_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.90/1.56 tff(2434,plain,
% 1.90/1.56 (hskp19),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2433, 2403, 2362, 1989, 336, 107, 106, 2376, 2377, 2395, 108, 55])).
% 1.90/1.56 tff(2435,plain,
% 1.90/1.56 (c1_1(a445)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[458, 2434])).
% 1.90/1.56 tff(2436,plain,
% 1.90/1.56 (c3_1(a445)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[470, 2434])).
% 1.90/1.56 tff(2437,plain,
% 1.90/1.56 (~c0_1(a445)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[332, 2434])).
% 1.90/1.56 tff(2438,plain,
% 1.90/1.56 ($false),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[1548, 2437, 2436, 1995, 105, 12, 2376, 2435])).
% 1.90/1.56 tff(2439,plain,(hskp1 | c1_1(a402) | c0_1(a403) | (~c1_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.90/1.56 tff(2440,plain,
% 1.90/1.56 (hskp1),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[2439, 336, 105, 107, 106, 108, 55])).
% 1.90/1.56 tff(2441,plain,
% 1.90/1.56 (~c3_1(a401)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[794, 2440])).
% 1.90/1.56 tff(2442,plain,
% 1.90/1.56 (c1_1(a401)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[805, 2440])).
% 1.90/1.56 tff(2443,plain,
% 1.90/1.56 (c0_1(a401)),
% 1.90/1.56 inference(unit_resolution,[status(thm)],[816, 2440])).
% 1.90/1.56 tff(2444,plain,
% 1.90/1.56 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.90/1.56 inference(rewrite,[status(thm)],[])).
% 1.90/1.56 tff(2445,plain,
% 1.90/1.56 ((hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403))) <=> (hskp11 | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.90/1.56 inference(rewrite,[status(thm)],[])).
% 1.90/1.56 tff(2446,plain,
% 1.90/1.56 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401))))),
% 1.90/1.56 inference(monotonicity,[status(thm)],[2445])).
% 1.90/1.56 tff(2447,plain,
% 1.90/1.56 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.90/1.57 inference(transitivity,[status(thm)],[2446, 2444])).
% 1.90/1.57 tff(2448,plain,
% 1.90/1.57 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)))),
% 1.90/1.57 inference(quant_inst,[status(thm)],[])).
% 1.90/1.57 tff(2449,plain,
% 1.90/1.57 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401))),
% 1.90/1.57 inference(modus_ponens,[status(thm)],[2448, 2447])).
% 1.90/1.57 tff(2450,plain,
% 1.90/1.57 (hskp11),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2449, 150, 2443, 2442, 336, 2362, 1989, 2441, 1117])).
% 1.90/1.57 tff(2451,plain,
% 1.90/1.57 (~c2_1(a420)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1223, 2450])).
% 1.90/1.57 tff(2452,plain,
% 1.90/1.57 (~c1_1(a420)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1106, 2450])).
% 1.90/1.57 tff(2453,plain,
% 1.90/1.57 (~c0_1(a420)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1100, 2450])).
% 1.90/1.57 tff(2454,plain,
% 1.90/1.57 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0))),
% 1.90/1.57 inference(rewrite,[status(thm)],[])).
% 1.90/1.57 tff(2455,plain,
% 1.90/1.57 ((hskp0 | (~ndr1_0) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c2_1(a420) | c1_1(a420) | c0_1(a420)) <=> (hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0))),
% 1.90/1.57 inference(rewrite,[status(thm)],[])).
% 1.90/1.57 tff(2456,plain,
% 1.90/1.57 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c2_1(a420) | c1_1(a420) | c0_1(a420))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0)))),
% 1.90/1.57 inference(monotonicity,[status(thm)],[2455])).
% 1.90/1.57 tff(2457,plain,
% 1.90/1.57 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c2_1(a420) | c1_1(a420) | c0_1(a420))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0))),
% 1.90/1.57 inference(transitivity,[status(thm)],[2456, 2454])).
% 1.90/1.57 tff(2458,plain,
% 1.90/1.57 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | c2_1(a420) | c1_1(a420) | c0_1(a420))),
% 1.90/1.57 inference(quant_inst,[status(thm)],[])).
% 1.90/1.57 tff(2459,plain,
% 1.90/1.57 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a420) | c1_1(a420) | c2_1(a420) | c0_1(a403) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0)),
% 1.90/1.57 inference(modus_ponens,[status(thm)],[2458, 2457])).
% 1.90/1.57 tff(2460,plain,
% 1.90/1.57 (hskp0),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2459, 150, 2453, 2452, 2451, 336, 2362, 1989, 2150])).
% 1.90/1.57 tff(2461,plain,
% 1.90/1.57 (~c3_1(a400)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[405, 2460])).
% 1.90/1.57 tff(2462,plain,
% 1.90/1.57 (c2_1(a400)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[374, 2460])).
% 1.90/1.57 tff(2463,plain,
% 1.90/1.57 (c1_1(a400)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[385, 2460])).
% 1.90/1.57 tff(2464,plain,
% 1.90/1.57 (c3_1(a420)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2359, 150, 1995, 2463, 2462, 2453, 2452, 2461, 1426])).
% 1.90/1.57 tff(2465,plain,
% 1.90/1.57 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)))),
% 1.90/1.57 inference(rewrite,[status(thm)],[])).
% 1.90/1.57 tff(2466,plain,
% 1.90/1.57 ((hskp5 | hskp3 | (~ndr1_0) | c2_1(a420) | c0_1(a420) | (~c3_1(a420))) <=> (hskp5 | hskp3 | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)))),
% 1.90/1.57 inference(rewrite,[status(thm)],[])).
% 1.90/1.57 tff(2467,plain,
% 1.90/1.57 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a420) | c0_1(a420) | (~c3_1(a420)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420))))),
% 1.90/1.57 inference(monotonicity,[status(thm)],[2466])).
% 1.90/1.57 tff(2468,plain,
% 1.90/1.57 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a420) | c0_1(a420) | (~c3_1(a420)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)))),
% 1.90/1.57 inference(transitivity,[status(thm)],[2467, 2465])).
% 1.90/1.57 tff(2469,plain,
% 1.90/1.57 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a420) | c0_1(a420) | (~c3_1(a420)))),
% 1.90/1.57 inference(quant_inst,[status(thm)],[])).
% 1.90/1.57 tff(2470,plain,
% 1.90/1.57 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420))),
% 1.90/1.57 inference(modus_ponens,[status(thm)],[2469, 2468])).
% 1.90/1.57 tff(2471,plain,
% 1.90/1.57 (hskp5 | (~c3_1(a420))),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2470, 150, 1995, 2453, 2451, 54])).
% 1.90/1.57 tff(2472,plain,
% 1.90/1.57 (hskp5),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2471, 2464])).
% 1.90/1.57 tff(2473,plain,
% 1.90/1.57 (~c0_1(a408)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1334, 2472])).
% 1.90/1.57 tff(2474,plain,
% 1.90/1.57 (hskp20),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[823, 150, 2443, 2442, 2441, 483])).
% 1.90/1.57 tff(2475,plain,
% 1.90/1.57 (~c2_1(a449)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[914, 2474])).
% 1.90/1.57 tff(2476,plain,
% 1.90/1.57 (c3_1(a449)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[908, 2474])).
% 1.90/1.57 tff(2477,plain,
% 1.90/1.57 (c1_1(a449)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[834, 2474])).
% 1.90/1.57 tff(2478,plain,
% 1.90/1.57 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a449) | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c3_1(a449)) | (~c1_1(a449)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a449) | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.90/1.57 inference(rewrite,[status(thm)],[])).
% 1.90/1.57 tff(2479,plain,
% 1.90/1.57 ((hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a420) | c0_1(a420) | (~c3_1(a420))) <=> (hskp10 | c2_1(a449) | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.90/1.57 inference(rewrite,[status(thm)],[])).
% 1.90/1.57 tff(2480,plain,
% 1.90/1.57 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a420) | c0_1(a420) | (~c3_1(a420)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c2_1(a449) | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c3_1(a449)) | (~c1_1(a449))))),
% 1.90/1.57 inference(monotonicity,[status(thm)],[2479])).
% 1.90/1.57 tff(2481,plain,
% 1.90/1.57 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a420) | c0_1(a420) | (~c3_1(a420)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a449) | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.90/1.57 inference(transitivity,[status(thm)],[2480, 2478])).
% 1.90/1.57 tff(2482,plain,
% 1.90/1.57 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a420) | c0_1(a420) | (~c3_1(a420)))),
% 1.90/1.57 inference(quant_inst,[status(thm)],[])).
% 1.90/1.57 tff(2483,plain,
% 1.90/1.57 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c2_1(a449) | c0_1(a420) | c2_1(a420) | (~ndr1_0) | (~c3_1(a420)) | (~c3_1(a449)) | (~c1_1(a449))),
% 1.90/1.57 inference(modus_ponens,[status(thm)],[2482, 2481])).
% 1.90/1.57 tff(2484,plain,
% 1.90/1.57 (hskp10 | (~c3_1(a420))),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2483, 150, 2477, 2476, 2475, 2453, 2451, 2169])).
% 1.90/1.57 tff(2485,plain,
% 1.90/1.57 (hskp10),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2484, 2464])).
% 1.90/1.57 tff(2486,plain,
% 1.90/1.57 (~c2_1(a418)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2181, 2485])).
% 1.90/1.57 tff(2487,plain,
% 1.90/1.57 (~c0_1(a418)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2187, 2485])).
% 1.90/1.57 tff(2488,plain,
% 1.90/1.57 (c3_1(a408)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1345, 2472])).
% 1.90/1.57 tff(2489,plain,
% 1.90/1.57 (c2_1(a408)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1356, 2472])).
% 1.90/1.57 tff(2490,plain,
% 1.90/1.57 (c1_1(a418)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2200, 2485])).
% 1.90/1.57 tff(2491,plain,
% 1.90/1.57 ($false),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2341, 150, 2490, 2489, 2488, 2452, 2451, 2487, 2486, 2473, 43, 2464])).
% 1.90/1.57 tff(2492,plain,(c0_1(a403) | c1_1(a402) | (~c1_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.90/1.57 tff(2493,plain,
% 1.90/1.57 (c0_1(a403)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2492, 105, 93, 82, 104, 55])).
% 1.90/1.57 tff(2494,plain,
% 1.90/1.57 (c3_1(a402)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2028, 23, 12, 1997, 1996, 1995, 105, 333])).
% 1.90/1.57 tff(2495,plain,
% 1.90/1.57 ((~c3_1(a402)) | (~c2_1(a434))),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2040, 150, 12, 2030, 2034, 2033, 2031, 1595])).
% 1.90/1.57 tff(2496,plain,
% 1.90/1.57 (~c2_1(a434)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2495, 2494])).
% 1.90/1.57 tff(2497,plain,
% 1.90/1.57 (hskp7 | c2_1(a434)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1032, 150, 23, 2042, 2033, 118])).
% 1.90/1.57 tff(2498,plain,
% 1.90/1.57 (hskp7),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2497, 2496])).
% 1.90/1.57 tff(2499,plain,
% 1.90/1.57 (~c3_1(a410)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[254, 2498])).
% 1.90/1.57 tff(2500,plain,
% 1.90/1.57 (~c1_1(a410)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[260, 2498])).
% 1.90/1.57 tff(2501,plain,
% 1.90/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a402) | c0_1(a434) | c2_1(a403) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | c2_1(a434) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a402) | c0_1(a434) | c2_1(a403) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | c2_1(a434) | (~c1_1(a434)))),
% 1.90/1.57 inference(rewrite,[status(thm)],[])).
% 1.90/1.57 tff(2502,plain,
% 1.90/1.57 (((~ndr1_0) | c2_1(a403) | c1_1(a403) | (~c3_1(a403)) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a434) | c2_1(a434) | (~c1_1(a434))) <=> (c0_1(a402) | c0_1(a434) | c2_1(a403) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | c2_1(a434) | (~c1_1(a434)))),
% 1.90/1.57 inference(rewrite,[status(thm)],[])).
% 1.90/1.57 tff(2503,plain,
% 1.90/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a403) | c1_1(a403) | (~c3_1(a403)) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a434) | c2_1(a434) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a402) | c0_1(a434) | c2_1(a403) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | c2_1(a434) | (~c1_1(a434))))),
% 1.90/1.57 inference(monotonicity,[status(thm)],[2502])).
% 1.90/1.57 tff(2504,plain,
% 1.90/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a403) | c1_1(a403) | (~c3_1(a403)) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a434) | c2_1(a434) | (~c1_1(a434)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a402) | c0_1(a434) | c2_1(a403) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | c2_1(a434) | (~c1_1(a434)))),
% 1.90/1.57 inference(transitivity,[status(thm)],[2503, 2501])).
% 1.90/1.57 tff(2505,plain,
% 1.90/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a403) | c1_1(a403) | (~c3_1(a403)) | c0_1(a402) | (~c2_1(a402)) | (~c3_1(a402)) | c0_1(a434) | c2_1(a434) | (~c1_1(a434)))),
% 1.90/1.57 inference(quant_inst,[status(thm)],[])).
% 1.90/1.57 tff(2506,plain,
% 1.90/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a402) | c0_1(a434) | c2_1(a403) | (~c3_1(a403)) | (~c2_1(a402)) | (~ndr1_0) | (~c3_1(a402)) | c1_1(a403) | c2_1(a434) | (~c1_1(a434))),
% 1.90/1.57 inference(modus_ponens,[status(thm)],[2505, 2504])).
% 1.90/1.57 tff(2507,plain,
% 1.90/1.57 ((~c3_1(a402)) | c1_1(a403) | c2_1(a434)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2506, 150, 2042, 2030, 2034, 335, 1989, 2031, 43])).
% 1.90/1.57 tff(2508,plain,
% 1.90/1.57 (c1_1(a403)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2507, 2496, 2494])).
% 1.90/1.57 tff(2509,plain,
% 1.90/1.57 (hskp13),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2301, 2508, 335, 23])).
% 1.90/1.57 tff(2510,plain,
% 1.90/1.57 (~c0_1(a427)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[284, 2509])).
% 1.90/1.57 tff(2511,plain,
% 1.90/1.57 (c0_1(a410)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[295, 2498])).
% 1.90/1.57 tff(2512,plain,
% 1.90/1.57 (c2_1(a427)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[306, 2509])).
% 1.90/1.57 tff(2513,plain,
% 1.90/1.57 (c1_1(a427)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[317, 2509])).
% 1.90/1.57 tff(2514,plain,
% 1.90/1.57 ($false),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[324, 150, 12, 2513, 2512, 2511, 2510, 2500, 2499, 22])).
% 1.90/1.57 tff(2515,plain,(hskp2 | hskp1 | c2_1(a403) | c1_1(a402) | (~c0_1(a405)) | (~c1_1(a405)) | (~c3_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.90/1.57 tff(2516,plain,
% 1.90/1.57 (hskp2),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2515, 12, 335, 105, 104, 93, 82, 55])).
% 1.90/1.57 tff(2517,plain,
% 1.90/1.57 (c0_1(a402)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[520, 2516])).
% 1.90/1.57 tff(2518,plain,
% 1.90/1.57 (~c2_1(a402)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[509, 2516])).
% 1.90/1.57 tff(2519,plain,
% 1.90/1.57 (hskp19),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2132, 2518, 105, 2517, 56, 12, 55])).
% 1.90/1.57 tff(2520,plain,
% 1.90/1.57 (c1_1(a445)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[458, 2519])).
% 1.90/1.57 tff(2521,plain,
% 1.90/1.57 (c3_1(a445)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[470, 2519])).
% 1.90/1.57 tff(2522,plain,
% 1.90/1.57 (~c0_1(a445)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[332, 2519])).
% 1.90/1.57 tff(2523,plain,
% 1.90/1.57 ($false),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1548, 2522, 2521, 2056, 105, 12, 2517, 2520])).
% 1.90/1.57 tff(2524,plain,(hskp1 | c1_1(a402) | hskp21 | hskp24 | c2_1(a403)), inference(lemma,lemma(discharge,[]))).
% 1.90/1.57 tff(2525,plain,
% 1.90/1.57 (hskp1),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2524, 335, 56, 55, 105])).
% 1.90/1.57 tff(2526,plain,
% 1.90/1.57 (~c3_1(a401)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[794, 2525])).
% 1.90/1.57 tff(2527,plain,
% 1.90/1.57 (c1_1(a401)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[805, 2525])).
% 1.90/1.57 tff(2528,plain,
% 1.90/1.57 (c0_1(a401)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[816, 2525])).
% 1.90/1.57 tff(2529,assumption,(~c2_1(a401)), introduced(assumption)).
% 1.90/1.57 tff(2530,plain,
% 1.90/1.57 (hskp11 | hskp2 | c2_1(a401)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[949, 150, 836, 837, 687])).
% 1.90/1.57 tff(2531,plain,
% 1.90/1.57 (hskp11),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2530, 2529, 23])).
% 1.90/1.57 tff(2532,plain,
% 1.90/1.57 (~c2_1(a420)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1223, 2531])).
% 1.90/1.57 tff(2533,plain,
% 1.90/1.57 (~c1_1(a420)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1106, 2531])).
% 1.90/1.57 tff(2534,plain,
% 1.90/1.57 (~c0_1(a420)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1100, 2531])).
% 1.90/1.57 tff(2535,plain,
% 1.90/1.57 (hskp7 | hskp2 | c2_1(a401)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1186, 150, 838, 837, 118])).
% 1.90/1.57 tff(2536,plain,
% 1.90/1.57 (hskp7),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2535, 2529, 23])).
% 1.90/1.57 tff(2537,plain,
% 1.90/1.57 (hskp22),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[992, 2536, 836, 838, 837])).
% 1.90/1.57 tff(2538,plain,
% 1.90/1.57 (c2_1(a451)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[855, 2537])).
% 1.90/1.57 tff(2539,plain,
% 1.90/1.57 (c0_1(a451)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[866, 2537])).
% 1.90/1.57 tff(2540,plain,
% 1.90/1.57 (~c3_1(a451)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1631, 150, 2539, 2538, 836, 838, 2534, 2533, 2532, 837, 11])).
% 1.90/1.57 tff(2541,plain,
% 1.90/1.57 (~c1_1(a451)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[844, 2537])).
% 1.90/1.57 tff(2542,plain,
% 1.90/1.57 ($false),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[892, 150, 2538, 836, 838, 2541, 837, 886, 2540])).
% 1.90/1.57 tff(2543,plain,(c2_1(a401) | (~c0_1(a401)) | (~c1_1(a401)) | c3_1(a401) | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.90/1.57 tff(2544,plain,
% 1.90/1.57 (c2_1(a401)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2543, 23, 838, 837, 836])).
% 1.90/1.57 tff(2545,plain,
% 1.90/1.57 (((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401)) | (~c0_1(a401)))) <=> ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.90/1.57 inference(rewrite,[status(thm)],[])).
% 1.90/1.57 tff(2546,plain,
% 1.90/1.57 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.90/1.57 inference(quant_inst,[status(thm)],[])).
% 1.90/1.57 tff(2547,plain,
% 1.90/1.57 ((~![U: $i] : (hskp24 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp19 | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401)) | (~c0_1(a401))),
% 1.90/1.57 inference(modus_ponens,[status(thm)],[2546, 2545])).
% 1.90/1.57 tff(2548,plain,
% 1.90/1.57 (hskp19 | (~c2_1(a401))),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2547, 150, 55, 836, 838, 129])).
% 1.90/1.57 tff(2549,plain,
% 1.90/1.57 (hskp19),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2548, 2544])).
% 1.90/1.57 tff(2550,plain,
% 1.90/1.57 (~c0_1(a445)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[332, 2549])).
% 1.90/1.57 tff(2551,plain,
% 1.90/1.57 (c1_1(a445)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[458, 2549])).
% 1.90/1.57 tff(2552,plain,
% 1.90/1.57 (c3_1(a445)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[470, 2549])).
% 1.90/1.57 tff(2553,plain,
% 1.90/1.57 (~hskp22),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[897, 2552, 837, 838, 836, 2551, 2550])).
% 1.90/1.57 tff(2554,plain,
% 1.90/1.57 (~hskp7),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[992, 2553, 836, 838, 837])).
% 1.90/1.57 tff(2555,plain,
% 1.90/1.57 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~c0_1(a403)) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~c0_1(a403)) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0))),
% 1.90/1.57 inference(rewrite,[status(thm)],[])).
% 1.90/1.57 tff(2556,plain,
% 1.90/1.57 ((hskp16 | hskp7 | (~ndr1_0) | c2_1(a403) | (~c3_1(a403)) | (~c0_1(a403))) <=> (hskp16 | hskp7 | (~c0_1(a403)) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0))),
% 1.90/1.57 inference(rewrite,[status(thm)],[])).
% 1.90/1.57 tff(2557,plain,
% 1.90/1.57 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a403) | (~c3_1(a403)) | (~c0_1(a403)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~c0_1(a403)) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0)))),
% 1.90/1.57 inference(monotonicity,[status(thm)],[2556])).
% 1.90/1.57 tff(2558,plain,
% 1.90/1.57 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a403) | (~c3_1(a403)) | (~c0_1(a403)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~c0_1(a403)) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0))),
% 1.90/1.57 inference(transitivity,[status(thm)],[2557, 2555])).
% 1.90/1.57 tff(2559,plain,
% 1.90/1.57 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a403) | (~c3_1(a403)) | (~c0_1(a403)))),
% 1.90/1.57 inference(quant_inst,[status(thm)],[])).
% 1.90/1.57 tff(2560,plain,
% 1.90/1.57 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~c0_1(a403)) | c2_1(a403) | (~c3_1(a403)) | (~ndr1_0)),
% 1.90/1.57 inference(modus_ponens,[status(thm)],[2559, 2558])).
% 1.90/1.57 tff(2561,plain,
% 1.90/1.57 (hskp16 | hskp7 | (~c0_1(a403)) | c2_1(a403)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2560, 150, 2379, 1003])).
% 1.90/1.57 tff(2562,plain,
% 1.90/1.57 (hskp16),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2561, 2554, 1257, 335])).
% 1.90/1.57 tff(2563,plain,
% 1.90/1.57 (~c0_1(a434)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1022, 2562])).
% 1.90/1.57 tff(2564,plain,
% 1.90/1.57 (~c3_1(a434)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1016, 2562])).
% 1.90/1.57 tff(2565,plain,
% 1.90/1.57 (c2_1(a434)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1055, 2564, 106, 836, 838, 2563, 837, 2554, 23, 108])).
% 1.90/1.57 tff(2566,plain,
% 1.90/1.57 (hskp14),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1072, 2554, 106, 23, 838, 837, 836, 2562, 108])).
% 1.90/1.57 tff(2567,plain,
% 1.90/1.57 (~c1_1(a428)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[421, 2566])).
% 1.90/1.57 tff(2568,plain,
% 1.90/1.57 (hskp15),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1713, 2554, 2382])).
% 1.90/1.57 tff(2569,plain,
% 1.90/1.57 (~c3_1(a430)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1719, 2568])).
% 1.90/1.57 tff(2570,plain,
% 1.90/1.57 (c2_1(a428)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[438, 2566])).
% 1.90/1.57 tff(2571,plain,
% 1.90/1.57 (c2_1(a430)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1732, 2568])).
% 1.90/1.57 tff(2572,plain,
% 1.90/1.57 (c0_1(a430)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1743, 2568])).
% 1.90/1.57 tff(2573,plain,
% 1.90/1.57 (c1_1(a434)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1044, 2562])).
% 1.90/1.57 tff(2574,plain,
% 1.90/1.57 (~c3_1(a428)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1750, 150, 2573, 2572, 2571, 2570, 2563, 2569, 2567, 704, 2565])).
% 1.90/1.57 tff(2575,plain,
% 1.90/1.57 ($false),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1092, 150, 2570, 836, 838, 2567, 837, 886, 2574])).
% 1.90/1.57 tff(2576,plain,(hskp2 | (~c0_1(a401)) | (~c1_1(a401)) | c3_1(a401) | (~c3_1(a405)) | (~c0_1(a405)) | (~c0_1(a403)) | c2_1(a403) | (~c3_1(a403)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.90/1.57 tff(2577,plain,
% 1.90/1.57 (hskp2),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2576, 2528, 2527, 2526, 82, 104, 2493, 335, 2055, 55])).
% 1.90/1.57 tff(2578,plain,
% 1.90/1.57 (~c2_1(a402)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[509, 2577])).
% 1.90/1.57 tff(2579,plain,
% 1.90/1.57 ($false),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[892, 150, 856, 836, 838, 845, 837, 886, 2064])).
% 1.90/1.57 tff(2580,plain,((~hskp22) | (~c0_1(a401)) | (~c1_1(a401)) | c3_1(a401) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.90/1.57 tff(2581,plain,
% 1.90/1.57 (~hskp22),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2580, 2528, 2527, 2526, 2056])).
% 1.90/1.57 tff(2582,plain,
% 1.90/1.57 (hskp20),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[823, 150, 2528, 2527, 2526, 483])).
% 1.90/1.57 tff(2583,plain,
% 1.90/1.57 (~c2_1(a449)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[914, 2582])).
% 1.90/1.57 tff(2584,plain,
% 1.90/1.57 (c0_1(a402)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[520, 2577])).
% 1.90/1.57 tff(2585,plain,
% 1.90/1.57 (c3_1(a449)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[908, 2582])).
% 1.90/1.57 tff(2586,plain,
% 1.90/1.57 (c1_1(a449)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[834, 2582])).
% 1.90/1.57 tff(2587,plain,
% 1.90/1.57 (hskp22 | c3_1(a402)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[940, 150, 2586, 2585, 2584, 2583, 2578, 929])).
% 1.90/1.57 tff(2588,plain,
% 1.90/1.57 (c3_1(a402)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2587, 2581])).
% 1.90/1.57 tff(2589,plain,
% 1.90/1.57 (hskp18),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2099, 2588, 2056, 2578])).
% 1.90/1.57 tff(2590,plain,
% 1.90/1.57 (~c3_1(a440)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1521, 2589])).
% 1.90/1.57 tff(2591,plain,
% 1.90/1.57 (~c2_1(a440)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1527, 2589])).
% 1.90/1.57 tff(2592,plain,
% 1.90/1.57 (c0_1(a440)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1539, 2589])).
% 1.90/1.57 tff(2593,plain,
% 1.90/1.57 ($false),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2130, 150, 2581, 2586, 2585, 2592, 2583, 2591, 2590, 929])).
% 1.90/1.57 tff(2594,plain,(c2_1(a403) | c1_1(a402) | hskp24 | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.90/1.57 tff(2595,plain,
% 1.90/1.57 (c2_1(a403)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2594, 105, 55, 56])).
% 1.90/1.57 tff(2596,plain,
% 1.90/1.57 (c1_1(a401)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[805, 2139])).
% 1.90/1.57 tff(2597,plain,
% 1.90/1.57 (c0_1(a401)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[816, 2139])).
% 1.90/1.57 tff(2598,plain,
% 1.90/1.57 (~hskp22),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2580, 2597, 2596, 2140, 2056])).
% 1.90/1.57 tff(2599,plain,
% 1.90/1.57 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp11 | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0))),
% 1.90/1.57 inference(rewrite,[status(thm)],[])).
% 1.90/1.57 tff(2600,plain,
% 1.90/1.57 ((hskp22 | hskp11 | (~ndr1_0) | (~c2_1(a403)) | (~c3_1(a403)) | (~c0_1(a403))) <=> (hskp22 | hskp11 | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0))),
% 1.90/1.57 inference(rewrite,[status(thm)],[])).
% 1.90/1.57 tff(2601,plain,
% 1.90/1.57 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(a403)) | (~c3_1(a403)) | (~c0_1(a403)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0)))),
% 1.90/1.57 inference(monotonicity,[status(thm)],[2600])).
% 1.90/1.57 tff(2602,plain,
% 1.90/1.57 (((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(a403)) | (~c3_1(a403)) | (~c0_1(a403)))) <=> ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp11 | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0))),
% 1.90/1.57 inference(transitivity,[status(thm)],[2601, 2599])).
% 1.90/1.57 tff(2603,plain,
% 1.90/1.57 ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(a403)) | (~c3_1(a403)) | (~c0_1(a403)))),
% 1.90/1.57 inference(quant_inst,[status(thm)],[])).
% 1.90/1.57 tff(2604,plain,
% 1.90/1.57 ((~![U: $i] : (hskp22 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp11 | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | (~ndr1_0)),
% 1.90/1.57 inference(modus_ponens,[status(thm)],[2603, 2602])).
% 1.90/1.57 tff(2605,plain,
% 1.90/1.57 (hskp22 | hskp11 | (~c0_1(a403)) | (~c2_1(a403))),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2604, 150, 2055, 961])).
% 1.90/1.57 tff(2606,plain,
% 1.90/1.57 (hskp11),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[2605, 2598, 2493, 2595])).
% 1.90/1.57 tff(2607,plain,
% 1.90/1.57 (~c2_1(a420)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1223, 2606])).
% 1.90/1.57 tff(2608,plain,
% 1.90/1.57 (~c1_1(a420)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1106, 2606])).
% 1.90/1.57 tff(2609,plain,
% 1.90/1.57 (~c0_1(a420)),
% 1.90/1.57 inference(unit_resolution,[status(thm)],[1100, 2606])).
% 1.90/1.57 tff(2610,plain,
% 1.90/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a420) | c1_1(a420) | c2_1(a420) | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.90/1.57 inference(rewrite,[status(thm)],[])).
% 1.90/1.57 tff(2611,plain,
% 1.90/1.57 (((~ndr1_0) | (~c2_1(a403)) | (~c3_1(a403)) | (~c0_1(a403)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420)) <=> (c0_1(a420) | c1_1(a420) | c2_1(a420) | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.90/1.57 inference(rewrite,[status(thm)],[])).
% 1.90/1.57 tff(2612,plain,
% 1.90/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a403)) | (~c3_1(a403)) | (~c0_1(a403)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a420) | c1_1(a420) | c2_1(a420) | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401))))),
% 1.90/1.57 inference(monotonicity,[status(thm)],[2611])).
% 1.90/1.57 tff(2613,plain,
% 1.90/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a403)) | (~c3_1(a403)) | (~c0_1(a403)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)))),
% 1.90/1.58 inference(transitivity,[status(thm)],[2612, 2610])).
% 1.90/1.58 tff(2614,plain,
% 1.90/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a403)) | (~c3_1(a403)) | (~c0_1(a403)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a420) | c0_1(a420) | c2_1(a420))),
% 1.90/1.58 inference(quant_inst,[status(thm)],[])).
% 1.90/1.58 tff(2615,plain,
% 1.90/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a420) | c1_1(a420) | c2_1(a420) | (~c0_1(a403)) | (~c2_1(a403)) | (~c3_1(a403)) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401))),
% 1.90/1.58 inference(modus_ponens,[status(thm)],[2614, 2613])).
% 1.90/1.58 tff(2616,plain,
% 1.90/1.58 ($false),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[2615, 150, 2597, 2596, 2609, 2608, 2607, 2493, 2595, 2055, 2140, 11])).
% 1.90/1.58 tff(2617,plain,(c1_1(a402) | hskp21 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.90/1.58 tff(2618,plain,
% 1.90/1.58 (c1_1(a402)),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[2617, 56, 55])).
% 1.90/1.58 tff(2619,plain,
% 1.90/1.58 (((~hskp2) | (~c1_1(a402))) <=> ((~hskp2) | (~c1_1(a402)))),
% 1.90/1.58 inference(rewrite,[status(thm)],[])).
% 1.90/1.58 tff(2620,plain,
% 1.90/1.58 (((~c1_1(a402)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a402)))),
% 1.90/1.58 inference(rewrite,[status(thm)],[])).
% 1.90/1.58 tff(2621,axiom,((~c1_1(a402)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.90/1.58 tff(2622,plain,
% 1.90/1.58 ((~hskp2) | (~c1_1(a402))),
% 1.90/1.58 inference(modus_ponens,[status(thm)],[2621, 2620])).
% 1.90/1.58 tff(2623,plain,
% 1.90/1.58 ((~hskp2) | (~c1_1(a402))),
% 1.90/1.58 inference(modus_ponens,[status(thm)],[2622, 2619])).
% 1.90/1.58 tff(2624,plain,
% 1.90/1.58 (~hskp2),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[2623, 2618])).
% 1.90/1.58 tff(2625,plain,
% 1.90/1.58 (hskp19),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[326, 12, 23, 108, 107, 106, 55])).
% 1.90/1.58 tff(2626,plain,
% 1.90/1.58 (c1_1(a445)),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[458, 2625])).
% 1.90/1.58 tff(2627,plain,
% 1.90/1.58 (~c0_1(a445)),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[332, 2625])).
% 1.90/1.58 tff(2628,plain,
% 1.90/1.58 (c3_1(a445)),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[470, 2625])).
% 1.90/1.58 tff(2629,plain,
% 1.90/1.58 (hskp16 | hskp3),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[1402, 150, 484, 473, 472, 1396])).
% 1.90/1.58 tff(2630,plain,
% 1.90/1.58 (hskp16),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[2629, 44])).
% 1.90/1.58 tff(2631,plain,
% 1.90/1.58 (~c3_1(a434)),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[1016, 2630])).
% 1.90/1.58 tff(2632,plain,
% 1.90/1.58 (~c0_1(a434)),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[1022, 2630])).
% 1.90/1.58 tff(2633,plain,
% 1.90/1.58 (c1_1(a434)),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[1044, 2630])).
% 1.90/1.58 tff(2634,assumption,(c1_1(a434)), introduced(assumption)).
% 1.90/1.58 tff(2635,plain,
% 1.90/1.58 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.90/1.58 inference(rewrite,[status(thm)],[])).
% 1.90/1.58 tff(2636,plain,
% 1.90/1.58 ((hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434))) <=> (hskp1 | c0_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.90/1.58 inference(rewrite,[status(thm)],[])).
% 1.90/1.58 tff(2637,plain,
% 1.90/1.58 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c0_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a434)) | (~c1_1(a434))))),
% 1.90/1.58 inference(monotonicity,[status(thm)],[2636])).
% 1.90/1.58 tff(2638,plain,
% 1.90/1.58 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.90/1.58 inference(transitivity,[status(thm)],[2637, 2635])).
% 1.90/1.58 tff(2639,plain,
% 1.90/1.58 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.90/1.58 inference(quant_inst,[status(thm)],[])).
% 1.90/1.58 tff(2640,plain,
% 1.90/1.58 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c0_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c2_1(a434)) | (~c1_1(a434))),
% 1.90/1.58 inference(modus_ponens,[status(thm)],[2639, 2638])).
% 1.90/1.58 tff(2641,plain,
% 1.90/1.58 (~c2_1(a434)),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[2640, 150, 12, 2634, 982, 1047, 972, 971, 22])).
% 1.90/1.58 tff(2642,plain,
% 1.90/1.58 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c1_1(a434)))),
% 1.90/1.58 inference(rewrite,[status(thm)],[])).
% 1.90/1.58 tff(2643,plain,
% 1.90/1.58 ((hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434))) <=> (hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c1_1(a434)))),
% 1.90/1.58 inference(rewrite,[status(thm)],[])).
% 1.90/1.58 tff(2644,plain,
% 1.90/1.58 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c1_1(a434))))),
% 1.90/1.58 inference(monotonicity,[status(thm)],[2643])).
% 1.90/1.58 tff(2645,plain,
% 1.90/1.58 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c1_1(a434)))),
% 1.90/1.58 inference(transitivity,[status(thm)],[2644, 2642])).
% 1.90/1.58 tff(2646,plain,
% 1.90/1.58 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a434) | c3_1(a434) | (~c1_1(a434)))),
% 1.90/1.58 inference(quant_inst,[status(thm)],[])).
% 1.90/1.58 tff(2647,plain,
% 1.90/1.58 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a434) | c3_1(a434) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | (~c1_1(a434))),
% 1.90/1.58 inference(modus_ponens,[status(thm)],[2646, 2645])).
% 1.90/1.58 tff(2648,plain,
% 1.90/1.58 (hskp9),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[2647, 150, 2634, 982, 1047, 1026, 972, 971, 640])).
% 1.90/1.58 tff(2649,plain,
% 1.90/1.58 (~c1_1(a416)),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[663, 2648])).
% 1.90/1.58 tff(2650,plain,
% 1.90/1.58 (~c0_1(a416)),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[669, 2648])).
% 1.90/1.58 tff(2651,plain,
% 1.90/1.58 (~c2_1(a416)),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[1486, 150, 2634, 1047, 1026, 2650, 2649, 346, 2641])).
% 1.90/1.58 tff(2652,plain,
% 1.90/1.58 ($false),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[676, 150, 23, 12, 2650, 2649, 33, 2651])).
% 1.90/1.58 tff(2653,plain,((~hskp7) | hskp2 | hskp1 | (~c1_1(a434)) | c0_1(a434) | c3_1(a434)), inference(lemma,lemma(discharge,[]))).
% 1.90/1.58 tff(2654,plain,
% 1.90/1.58 (~hskp7),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[2653, 2633, 12, 23, 2632, 2631])).
% 1.90/1.58 tff(2655,plain,
% 1.90/1.58 (hskp7 | c2_1(a434)),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[1032, 150, 23, 2633, 2631, 118])).
% 1.90/1.58 tff(2656,plain,
% 1.90/1.58 (c2_1(a434)),
% 1.90/1.58 inference(unit_resolution,[status(thm)],[2655, 2654])).
% 1.90/1.58 tff(2657,plain,
% 1.90/1.58 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a445) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c2_1(a445)) | (~c3_1(a445)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a445) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c2_1(a445)) | (~c3_1(a445)))),
% 1.90/1.58 inference(rewrite,[status(thm)],[])).
% 1.90/1.58 tff(2658,plain,
% 1.90/1.58 ((hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434))) <=> (hskp1 | c0_1(a445) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c2_1(a445)) | (~c3_1(a445)))),
% 1.90/1.58 inference(rewrite,[status(thm)],[])).
% 1.90/1.58 tff(2659,plain,
% 1.90/1.58 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a445) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c2_1(a445)) | (~c3_1(a445))))),
% 1.90/1.58 inference(monotonicity,[status(thm)],[2658])).
% 1.90/1.58 tff(2660,plain,
% 1.90/1.58 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a445) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c2_1(a445)) | (~c3_1(a445)))),
% 1.90/1.58 inference(transitivity,[status(thm)],[2659, 2657])).
% 1.90/1.58 tff(2661,plain,
% 1.90/1.58 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a445) | (~c2_1(a445)) | (~c3_1(a445)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))),
% 1.97/1.58 inference(quant_inst,[status(thm)],[])).
% 1.97/1.58 tff(2662,plain,
% 1.97/1.58 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a445) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c2_1(a445)) | (~c3_1(a445))),
% 1.97/1.58 inference(modus_ponens,[status(thm)],[2661, 2660])).
% 1.97/1.58 tff(2663,plain,
% 1.97/1.58 ((~c2_1(a434)) | (~c2_1(a445))),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[2662, 150, 12, 473, 472, 2632, 2631, 1595])).
% 1.97/1.58 tff(2664,plain,
% 1.97/1.58 (~c2_1(a445)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[2663, 2656])).
% 1.97/1.58 tff(2665,plain,
% 1.97/1.58 (hskp5 | hskp3 | c2_1(a445)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1447, 150, 473, 472, 54])).
% 1.97/1.58 tff(2666,plain,
% 1.97/1.58 (hskp5),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[2665, 2664, 44])).
% 1.97/1.58 tff(2667,plain,
% 1.97/1.58 (~c0_1(a408)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1334, 2666])).
% 1.97/1.58 tff(2668,plain,
% 1.97/1.58 (hskp13),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[2021, 2664])).
% 1.97/1.58 tff(2669,plain,
% 1.97/1.58 (~c0_1(a427)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[284, 2668])).
% 1.97/1.58 tff(2670,plain,
% 1.97/1.58 (c3_1(a408)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1345, 2666])).
% 1.97/1.58 tff(2671,plain,
% 1.97/1.58 (c2_1(a408)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1356, 2666])).
% 1.97/1.58 tff(2672,plain,
% 1.97/1.58 (c2_1(a427)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[306, 2668])).
% 1.97/1.58 tff(2673,plain,
% 1.97/1.58 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a427) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a427)) | c3_1(a427))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a427) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a427)) | c3_1(a427))),
% 1.97/1.58 inference(rewrite,[status(thm)],[])).
% 1.97/1.58 tff(2674,plain,
% 1.97/1.58 ((hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a427) | c3_1(a427) | (~c2_1(a427))) <=> (hskp1 | c0_1(a427) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a427)) | c3_1(a427))),
% 1.97/1.58 inference(rewrite,[status(thm)],[])).
% 1.97/1.58 tff(2675,plain,
% 1.97/1.58 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a427) | c3_1(a427) | (~c2_1(a427)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a427) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a427)) | c3_1(a427)))),
% 1.97/1.58 inference(monotonicity,[status(thm)],[2674])).
% 1.97/1.58 tff(2676,plain,
% 1.97/1.58 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a427) | c3_1(a427) | (~c2_1(a427)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a427) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a427)) | c3_1(a427))),
% 1.97/1.58 inference(transitivity,[status(thm)],[2675, 2673])).
% 1.97/1.58 tff(2677,plain,
% 1.97/1.58 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c0_1(a427) | c3_1(a427) | (~c2_1(a427)))),
% 1.97/1.58 inference(quant_inst,[status(thm)],[])).
% 1.97/1.58 tff(2678,plain,
% 1.97/1.58 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a427) | c0_1(a408) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | (~c2_1(a427)) | c3_1(a427)),
% 1.97/1.58 inference(modus_ponens,[status(thm)],[2677, 2676])).
% 1.97/1.58 tff(2679,plain,
% 1.97/1.58 (c3_1(a427)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[2678, 150, 12, 2672, 2671, 2670, 2669, 2667, 1595])).
% 1.97/1.58 tff(2680,plain,
% 1.97/1.58 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a427) | (~ndr1_0) | (~c2_1(a427)) | (~c3_1(a427)) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a427) | (~ndr1_0) | (~c2_1(a427)) | (~c3_1(a427)) | (~c2_1(a434)))),
% 1.97/1.58 inference(rewrite,[status(thm)],[])).
% 1.97/1.58 tff(2681,plain,
% 1.97/1.58 ((hskp1 | (~ndr1_0) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434))) <=> (hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a427) | (~ndr1_0) | (~c2_1(a427)) | (~c3_1(a427)) | (~c2_1(a434)))),
% 1.97/1.58 inference(rewrite,[status(thm)],[])).
% 1.97/1.58 tff(2682,plain,
% 1.97/1.58 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a427) | (~ndr1_0) | (~c2_1(a427)) | (~c3_1(a427)) | (~c2_1(a434))))),
% 1.97/1.58 inference(monotonicity,[status(thm)],[2681])).
% 1.97/1.58 tff(2683,plain,
% 1.97/1.58 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a427) | (~ndr1_0) | (~c2_1(a427)) | (~c3_1(a427)) | (~c2_1(a434)))),
% 1.97/1.58 inference(transitivity,[status(thm)],[2682, 2680])).
% 1.97/1.58 tff(2684,plain,
% 1.97/1.58 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)))),
% 1.97/1.58 inference(quant_inst,[status(thm)],[])).
% 1.97/1.58 tff(2685,plain,
% 1.97/1.58 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a434) | c3_1(a434) | c0_1(a427) | (~ndr1_0) | (~c2_1(a427)) | (~c3_1(a427)) | (~c2_1(a434))),
% 1.97/1.58 inference(modus_ponens,[status(thm)],[2684, 2683])).
% 1.97/1.58 tff(2686,plain,
% 1.97/1.58 ($false),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[2685, 150, 12, 2672, 2632, 2631, 2669, 1595, 2656, 2679])).
% 1.97/1.58 tff(2687,plain,(hskp3 | hskp1 | (~c3_1(a445)) | c0_1(a445) | hskp2 | (~c1_1(a445))), inference(lemma,lemma(discharge,[]))).
% 1.97/1.58 tff(2688,plain,
% 1.97/1.58 (hskp3),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[2687, 12, 2628, 2627, 23, 2626])).
% 1.97/1.58 tff(2689,plain,
% 1.97/1.58 (~c0_1(a403)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1272, 2688])).
% 1.97/1.58 tff(2690,plain,
% 1.97/1.58 (~c3_1(a403)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1994, 2688])).
% 1.97/1.58 tff(2691,plain,
% 1.97/1.58 (~c2_1(a403)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1644, 2688])).
% 1.97/1.58 tff(2692,plain,
% 1.97/1.58 (c1_1(a403)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[502, 150, 23, 12, 2689, 2691, 33])).
% 1.97/1.58 tff(2693,plain,
% 1.97/1.58 (hskp11),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[738, 2692, 23, 2628, 2626, 2691, 2690, 2627, 2689, 12])).
% 1.97/1.58 tff(2694,plain,
% 1.97/1.58 (~c2_1(a420)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1223, 2693])).
% 1.97/1.58 tff(2695,plain,
% 1.97/1.58 (~c1_1(a420)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1106, 2693])).
% 1.97/1.58 tff(2696,plain,
% 1.97/1.58 (~c0_1(a420)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1100, 2693])).
% 1.97/1.58 tff(2697,plain,
% 1.97/1.58 ($false),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1126, 150, 23, 12, 2696, 2695, 2694, 33])).
% 1.97/1.58 tff(2698,plain,(hskp1 | hskp2 | (~c0_1(a405)) | (~c1_1(a405)) | (~c3_1(a405)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.97/1.58 tff(2699,plain,
% 1.97/1.58 (hskp1),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[2698, 2624, 104, 93, 82, 55])).
% 1.97/1.58 tff(2700,plain,
% 1.97/1.58 (c0_1(a401)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[816, 2699])).
% 1.97/1.58 tff(2701,plain,
% 1.97/1.58 (~c3_1(a401)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[794, 2699])).
% 1.97/1.58 tff(2702,plain,
% 1.97/1.58 (c1_1(a401)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[805, 2699])).
% 1.97/1.58 tff(2703,plain,
% 1.97/1.58 (c2_1(a401)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[2543, 2702, 2624, 2701, 2700])).
% 1.97/1.58 tff(2704,plain,
% 1.97/1.58 (hskp19),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[2547, 150, 55, 2700, 2702, 129, 2703])).
% 1.97/1.58 tff(2705,plain,
% 1.97/1.58 (~c0_1(a445)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[332, 2704])).
% 1.97/1.58 tff(2706,plain,
% 1.97/1.58 (c1_1(a445)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[458, 2704])).
% 1.97/1.58 tff(2707,plain,
% 1.97/1.58 (c3_1(a445)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[470, 2704])).
% 1.97/1.58 tff(2708,plain,
% 1.97/1.58 (~hskp22),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[897, 2707, 2701, 2702, 2700, 2706, 2705])).
% 1.97/1.58 tff(2709,plain,
% 1.97/1.58 (~hskp7),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[992, 2708, 2700, 2702, 2701])).
% 1.97/1.58 tff(2710,plain,
% 1.97/1.58 (hskp11),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[968, 1189, 934])).
% 1.97/1.58 tff(2711,plain,
% 1.97/1.58 (~c1_1(a420)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1106, 2710])).
% 1.97/1.58 tff(2712,plain,
% 1.97/1.58 (~c0_1(a420)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1100, 2710])).
% 1.97/1.58 tff(2713,plain,
% 1.97/1.58 (~c2_1(a420)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1223, 2710])).
% 1.97/1.58 tff(2714,plain,
% 1.97/1.58 ($false),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1197, 2713, 2712, 106, 108, 838, 1189, 2711, 836, 837])).
% 1.97/1.58 tff(2715,plain,((~c2_1(a405)) | (~c3_1(a405)) | (~c0_1(a405)) | (~c1_1(a401)) | (~c0_1(a401)) | c3_1(a401) | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.97/1.58 tff(2716,plain,
% 1.97/1.58 (~c2_1(a405)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[2715, 82, 104, 2702, 2700, 2701, 2708])).
% 1.97/1.58 tff(2717,plain,
% 1.97/1.58 (hskp16 | hskp7 | c2_1(a405)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1009, 150, 104, 82, 1003])).
% 1.97/1.58 tff(2718,plain,
% 1.97/1.58 (hskp16),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[2717, 2716, 2709])).
% 1.97/1.58 tff(2719,plain,
% 1.97/1.58 (~c3_1(a434)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1016, 2718])).
% 1.97/1.58 tff(2720,plain,
% 1.97/1.58 (~c0_1(a434)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1022, 2718])).
% 1.97/1.58 tff(2721,plain,
% 1.97/1.58 (c2_1(a434)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1055, 2720, 82, 2700, 2702, 2719, 2701, 2709, 2624, 104])).
% 1.97/1.58 tff(2722,plain,
% 1.97/1.58 (hskp14),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1075, 2716, 104, 82, 2624, 2702, 2701, 2700, 2709])).
% 1.97/1.58 tff(2723,plain,
% 1.97/1.58 (~c1_1(a428)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[421, 2722])).
% 1.97/1.58 tff(2724,plain,
% 1.97/1.58 (c2_1(a428)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[438, 2722])).
% 1.97/1.58 tff(2725,plain,
% 1.97/1.58 (c1_1(a434)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1044, 2718])).
% 1.97/1.58 tff(2726,plain,
% 1.97/1.58 (~c3_1(a428)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1085, 150, 2725, 2724, 2700, 2720, 2723, 2701, 704, 2721, 2703])).
% 1.97/1.58 tff(2727,plain,
% 1.97/1.58 ($false),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[1092, 150, 2724, 2700, 2702, 2723, 2701, 886, 2726])).
% 1.97/1.58 tff(2728,plain,(hskp21 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.97/1.58 tff(2729,plain,
% 1.97/1.58 (hskp21),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[2728, 55])).
% 1.97/1.58 tff(2730,plain,
% 1.97/1.58 (((~hskp21) | (~c3_1(a450))) <=> ((~hskp21) | (~c3_1(a450)))),
% 1.97/1.58 inference(rewrite,[status(thm)],[])).
% 1.97/1.58 tff(2731,plain,
% 1.97/1.58 (((~c3_1(a450)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a450)))),
% 1.97/1.58 inference(rewrite,[status(thm)],[])).
% 1.97/1.58 tff(2732,axiom,((~c3_1(a450)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 1.97/1.58 tff(2733,plain,
% 1.97/1.58 ((~hskp21) | (~c3_1(a450))),
% 1.97/1.58 inference(modus_ponens,[status(thm)],[2732, 2731])).
% 1.97/1.58 tff(2734,plain,
% 1.97/1.58 ((~hskp21) | (~c3_1(a450))),
% 1.97/1.58 inference(modus_ponens,[status(thm)],[2733, 2730])).
% 1.97/1.58 tff(2735,plain,
% 1.97/1.58 (~c3_1(a450)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[2734, 2729])).
% 1.97/1.58 tff(2736,plain,
% 1.97/1.58 (((~hskp21) | (~c1_1(a450))) <=> ((~hskp21) | (~c1_1(a450)))),
% 1.97/1.58 inference(rewrite,[status(thm)],[])).
% 1.97/1.58 tff(2737,plain,
% 1.97/1.58 (((~c1_1(a450)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a450)))),
% 1.97/1.58 inference(rewrite,[status(thm)],[])).
% 1.97/1.58 tff(2738,axiom,((~c1_1(a450)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 1.97/1.58 tff(2739,plain,
% 1.97/1.58 ((~hskp21) | (~c1_1(a450))),
% 1.97/1.58 inference(modus_ponens,[status(thm)],[2738, 2737])).
% 1.97/1.58 tff(2740,plain,
% 1.97/1.58 ((~hskp21) | (~c1_1(a450))),
% 1.97/1.58 inference(modus_ponens,[status(thm)],[2739, 2736])).
% 1.97/1.58 tff(2741,plain,
% 1.97/1.58 (~c1_1(a450)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[2740, 2729])).
% 1.97/1.58 tff(2742,plain,
% 1.97/1.58 (((~hskp21) | (~c0_1(a450))) <=> ((~hskp21) | (~c0_1(a450)))),
% 1.97/1.58 inference(rewrite,[status(thm)],[])).
% 1.97/1.58 tff(2743,plain,
% 1.97/1.58 (((~c0_1(a450)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a450)))),
% 1.97/1.58 inference(rewrite,[status(thm)],[])).
% 1.97/1.58 tff(2744,axiom,((~c0_1(a450)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 1.97/1.58 tff(2745,plain,
% 1.97/1.58 ((~hskp21) | (~c0_1(a450))),
% 1.97/1.58 inference(modus_ponens,[status(thm)],[2744, 2743])).
% 1.97/1.58 tff(2746,plain,
% 1.97/1.58 ((~hskp21) | (~c0_1(a450))),
% 1.97/1.58 inference(modus_ponens,[status(thm)],[2745, 2742])).
% 1.97/1.58 tff(2747,plain,
% 1.97/1.58 (~c0_1(a450)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[2746, 2729])).
% 1.97/1.58 tff(2748,assumption,(~hskp25), introduced(assumption)).
% 1.97/1.58 tff(2749,plain,
% 1.97/1.58 (^[U: $i] : refl((hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.97/1.58 inference(bind,[status(th)],[])).
% 1.97/1.58 tff(2750,plain,
% 1.97/1.58 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.97/1.58 inference(quant_intro,[status(thm)],[2749])).
% 1.97/1.58 tff(2751,plain,
% 1.97/1.58 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.97/1.58 inference(rewrite,[status(thm)],[])).
% 1.97/1.58 tff(2752,plain,
% 1.97/1.58 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp25) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp25))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp25) | hskp3) <=> ((hskp25 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3))), rewrite(((hskp25 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3) <=> (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp25) | hskp3) <=> (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.97/1.58 inference(bind,[status(th)],[])).
% 1.97/1.58 tff(2753,plain,
% 1.97/1.58 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp25) | hskp3) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.97/1.58 inference(quant_intro,[status(thm)],[2752])).
% 1.97/1.58 tff(2754,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp25) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.97/1.58 tff(2755,plain,
% 1.97/1.58 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.97/1.58 inference(modus_ponens,[status(thm)],[2754, 2753])).
% 1.97/1.58 tff(2756,plain,
% 1.97/1.58 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.97/1.58 inference(modus_ponens,[status(thm)],[2755, 2751])).
% 1.97/1.58 tff(2757,plain,(
% 1.97/1.58 ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.97/1.58 inference(skolemize,[status(sab)],[2756])).
% 1.97/1.58 tff(2758,plain,
% 1.97/1.58 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.97/1.58 inference(modus_ponens,[status(thm)],[2757, 2750])).
% 1.97/1.58 tff(2759,plain,
% 1.97/1.58 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp25 | hskp3 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | (~c2_1(a450)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp25 | hskp3 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | (~c2_1(a450)))),
% 1.97/1.58 inference(rewrite,[status(thm)],[])).
% 1.97/1.58 tff(2760,plain,
% 1.97/1.58 ((hskp25 | hskp3 | (~ndr1_0) | c1_1(a450) | c0_1(a450) | (~c2_1(a450))) <=> (hskp25 | hskp3 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | (~c2_1(a450)))),
% 1.97/1.58 inference(rewrite,[status(thm)],[])).
% 1.97/1.58 tff(2761,plain,
% 1.97/1.58 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp25 | hskp3 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | (~c2_1(a450))))),
% 1.97/1.58 inference(monotonicity,[status(thm)],[2760])).
% 1.97/1.58 tff(2762,plain,
% 1.97/1.58 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp25 | hskp3 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | (~c2_1(a450)))),
% 1.97/1.58 inference(transitivity,[status(thm)],[2761, 2759])).
% 1.97/1.58 tff(2763,plain,
% 1.97/1.58 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)))),
% 1.97/1.58 inference(quant_inst,[status(thm)],[])).
% 1.97/1.58 tff(2764,plain,
% 1.97/1.58 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp25 | hskp3 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | (~c2_1(a450))),
% 1.97/1.58 inference(modus_ponens,[status(thm)],[2763, 2762])).
% 1.97/1.58 tff(2765,plain,
% 1.97/1.58 (hskp25 | hskp3 | (~c2_1(a450))),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[2764, 150, 2747, 2741, 2758])).
% 1.97/1.58 tff(2766,plain,
% 1.97/1.58 (~c2_1(a450)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[2765, 44, 2748])).
% 1.97/1.58 tff(2767,assumption,(hskp0), introduced(assumption)).
% 1.97/1.58 tff(2768,plain,
% 1.97/1.58 (~c3_1(a400)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[405, 2767])).
% 1.97/1.58 tff(2769,assumption,(~c3_1(a450)), introduced(assumption)).
% 1.97/1.58 tff(2770,assumption,(~c1_1(a450)), introduced(assumption)).
% 1.97/1.58 tff(2771,assumption,(~c0_1(a450)), introduced(assumption)).
% 1.97/1.58 tff(2772,plain,
% 1.97/1.58 (c2_1(a400)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[374, 2767])).
% 1.97/1.58 tff(2773,plain,
% 1.97/1.58 (c1_1(a400)),
% 1.97/1.58 inference(unit_resolution,[status(thm)],[385, 2767])).
% 1.97/1.58 tff(2774,plain,
% 1.97/1.58 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)))),
% 1.97/1.58 inference(rewrite,[status(thm)],[])).
% 1.97/1.58 tff(2775,plain,
% 1.97/1.59 ((hskp3 | (~ndr1_0) | c3_1(a400) | (~c2_1(a400)) | (~c1_1(a400)) | c1_1(a450) | c0_1(a450) | c3_1(a450)) <=> (hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)))),
% 1.97/1.59 inference(rewrite,[status(thm)],[])).
% 1.97/1.59 tff(2776,plain,
% 1.97/1.59 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a400) | (~c2_1(a400)) | (~c1_1(a400)) | c1_1(a450) | c0_1(a450) | c3_1(a450))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400))))),
% 1.97/1.59 inference(monotonicity,[status(thm)],[2775])).
% 1.97/1.59 tff(2777,plain,
% 1.97/1.59 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a400) | (~c2_1(a400)) | (~c1_1(a400)) | c1_1(a450) | c0_1(a450) | c3_1(a450))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400)))),
% 1.97/1.59 inference(transitivity,[status(thm)],[2776, 2774])).
% 1.97/1.59 tff(2778,plain,
% 1.97/1.59 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a400) | (~c2_1(a400)) | (~c1_1(a400)) | c1_1(a450) | c0_1(a450) | c3_1(a450))),
% 1.97/1.59 inference(quant_inst,[status(thm)],[])).
% 1.97/1.59 tff(2779,plain,
% 1.97/1.59 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | (~c1_1(a400))),
% 1.97/1.59 inference(modus_ponens,[status(thm)],[2778, 2777])).
% 1.97/1.59 tff(2780,plain,
% 1.97/1.59 ($false),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2779, 150, 44, 2773, 2772, 2771, 2770, 2769, 2768, 1426])).
% 1.97/1.59 tff(2781,plain,((~hskp0) | hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450)), inference(lemma,lemma(discharge,[]))).
% 1.97/1.59 tff(2782,plain,
% 1.97/1.59 (~hskp0),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2781, 44, 2747, 2741, 2735])).
% 1.97/1.59 tff(2783,plain,
% 1.97/1.59 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | c0_1(a450) | c3_1(a450) | (~ndr1_0) | c2_1(a450))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp0 | c0_1(a450) | c3_1(a450) | (~ndr1_0) | c2_1(a450))),
% 1.97/1.59 inference(rewrite,[status(thm)],[])).
% 1.97/1.59 tff(2784,plain,
% 1.97/1.59 ((hskp27 | hskp0 | (~ndr1_0) | c2_1(a450) | c0_1(a450) | c3_1(a450)) <=> (hskp27 | hskp0 | c0_1(a450) | c3_1(a450) | (~ndr1_0) | c2_1(a450))),
% 1.97/1.59 inference(rewrite,[status(thm)],[])).
% 1.97/1.59 tff(2785,plain,
% 1.97/1.59 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | (~ndr1_0) | c2_1(a450) | c0_1(a450) | c3_1(a450))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | c0_1(a450) | c3_1(a450) | (~ndr1_0) | c2_1(a450)))),
% 1.97/1.59 inference(monotonicity,[status(thm)],[2784])).
% 1.97/1.59 tff(2786,plain,
% 1.97/1.59 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | (~ndr1_0) | c2_1(a450) | c0_1(a450) | c3_1(a450))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp0 | c0_1(a450) | c3_1(a450) | (~ndr1_0) | c2_1(a450))),
% 1.97/1.59 inference(transitivity,[status(thm)],[2785, 2783])).
% 1.97/1.59 tff(2787,plain,
% 1.97/1.59 ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp0 | (~ndr1_0) | c2_1(a450) | c0_1(a450) | c3_1(a450))),
% 1.97/1.59 inference(quant_inst,[status(thm)],[])).
% 1.97/1.59 tff(2788,plain,
% 1.97/1.59 ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp0 | c0_1(a450) | c3_1(a450) | (~ndr1_0) | c2_1(a450)),
% 1.97/1.59 inference(modus_ponens,[status(thm)],[2787, 2786])).
% 1.97/1.59 tff(2789,plain,
% 1.97/1.59 (hskp27 | hskp0 | c2_1(a450)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2788, 150, 2747, 2735, 356])).
% 1.97/1.59 tff(2790,plain,
% 1.97/1.59 (hskp27),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2789, 2782, 2766])).
% 1.97/1.59 tff(2791,plain,
% 1.97/1.59 (hskp19),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[200, 2790, 55])).
% 1.97/1.59 tff(2792,plain,
% 1.97/1.59 (c1_1(a445)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[458, 2791])).
% 1.97/1.59 tff(2793,plain,
% 1.97/1.59 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | c2_1(a450))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | c2_1(a450))),
% 1.97/1.59 inference(rewrite,[status(thm)],[])).
% 1.97/1.59 tff(2794,plain,
% 1.97/1.59 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a450) | c1_1(a450) | c0_1(a450)) <=> (hskp2 | hskp1 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | c2_1(a450))),
% 1.97/1.59 inference(rewrite,[status(thm)],[])).
% 1.97/1.59 tff(2795,plain,
% 1.97/1.59 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a450) | c1_1(a450) | c0_1(a450))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | c2_1(a450)))),
% 1.97/1.59 inference(monotonicity,[status(thm)],[2794])).
% 1.97/1.59 tff(2796,plain,
% 1.97/1.59 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a450) | c1_1(a450) | c0_1(a450))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | c2_1(a450))),
% 1.97/1.59 inference(transitivity,[status(thm)],[2795, 2793])).
% 1.97/1.59 tff(2797,plain,
% 1.97/1.59 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a450) | c1_1(a450) | c0_1(a450))),
% 1.97/1.59 inference(quant_inst,[status(thm)],[])).
% 1.97/1.59 tff(2798,plain,
% 1.97/1.59 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a450) | c1_1(a450) | (~ndr1_0) | c2_1(a450)),
% 1.97/1.59 inference(modus_ponens,[status(thm)],[2797, 2796])).
% 1.97/1.59 tff(2799,plain,
% 1.97/1.59 (hskp2 | hskp1 | c2_1(a450)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2798, 150, 2771, 2770, 33])).
% 1.97/1.59 tff(2800,plain,
% 1.97/1.59 (c2_1(a450)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2799, 23, 12])).
% 1.97/1.59 tff(2801,plain,
% 1.97/1.59 (hskp25 | hskp3 | (~c2_1(a450))),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2764, 150, 2771, 2770, 2758])).
% 1.97/1.59 tff(2802,plain,
% 1.97/1.59 (hskp3),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2801, 2800, 2748])).
% 1.97/1.59 tff(2803,plain,
% 1.97/1.59 (~c3_1(a403)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[1994, 2802])).
% 1.97/1.59 tff(2804,plain,
% 1.97/1.59 (~c2_1(a403)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[1644, 2802])).
% 1.97/1.59 tff(2805,plain,
% 1.97/1.59 (~c0_1(a403)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[1272, 2802])).
% 1.97/1.59 tff(2806,plain,
% 1.97/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a450) | c1_1(a450) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a450)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a450) | c1_1(a450) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a450)))),
% 1.97/1.59 inference(rewrite,[status(thm)],[])).
% 1.97/1.59 tff(2807,plain,
% 1.97/1.59 (((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)) | c3_1(a403) | c0_1(a403) | c2_1(a403)) <=> (c0_1(a450) | c1_1(a450) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a450)))),
% 1.97/1.59 inference(rewrite,[status(thm)],[])).
% 1.97/1.59 tff(2808,plain,
% 1.97/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)) | c3_1(a403) | c0_1(a403) | c2_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a450) | c1_1(a450) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a450))))),
% 1.97/1.59 inference(monotonicity,[status(thm)],[2807])).
% 1.97/1.59 tff(2809,plain,
% 1.97/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)) | c3_1(a403) | c0_1(a403) | c2_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a450) | c1_1(a450) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a450)))),
% 1.97/1.59 inference(transitivity,[status(thm)],[2808, 2806])).
% 1.97/1.59 tff(2810,plain,
% 1.97/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a403) | c3_1(a403) | (~c1_1(a403)) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)) | c3_1(a403) | c0_1(a403) | c2_1(a403))),
% 1.97/1.59 inference(quant_inst,[status(thm)],[])).
% 1.97/1.59 tff(2811,plain,
% 1.97/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a450) | c1_1(a450) | c0_1(a403) | c2_1(a403) | c3_1(a403) | (~ndr1_0) | (~c1_1(a403)) | (~c2_1(a450))),
% 1.97/1.59 inference(modus_ponens,[status(thm)],[2810, 2809])).
% 1.97/1.59 tff(2812,plain,
% 1.97/1.59 (~c1_1(a403)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2811, 150, 2771, 2770, 2805, 2804, 2803, 346, 2800])).
% 1.97/1.59 tff(2813,plain,
% 1.97/1.59 ($false),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[502, 150, 23, 12, 2805, 2804, 33, 2812])).
% 1.97/1.59 tff(2814,plain,(hskp2 | hskp1 | c0_1(a450) | c1_1(a450) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.97/1.59 tff(2815,plain,
% 1.97/1.59 (hskp2),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2814, 2748, 2747, 2741, 12])).
% 1.97/1.59 tff(2816,plain,
% 1.97/1.59 (c0_1(a402)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[520, 2815])).
% 1.97/1.59 tff(2817,plain,
% 1.97/1.59 (~c1_1(a402)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2623, 2815])).
% 1.97/1.59 tff(2818,plain,
% 1.97/1.59 (c3_1(a445)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[470, 2791])).
% 1.97/1.59 tff(2819,plain,
% 1.97/1.59 (~c0_1(a445)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[332, 2791])).
% 1.97/1.59 tff(2820,plain,
% 1.97/1.59 ($false),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[1548, 2819, 2818, 2817, 44, 12, 2816, 2792])).
% 1.97/1.59 tff(2821,plain,(hskp3 | hskp1 | hskp24 | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.97/1.59 tff(2822,plain,
% 1.97/1.59 (hskp3),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2821, 2748, 55, 12])).
% 1.97/1.59 tff(2823,plain,
% 1.97/1.59 (~c3_1(a403)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[1994, 2822])).
% 1.97/1.59 tff(2824,plain,
% 1.97/1.59 (~c2_1(a403)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[1644, 2822])).
% 1.97/1.59 tff(2825,plain,
% 1.97/1.59 (~c0_1(a403)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[1272, 2822])).
% 1.97/1.59 tff(2826,plain,
% 1.97/1.59 (~c2_1(a402)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[509, 2815])).
% 1.97/1.59 tff(2827,plain,
% 1.97/1.59 (hskp27 | hskp0),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[362, 150, 336, 335, 334, 356])).
% 1.97/1.59 tff(2828,plain,
% 1.97/1.59 (hskp0),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2827, 201])).
% 1.97/1.59 tff(2829,plain,
% 1.97/1.59 (c2_1(a400)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[374, 2828])).
% 1.97/1.59 tff(2830,plain,
% 1.97/1.59 (c1_1(a400)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[385, 2828])).
% 1.97/1.59 tff(2831,plain,
% 1.97/1.59 (~c0_1(a400)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[389, 150, 55, 119, 2830, 2829, 129])).
% 1.97/1.59 tff(2832,plain,
% 1.97/1.59 (c3_1(a402)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[626, 150, 12, 1439, 2830, 2829, 105, 22, 2831])).
% 1.97/1.59 tff(2833,plain,
% 1.97/1.59 (~c3_1(a400)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[405, 2828])).
% 1.97/1.59 tff(2834,plain,
% 1.97/1.59 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.97/1.59 inference(bind,[status(th)],[])).
% 1.97/1.59 tff(2835,plain,
% 1.97/1.59 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.97/1.59 inference(quant_intro,[status(thm)],[2834])).
% 1.97/1.59 tff(2836,plain,
% 1.97/1.59 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.97/1.59 inference(rewrite,[status(thm)],[])).
% 1.97/1.59 tff(2837,plain,
% 1.97/1.59 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.97/1.59 inference(bind,[status(th)],[])).
% 1.97/1.59 tff(2838,plain,
% 1.97/1.59 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.97/1.59 inference(quant_intro,[status(thm)],[2837])).
% 1.97/1.59 tff(2839,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 1.97/1.59 tff(2840,plain,
% 1.97/1.59 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.97/1.59 inference(modus_ponens,[status(thm)],[2839, 2838])).
% 1.97/1.59 tff(2841,plain,
% 1.97/1.59 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.97/1.59 inference(modus_ponens,[status(thm)],[2840, 2836])).
% 1.97/1.59 tff(2842,plain,(
% 1.97/1.59 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.97/1.59 inference(skolemize,[status(sab)],[2841])).
% 1.97/1.59 tff(2843,plain,
% 1.97/1.59 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.97/1.59 inference(modus_ponens,[status(thm)],[2842, 2835])).
% 1.97/1.59 tff(2844,plain,
% 1.97/1.59 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp9 | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp9 | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c0_1(a402)))),
% 1.97/1.59 inference(rewrite,[status(thm)],[])).
% 1.97/1.59 tff(2845,plain,
% 1.97/1.59 ((hskp9 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400))) <=> (hskp9 | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c0_1(a402)))),
% 1.97/1.59 inference(rewrite,[status(thm)],[])).
% 1.97/1.59 tff(2846,plain,
% 1.97/1.59 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp9 | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c0_1(a402))))),
% 1.97/1.59 inference(monotonicity,[status(thm)],[2845])).
% 1.97/1.59 tff(2847,plain,
% 1.97/1.59 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp9 | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c0_1(a402)))),
% 1.97/1.59 inference(transitivity,[status(thm)],[2846, 2844])).
% 1.97/1.59 tff(2848,plain,
% 1.97/1.59 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)))),
% 1.97/1.59 inference(quant_inst,[status(thm)],[])).
% 1.97/1.59 tff(2849,plain,
% 1.97/1.59 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp9 | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c0_1(a402))),
% 1.97/1.59 inference(modus_ponens,[status(thm)],[2848, 2847])).
% 1.97/1.59 tff(2850,plain,
% 1.97/1.59 (hskp9),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2849, 150, 1439, 2829, 105, 2054, 2833, 2843, 2831])).
% 1.97/1.59 tff(2851,plain,
% 1.97/1.59 (~c1_1(a416)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[663, 2850])).
% 1.97/1.59 tff(2852,plain,
% 1.97/1.59 (~c0_1(a416)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[669, 2850])).
% 1.97/1.59 tff(2853,plain,
% 1.97/1.59 (c3_1(a416)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[727, 2850])).
% 1.97/1.59 tff(2854,plain,
% 1.97/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a416) | c1_1(a416) | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c3_1(a402)) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a416) | c1_1(a416) | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c3_1(a402)) | (~c3_1(a416)))),
% 1.97/1.59 inference(rewrite,[status(thm)],[])).
% 1.97/1.59 tff(2855,plain,
% 1.97/1.59 (((~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c3_1(a402)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416))) <=> (c0_1(a416) | c1_1(a416) | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c3_1(a402)) | (~c3_1(a416)))),
% 1.97/1.59 inference(rewrite,[status(thm)],[])).
% 1.97/1.59 tff(2856,plain,
% 1.97/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c3_1(a402)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a416) | c1_1(a416) | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c3_1(a402)) | (~c3_1(a416))))),
% 1.97/1.59 inference(monotonicity,[status(thm)],[2855])).
% 1.97/1.59 tff(2857,plain,
% 1.97/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c3_1(a402)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a416) | c1_1(a416) | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c3_1(a402)) | (~c3_1(a416)))),
% 1.97/1.59 inference(transitivity,[status(thm)],[2856, 2854])).
% 1.97/1.59 tff(2858,plain,
% 1.97/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a402) | c1_1(a402) | (~c3_1(a402)) | c0_1(a400) | c3_1(a400) | (~c2_1(a400)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)))),
% 1.97/1.59 inference(quant_inst,[status(thm)],[])).
% 1.97/1.59 tff(2859,plain,
% 1.97/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a416) | c1_1(a416) | c1_1(a402) | c2_1(a402) | c3_1(a400) | (~ndr1_0) | (~c2_1(a400)) | c0_1(a400) | (~c3_1(a402)) | (~c3_1(a416))),
% 1.97/1.59 inference(modus_ponens,[status(thm)],[2858, 2857])).
% 1.97/1.59 tff(2860,plain,
% 1.97/1.59 ($false),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2859, 150, 2853, 2829, 2852, 2851, 105, 2054, 2833, 778, 2831, 2832])).
% 1.97/1.59 tff(2861,plain,(hskp19 | c1_1(a402) | c2_1(a402) | (~c0_1(a402)) | hskp1 | hskp24 | c0_1(a403) | c2_1(a403) | c3_1(a403)), inference(lemma,lemma(discharge,[]))).
% 1.97/1.59 tff(2862,plain,
% 1.97/1.59 (hskp19),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2861, 2817, 2826, 2816, 12, 55, 2825, 2824, 2823])).
% 1.97/1.59 tff(2863,plain,
% 1.97/1.59 (c1_1(a445)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[458, 2862])).
% 1.97/1.59 tff(2864,plain,
% 1.97/1.59 (~c0_1(a445)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[332, 2862])).
% 1.97/1.59 tff(2865,plain,
% 1.97/1.59 (c3_1(a445)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[470, 2862])).
% 1.97/1.59 tff(2866,plain,
% 1.97/1.59 (hskp11),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[788, 2865, 2817, 2824, 12, 2825, 2823, 2864, 2863])).
% 1.97/1.59 tff(2867,plain,
% 1.97/1.59 (~c2_1(a420)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[1223, 2866])).
% 1.97/1.59 tff(2868,plain,
% 1.97/1.59 (~c0_1(a420)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[1100, 2866])).
% 1.97/1.59 tff(2869,plain,
% 1.97/1.59 (~c1_1(a420)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[1106, 2866])).
% 1.97/1.59 tff(2870,plain,
% 1.97/1.59 ($false),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[1169, 2869, 2868, 2817, 2825, 2863, 2864, 2865, 12, 2867, 2824, 2823])).
% 1.97/1.59 tff(2871,plain,(hskp25 | hskp1 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.97/1.59 tff(2872,plain,
% 1.97/1.59 (hskp25),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2871, 12, 55])).
% 1.97/1.59 tff(2873,plain,
% 1.97/1.59 (c1_1(a405)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[92, 2872])).
% 1.97/1.59 tff(2874,plain,
% 1.97/1.59 (c3_1(a405)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[81, 2872])).
% 1.97/1.59 tff(2875,plain,
% 1.97/1.59 (c0_1(a405)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[103, 2872])).
% 1.97/1.59 tff(2876,plain,
% 1.97/1.59 (hskp2),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2698, 2875, 12, 2873, 2874, 55])).
% 1.97/1.59 tff(2877,plain,
% 1.97/1.59 (~c1_1(a402)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2623, 2876])).
% 1.97/1.59 tff(2878,plain,
% 1.97/1.59 (c3_1(a403)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[1988, 2877, 2875, 2874, 2873, 55])).
% 1.97/1.59 tff(2879,plain,
% 1.97/1.59 (~hskp3),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[1994, 2878])).
% 1.97/1.59 tff(2880,plain,
% 1.97/1.59 (~hskp0),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2781, 2879, 2747, 2741, 2735])).
% 1.97/1.59 tff(2881,plain,
% 1.97/1.59 (c2_1(a450)),
% 1.97/1.59 inference(unit_resolution,[status(thm)],[2789, 201, 2880])).
% 1.97/1.59 tff(2882,plain,
% 1.97/1.59 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.97/1.59 inference(bind,[status(th)],[])).
% 1.97/1.59 tff(2883,plain,
% 1.97/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.97/1.59 inference(quant_intro,[status(thm)],[2882])).
% 1.97/1.59 tff(2884,plain,
% 1.97/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.97/1.59 inference(rewrite,[status(thm)],[])).
% 1.97/1.59 tff(2885,plain,
% 1.97/1.59 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | 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(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.97/1.60 inference(bind,[status(th)],[])).
% 1.97/1.60 tff(2886,plain,
% 1.97/1.60 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.97/1.60 inference(quant_intro,[status(thm)],[2885])).
% 1.97/1.60 tff(2887,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 1.97/1.60 tff(2888,plain,
% 1.97/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2887, 2886])).
% 1.97/1.60 tff(2889,plain,
% 1.97/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2888, 2884])).
% 1.97/1.60 tff(2890,plain,(
% 1.97/1.60 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.97/1.60 inference(skolemize,[status(sab)],[2889])).
% 1.97/1.60 tff(2891,plain,
% 1.97/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2890, 2883])).
% 1.97/1.60 tff(2892,plain,
% 1.97/1.60 (~c2_1(a402)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[509, 2876])).
% 1.97/1.60 tff(2893,plain,
% 1.97/1.60 (c0_1(a402)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[520, 2876])).
% 1.97/1.60 tff(2894,plain,
% 1.97/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a450) | c1_1(a450) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a450)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a450) | c1_1(a450) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a450)))),
% 1.97/1.60 inference(rewrite,[status(thm)],[])).
% 1.97/1.60 tff(2895,plain,
% 1.97/1.60 (((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a450) | c0_1(a450) | (~c2_1(a450))) <=> (c0_1(a450) | c1_1(a450) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a450)))),
% 1.97/1.60 inference(rewrite,[status(thm)],[])).
% 1.97/1.60 tff(2896,plain,
% 1.97/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a450) | c1_1(a450) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a450))))),
% 1.97/1.60 inference(monotonicity,[status(thm)],[2895])).
% 1.97/1.60 tff(2897,plain,
% 1.97/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a450) | c1_1(a450) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a450)))),
% 1.97/1.60 inference(transitivity,[status(thm)],[2896, 2894])).
% 1.97/1.60 tff(2898,plain,
% 1.97/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a450) | c0_1(a450) | (~c2_1(a450)))),
% 1.97/1.60 inference(quant_inst,[status(thm)],[])).
% 1.97/1.60 tff(2899,plain,
% 1.97/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a450) | c1_1(a450) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a450))),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2898, 2897])).
% 1.97/1.60 tff(2900,plain,
% 1.97/1.60 ((~c3_1(a402)) | (~c2_1(a450))),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2899, 150, 2893, 2747, 2741, 2877, 2892, 2891])).
% 1.97/1.60 tff(2901,plain,
% 1.97/1.60 (~c3_1(a402)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2900, 2881])).
% 1.97/1.60 tff(2902,plain,
% 1.97/1.60 (hskp19 | (~c2_1(a405))),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[156, 150, 55, 2875, 2873, 129])).
% 1.97/1.60 tff(2903,plain,
% 1.97/1.60 (~c2_1(a405)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2902, 119])).
% 1.97/1.60 tff(2904,plain,
% 1.97/1.60 (hskp27 | hskp23 | c2_1(a405)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[217, 150, 2875, 2873, 211])).
% 1.97/1.60 tff(2905,plain,
% 1.97/1.60 (hskp23),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2904, 201, 2903])).
% 1.97/1.60 tff(2906,plain,
% 1.97/1.60 (c1_1(a460)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[241, 2905])).
% 1.97/1.60 tff(2907,plain,
% 1.97/1.60 (~c3_1(a460)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[224, 2905])).
% 1.97/1.60 tff(2908,plain,
% 1.97/1.60 (~c2_1(a460)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[230, 2905])).
% 1.97/1.60 tff(2909,plain,
% 1.97/1.60 (~hskp22),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2083, 2908, 12, 201, 2907, 2906, 2879])).
% 1.97/1.60 tff(2910,plain,
% 1.97/1.60 ($false),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2090, 150, 2909, 2873, 2874, 2893, 2892, 929, 2903, 2901])).
% 1.97/1.60 tff(2911,plain,(hskp19 | hskp1 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.97/1.60 tff(2912,plain,
% 1.97/1.60 (hskp19),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2911, 12, 55])).
% 1.97/1.60 tff(2913,plain,
% 1.97/1.60 (c1_1(a445)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[458, 2912])).
% 1.97/1.60 tff(2914,plain,
% 1.97/1.60 (c3_1(a445)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[470, 2912])).
% 1.97/1.60 tff(2915,plain,
% 1.97/1.60 (~c0_1(a445)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[332, 2912])).
% 1.97/1.60 tff(2916,plain,
% 1.97/1.60 ($false),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[1548, 2915, 2914, 2877, 2879, 12, 2893, 2913])).
% 1.97/1.60 tff(2917,plain,(hskp1 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.97/1.60 tff(2918,plain,
% 1.97/1.60 (hskp1),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2917, 55])).
% 1.97/1.60 tff(2919,plain,
% 1.97/1.60 (c0_1(a401)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[816, 2918])).
% 1.97/1.60 tff(2920,plain,
% 1.97/1.60 (~c3_1(a401)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[794, 2918])).
% 1.97/1.60 tff(2921,plain,
% 1.97/1.60 (c1_1(a401)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[805, 2918])).
% 1.97/1.60 tff(2922,plain,
% 1.97/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a450)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a450)))),
% 1.97/1.60 inference(rewrite,[status(thm)],[])).
% 1.97/1.60 tff(2923,plain,
% 1.97/1.60 (((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a450) | c3_1(a450) | (~c2_1(a450))) <=> (c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a450)))),
% 1.97/1.60 inference(rewrite,[status(thm)],[])).
% 1.97/1.60 tff(2924,plain,
% 1.97/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a450) | c3_1(a450) | (~c2_1(a450)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a450))))),
% 1.97/1.60 inference(monotonicity,[status(thm)],[2923])).
% 1.97/1.60 tff(2925,plain,
% 1.97/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a450) | c3_1(a450) | (~c2_1(a450)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a450)))),
% 1.97/1.60 inference(transitivity,[status(thm)],[2924, 2922])).
% 1.97/1.60 tff(2926,plain,
% 1.97/1.60 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | ((~ndr1_0) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a450) | c3_1(a450) | (~c2_1(a450)))),
% 1.97/1.60 inference(quant_inst,[status(thm)],[])).
% 1.97/1.60 tff(2927,plain,
% 1.97/1.60 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a450))),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2926, 2925])).
% 1.97/1.60 tff(2928,plain,
% 1.97/1.60 (~c2_1(a450)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2927, 150, 2919, 2921, 2741, 2735, 2920, 886])).
% 1.97/1.60 tff(2929,assumption,(~c2_1(a450)), introduced(assumption)).
% 1.97/1.60 tff(2930,assumption,(hskp28), introduced(assumption)).
% 1.97/1.60 tff(2931,plain,
% 1.97/1.60 (((~hskp28) | c3_1(a414)) <=> ((~hskp28) | c3_1(a414))),
% 1.97/1.60 inference(rewrite,[status(thm)],[])).
% 1.97/1.60 tff(2932,axiom,((~hskp28) | c3_1(a414)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 1.97/1.60 tff(2933,plain,
% 1.97/1.60 ((~hskp28) | c3_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2932, 2931])).
% 1.97/1.60 tff(2934,plain,
% 1.97/1.60 ((~hskp28) | c3_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2933, 2931])).
% 1.97/1.60 tff(2935,plain,
% 1.97/1.60 ((~hskp28) | c3_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2934, 2931])).
% 1.97/1.60 tff(2936,plain,
% 1.97/1.60 ((~hskp28) | c3_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2935, 2931])).
% 1.97/1.60 tff(2937,plain,
% 1.97/1.60 ((~hskp28) | c3_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2936, 2931])).
% 1.97/1.60 tff(2938,plain,
% 1.97/1.60 ((~hskp28) | c3_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2937, 2931])).
% 1.97/1.60 tff(2939,plain,
% 1.97/1.60 ((~hskp28) | c3_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2938, 2931])).
% 1.97/1.60 tff(2940,plain,
% 1.97/1.60 ((~hskp28) | c3_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2939, 2931])).
% 1.97/1.60 tff(2941,plain,
% 1.97/1.60 (c3_1(a414)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2940, 2930])).
% 1.97/1.60 tff(2942,plain,
% 1.97/1.60 (((~hskp28) | c2_1(a414)) <=> ((~hskp28) | c2_1(a414))),
% 1.97/1.60 inference(rewrite,[status(thm)],[])).
% 1.97/1.60 tff(2943,axiom,((~hskp28) | c2_1(a414)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 1.97/1.60 tff(2944,plain,
% 1.97/1.60 ((~hskp28) | c2_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2943, 2942])).
% 1.97/1.60 tff(2945,plain,
% 1.97/1.60 ((~hskp28) | c2_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2944, 2942])).
% 1.97/1.60 tff(2946,plain,
% 1.97/1.60 ((~hskp28) | c2_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2945, 2942])).
% 1.97/1.60 tff(2947,plain,
% 1.97/1.60 ((~hskp28) | c2_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2946, 2942])).
% 1.97/1.60 tff(2948,plain,
% 1.97/1.60 ((~hskp28) | c2_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2947, 2942])).
% 1.97/1.60 tff(2949,plain,
% 1.97/1.60 ((~hskp28) | c2_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2948, 2942])).
% 1.97/1.60 tff(2950,plain,
% 1.97/1.60 ((~hskp28) | c2_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2949, 2942])).
% 1.97/1.60 tff(2951,plain,
% 1.97/1.60 ((~hskp28) | c2_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2950, 2942])).
% 1.97/1.60 tff(2952,plain,
% 1.97/1.60 (c2_1(a414)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2951, 2930])).
% 1.97/1.60 tff(2953,plain,
% 1.97/1.60 (((~hskp28) | c0_1(a414)) <=> ((~hskp28) | c0_1(a414))),
% 1.97/1.60 inference(rewrite,[status(thm)],[])).
% 1.97/1.60 tff(2954,axiom,((~hskp28) | c0_1(a414)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 1.97/1.60 tff(2955,plain,
% 1.97/1.60 ((~hskp28) | c0_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2954, 2953])).
% 1.97/1.60 tff(2956,plain,
% 1.97/1.60 ((~hskp28) | c0_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2955, 2953])).
% 1.97/1.60 tff(2957,plain,
% 1.97/1.60 ((~hskp28) | c0_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2956, 2953])).
% 1.97/1.60 tff(2958,plain,
% 1.97/1.60 ((~hskp28) | c0_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2957, 2953])).
% 1.97/1.60 tff(2959,plain,
% 1.97/1.60 ((~hskp28) | c0_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2958, 2953])).
% 1.97/1.60 tff(2960,plain,
% 1.97/1.60 ((~hskp28) | c0_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2959, 2953])).
% 1.97/1.60 tff(2961,plain,
% 1.97/1.60 ((~hskp28) | c0_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2960, 2953])).
% 1.97/1.60 tff(2962,plain,
% 1.97/1.60 ((~hskp28) | c0_1(a414)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2961, 2953])).
% 1.97/1.60 tff(2963,plain,
% 1.97/1.60 (c0_1(a414)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2962, 2930])).
% 1.97/1.60 tff(2964,plain,
% 1.97/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a450) | c1_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c2_1(a450))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a450) | c1_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c2_1(a450))),
% 1.97/1.60 inference(rewrite,[status(thm)],[])).
% 1.97/1.60 tff(2965,plain,
% 1.97/1.60 (((~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a450) | c0_1(a450) | c2_1(a450)) <=> (c0_1(a450) | c1_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c2_1(a450))),
% 1.97/1.60 inference(rewrite,[status(thm)],[])).
% 1.97/1.60 tff(2966,plain,
% 1.97/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a450) | c0_1(a450) | c2_1(a450))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a450) | c1_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c2_1(a450)))),
% 1.97/1.60 inference(monotonicity,[status(thm)],[2965])).
% 1.97/1.60 tff(2967,plain,
% 1.97/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a450) | c0_1(a450) | c2_1(a450))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a450) | c1_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c2_1(a450))),
% 1.97/1.60 inference(transitivity,[status(thm)],[2966, 2964])).
% 1.97/1.60 tff(2968,plain,
% 1.97/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a450) | c0_1(a450) | c2_1(a450))),
% 1.97/1.60 inference(quant_inst,[status(thm)],[])).
% 1.97/1.60 tff(2969,plain,
% 1.97/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a450) | c1_1(a450) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c2_1(a450)),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2968, 2967])).
% 1.97/1.60 tff(2970,plain,
% 1.97/1.60 ($false),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2969, 150, 2963, 2952, 2941, 836, 838, 2771, 2770, 837, 11, 2929])).
% 1.97/1.60 tff(2971,plain,((~hskp28) | (~c0_1(a401)) | (~c1_1(a401)) | c0_1(a450) | c1_1(a450) | c3_1(a401) | c2_1(a450)), inference(lemma,lemma(discharge,[]))).
% 1.97/1.60 tff(2972,plain,
% 1.97/1.60 (~hskp28),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2971, 2919, 2921, 2747, 2741, 2920, 2928])).
% 1.97/1.60 tff(2973,plain,
% 1.97/1.60 (^[U: $i] : refl((hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 1.97/1.60 inference(bind,[status(th)],[])).
% 1.97/1.60 tff(2974,plain,
% 1.97/1.60 (![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.97/1.60 inference(quant_intro,[status(thm)],[2973])).
% 1.97/1.60 tff(2975,plain,
% 1.97/1.60 (![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.97/1.60 inference(rewrite,[status(thm)],[])).
% 1.97/1.60 tff(2976,plain,
% 1.97/1.60 (^[U: $i] : 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)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp25))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp28) <=> ((hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp28))), rewrite(((hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp28) <=> (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp28) <=> (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 1.97/1.60 inference(bind,[status(th)],[])).
% 1.97/1.60 tff(2977,plain,
% 1.97/1.60 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp28) <=> ![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.97/1.60 inference(quant_intro,[status(thm)],[2976])).
% 1.97/1.60 tff(2978,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 1.97/1.60 tff(2979,plain,
% 1.97/1.60 (![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2978, 2977])).
% 1.97/1.60 tff(2980,plain,
% 1.97/1.60 (![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2979, 2975])).
% 1.97/1.60 tff(2981,plain,(
% 1.97/1.60 ![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.97/1.60 inference(skolemize,[status(sab)],[2980])).
% 1.97/1.60 tff(2982,plain,
% 1.97/1.60 (![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2981, 2974])).
% 1.97/1.60 tff(2983,plain,
% 1.97/1.60 (hskp20),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[823, 150, 2919, 2921, 2920, 483])).
% 1.97/1.60 tff(2984,plain,
% 1.97/1.60 (~c2_1(a449)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[914, 2983])).
% 1.97/1.60 tff(2985,plain,
% 1.97/1.60 (c3_1(a449)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[908, 2983])).
% 1.97/1.60 tff(2986,plain,
% 1.97/1.60 (c1_1(a449)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[834, 2983])).
% 1.97/1.60 tff(2987,plain,
% 1.97/1.60 (((~![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp25 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))) <=> ((~![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp28 | hskp25 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.97/1.60 inference(rewrite,[status(thm)],[])).
% 1.97/1.60 tff(2988,plain,
% 1.97/1.60 ((hskp28 | hskp25 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449))) <=> (hskp28 | hskp25 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.97/1.60 inference(rewrite,[status(thm)],[])).
% 1.97/1.60 tff(2989,plain,
% 1.97/1.60 (((~![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp25 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)))) <=> ((~![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp25 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449))))),
% 1.97/1.60 inference(monotonicity,[status(thm)],[2988])).
% 1.97/1.60 tff(2990,plain,
% 1.97/1.60 (((~![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp25 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)))) <=> ((~![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp28 | hskp25 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.97/1.60 inference(transitivity,[status(thm)],[2989, 2987])).
% 1.97/1.60 tff(2991,plain,
% 1.97/1.60 ((~![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp28 | hskp25 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)))),
% 1.97/1.60 inference(quant_inst,[status(thm)],[])).
% 1.97/1.60 tff(2992,plain,
% 1.97/1.60 ((~![U: $i] : (hskp28 | hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp28 | hskp25 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449))),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[2991, 2990])).
% 1.97/1.60 tff(2993,plain,
% 1.97/1.60 (hskp28 | hskp25),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2992, 150, 2986, 2985, 2984, 2982])).
% 1.97/1.60 tff(2994,plain,
% 1.97/1.60 (hskp25),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2993, 2972])).
% 1.97/1.60 tff(2995,plain,
% 1.97/1.60 (c0_1(a405)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[103, 2994])).
% 1.97/1.60 tff(2996,plain,
% 1.97/1.60 (c1_1(a405)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[92, 2994])).
% 1.97/1.60 tff(2997,plain,
% 1.97/1.60 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401)))),
% 1.97/1.60 inference(rewrite,[status(thm)],[])).
% 1.97/1.60 tff(2998,plain,
% 1.97/1.60 ((hskp3 | (~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c1_1(a401)) | c1_1(a450) | c0_1(a450) | c3_1(a450)) <=> (hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401)))),
% 1.97/1.60 inference(rewrite,[status(thm)],[])).
% 1.97/1.60 tff(2999,plain,
% 1.97/1.60 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c1_1(a401)) | c1_1(a450) | c0_1(a450) | c3_1(a450))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401))))),
% 1.97/1.60 inference(monotonicity,[status(thm)],[2998])).
% 1.97/1.60 tff(3000,plain,
% 1.97/1.60 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c1_1(a401)) | c1_1(a450) | c0_1(a450) | c3_1(a450))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401)))),
% 1.97/1.60 inference(transitivity,[status(thm)],[2999, 2997])).
% 1.97/1.60 tff(3001,plain,
% 1.97/1.60 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c1_1(a401)) | c1_1(a450) | c0_1(a450) | c3_1(a450))),
% 1.97/1.60 inference(quant_inst,[status(thm)],[])).
% 1.97/1.60 tff(3002,plain,
% 1.97/1.60 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c0_1(a450) | c1_1(a450) | c3_1(a450) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c1_1(a401))),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[3001, 3000])).
% 1.97/1.60 tff(3003,plain,
% 1.97/1.60 (hskp3 | (~c2_1(a401))),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[3002, 150, 2921, 2747, 2741, 2735, 2920, 1426])).
% 1.97/1.60 tff(3004,plain,
% 1.97/1.60 (~c2_1(a401)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[3003, 44])).
% 1.97/1.60 tff(3005,plain,
% 1.97/1.60 (hskp2),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2543, 3004, 2921, 2920, 2919])).
% 1.97/1.60 tff(3006,plain,
% 1.97/1.60 (~c1_1(a402)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2623, 3005])).
% 1.97/1.60 tff(3007,plain,
% 1.97/1.60 (hskp27),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2789, 2782, 2928])).
% 1.97/1.60 tff(3008,plain,
% 1.97/1.60 (hskp19),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[200, 3007, 55])).
% 1.97/1.60 tff(3009,plain,
% 1.97/1.60 (~c0_1(a445)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[332, 3008])).
% 1.97/1.60 tff(3010,plain,
% 1.97/1.60 (~hskp22),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2580, 44, 2921, 2920, 2919])).
% 1.97/1.60 tff(3011,plain,
% 1.97/1.60 (c1_1(a445)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[458, 3008])).
% 1.97/1.60 tff(3012,plain,
% 1.97/1.60 (c3_1(a445)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[470, 3008])).
% 1.97/1.60 tff(3013,plain,
% 1.97/1.60 ($false),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[942, 3012, 3011, 2985, 3010, 3005, 2986, 2984, 3009, 3006])).
% 1.97/1.60 tff(3014,plain,(hskp3 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.97/1.60 tff(3015,plain,
% 1.97/1.60 (hskp3),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[3014, 55])).
% 1.97/1.60 tff(3016,plain,
% 1.97/1.60 (~c3_1(a403)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[1994, 3015])).
% 1.97/1.60 tff(3017,plain,
% 1.97/1.60 (~c2_1(a403)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[1644, 3015])).
% 1.97/1.60 tff(3018,plain,
% 1.97/1.60 (c3_1(a405)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[81, 2994])).
% 1.97/1.60 tff(3019,plain,
% 1.97/1.60 (c1_1(a402)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[1559, 3018, 3017, 3016, 2996, 2995, 55])).
% 1.97/1.60 tff(3020,plain,
% 1.97/1.60 (~hskp2),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2623, 3019])).
% 1.97/1.60 tff(3021,plain,
% 1.97/1.60 (c2_1(a401)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2543, 3020, 2921, 2920, 2919])).
% 1.97/1.60 tff(3022,plain,
% 1.97/1.60 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.97/1.60 inference(rewrite,[status(thm)],[])).
% 1.97/1.60 tff(3023,plain,
% 1.97/1.60 ((hskp13 | hskp2 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449))) <=> (hskp13 | hskp2 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.97/1.60 inference(rewrite,[status(thm)],[])).
% 1.97/1.60 tff(3024,plain,
% 1.97/1.60 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449))))),
% 1.97/1.60 inference(monotonicity,[status(thm)],[3023])).
% 1.97/1.60 tff(3025,plain,
% 1.97/1.60 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.97/1.60 inference(transitivity,[status(thm)],[3024, 3022])).
% 1.97/1.60 tff(3026,plain,
% 1.97/1.60 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)))),
% 1.97/1.60 inference(quant_inst,[status(thm)],[])).
% 1.97/1.60 tff(3027,plain,
% 1.97/1.60 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449))),
% 1.97/1.60 inference(modus_ponens,[status(thm)],[3026, 3025])).
% 1.97/1.60 tff(3028,plain,
% 1.97/1.60 (hskp13 | hskp2),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[3027, 150, 2986, 2985, 2984, 271])).
% 1.97/1.60 tff(3029,plain,
% 1.97/1.60 (hskp13),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[3028, 3020])).
% 1.97/1.60 tff(3030,plain,
% 1.97/1.60 (~c0_1(a427)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[284, 3029])).
% 1.97/1.60 tff(3031,plain,
% 1.97/1.60 (~c0_1(a403)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[1272, 3015])).
% 1.97/1.60 tff(3032,plain,
% 1.97/1.60 (hskp19),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[447, 2995, 3031, 3017, 3016, 2996, 3018, 55])).
% 1.97/1.60 tff(3033,plain,
% 1.97/1.60 (~c0_1(a445)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[332, 3032])).
% 1.97/1.60 tff(3034,plain,
% 1.97/1.60 (c1_1(a445)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[458, 3032])).
% 1.97/1.60 tff(3035,plain,
% 1.97/1.60 (c3_1(a445)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[470, 3032])).
% 1.97/1.60 tff(3036,plain,
% 1.97/1.60 (~hskp22),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[897, 3035, 2920, 2921, 2919, 3034, 3033])).
% 1.97/1.60 tff(3037,plain,
% 1.97/1.60 (~c2_1(a405)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[2715, 3036, 2995, 2921, 2919, 2920, 3018])).
% 1.97/1.60 tff(3038,plain,
% 1.97/1.60 (~hskp7),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[992, 3036, 2919, 2921, 2920])).
% 1.97/1.60 tff(3039,plain,
% 1.97/1.60 (hskp14),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[1075, 3038, 2995, 3018, 2919, 2921, 2920, 3020, 3037])).
% 1.97/1.60 tff(3040,plain,
% 1.97/1.60 (~c1_1(a428)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[421, 3039])).
% 1.97/1.60 tff(3041,plain,
% 1.97/1.60 (c2_1(a427)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[306, 3029])).
% 1.97/1.60 tff(3042,plain,
% 1.97/1.60 (c1_1(a427)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[317, 3029])).
% 1.97/1.60 tff(3043,plain,
% 1.97/1.60 (c2_1(a428)),
% 1.97/1.60 inference(unit_resolution,[status(thm)],[438, 3039])).
% 1.97/1.60 tff(3044,plain,
% 1.97/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a428) | c0_1(a427) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a427)) | (~c1_1(a427)) | (~c2_1(a428)) | (~c3_1(a428)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a428) | c0_1(a427) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a427)) | (~c1_1(a427)) | (~c2_1(a428)) | (~c3_1(a428)))),
% 1.97/1.60 inference(rewrite,[status(thm)],[])).
% 1.97/1.60 tff(3045,plain,
% 1.97/1.60 (((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427))) <=> (c1_1(a428) | c0_1(a427) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a427)) | (~c1_1(a427)) | (~c2_1(a428)) | (~c3_1(a428)))),
% 1.97/1.60 inference(rewrite,[status(thm)],[])).
% 1.97/1.60 tff(3046,plain,
% 1.97/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a428) | c0_1(a427) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a427)) | (~c1_1(a427)) | (~c2_1(a428)) | (~c3_1(a428))))),
% 1.97/1.60 inference(monotonicity,[status(thm)],[3045])).
% 1.97/1.60 tff(3047,plain,
% 1.97/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a428) | c0_1(a427) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a427)) | (~c1_1(a427)) | (~c2_1(a428)) | (~c3_1(a428)))),
% 1.97/1.60 inference(transitivity,[status(thm)],[3046, 3044])).
% 1.97/1.60 tff(3048,plain,
% 1.97/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a428) | (~c2_1(a428)) | (~c3_1(a428)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))),
% 1.97/1.60 inference(quant_inst,[status(thm)],[])).
% 1.97/1.60 tff(3049,plain,
% 1.97/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a428) | c0_1(a427) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a427)) | (~c1_1(a427)) | (~c2_1(a428)) | (~c3_1(a428))),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3048, 3047])).
% 1.97/1.61 tff(3050,plain,
% 1.97/1.61 (~c3_1(a428)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3049, 150, 3043, 3042, 3041, 2919, 3040, 3030, 2920, 704, 3021])).
% 1.97/1.61 tff(3051,plain,
% 1.97/1.61 ($false),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[1092, 150, 3043, 2919, 2921, 3040, 2920, 886, 3050])).
% 1.97/1.61 tff(3052,plain,(hskp24), inference(lemma,lemma(discharge,[]))).
% 1.97/1.61 tff(3053,plain,
% 1.97/1.61 (((~hskp24) | (~c2_1(a477))) <=> ((~hskp24) | (~c2_1(a477)))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3054,plain,
% 1.97/1.61 (((~c2_1(a477)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a477)))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3055,axiom,((~c2_1(a477)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.97/1.61 tff(3056,plain,
% 1.97/1.61 ((~hskp24) | (~c2_1(a477))),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3055, 3054])).
% 1.97/1.61 tff(3057,plain,
% 1.97/1.61 ((~hskp24) | (~c2_1(a477))),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3056, 3053])).
% 1.97/1.61 tff(3058,plain,
% 1.97/1.61 (~c2_1(a477)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3057, 3052])).
% 1.97/1.61 tff(3059,plain,
% 1.97/1.61 (((~hskp24) | (~c0_1(a477))) <=> ((~hskp24) | (~c0_1(a477)))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3060,plain,
% 1.97/1.61 (((~c0_1(a477)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a477)))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3061,axiom,((~c0_1(a477)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 1.97/1.61 tff(3062,plain,
% 1.97/1.61 ((~hskp24) | (~c0_1(a477))),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3061, 3060])).
% 1.97/1.61 tff(3063,plain,
% 1.97/1.61 ((~hskp24) | (~c0_1(a477))),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3062, 3059])).
% 1.97/1.61 tff(3064,plain,
% 1.97/1.61 (~c0_1(a477)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3063, 3052])).
% 1.97/1.61 tff(3065,plain,
% 1.97/1.61 (((~hskp24) | c3_1(a477)) <=> ((~hskp24) | c3_1(a477))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3066,axiom,((~hskp24) | c3_1(a477)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 1.97/1.61 tff(3067,plain,
% 1.97/1.61 ((~hskp24) | c3_1(a477)),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3066, 3065])).
% 1.97/1.61 tff(3068,plain,
% 1.97/1.61 ((~hskp24) | c3_1(a477)),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3067, 3065])).
% 1.97/1.61 tff(3069,plain,
% 1.97/1.61 ((~hskp24) | c3_1(a477)),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3068, 3065])).
% 1.97/1.61 tff(3070,plain,
% 1.97/1.61 ((~hskp24) | c3_1(a477)),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3069, 3065])).
% 1.97/1.61 tff(3071,plain,
% 1.97/1.61 ((~hskp24) | c3_1(a477)),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3070, 3065])).
% 1.97/1.61 tff(3072,plain,
% 1.97/1.61 ((~hskp24) | c3_1(a477)),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3071, 3065])).
% 1.97/1.61 tff(3073,plain,
% 1.97/1.61 ((~hskp24) | c3_1(a477)),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3072, 3065])).
% 1.97/1.61 tff(3074,plain,
% 1.97/1.61 ((~hskp24) | c3_1(a477)),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3073, 3065])).
% 1.97/1.61 tff(3075,plain,
% 1.97/1.61 (c3_1(a477)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3074, 3052])).
% 1.97/1.61 tff(3076,plain,
% 1.97/1.61 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3077,plain,
% 1.97/1.61 ((hskp5 | hskp3 | (~ndr1_0) | c2_1(a477) | c0_1(a477) | (~c3_1(a477))) <=> (hskp5 | hskp3 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3078,plain,
% 1.97/1.61 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c3_1(a477))))),
% 1.97/1.61 inference(monotonicity,[status(thm)],[3077])).
% 1.97/1.61 tff(3079,plain,
% 1.97/1.61 (((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)))),
% 1.97/1.61 inference(transitivity,[status(thm)],[3078, 3076])).
% 1.97/1.61 tff(3080,plain,
% 1.97/1.61 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp5 | hskp3 | (~ndr1_0) | c2_1(a477) | c0_1(a477) | (~c3_1(a477)))),
% 1.97/1.61 inference(quant_inst,[status(thm)],[])).
% 1.97/1.61 tff(3081,plain,
% 1.97/1.61 ((~![U: $i] : (hskp5 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp5 | hskp3 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c3_1(a477))),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3080, 3079])).
% 1.97/1.61 tff(3082,plain,
% 1.97/1.61 (hskp5 | hskp3),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3081, 150, 3075, 3064, 3058, 54])).
% 1.97/1.61 tff(3083,plain,
% 1.97/1.61 (hskp5),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3082, 44])).
% 1.97/1.61 tff(3084,plain,
% 1.97/1.61 (~c0_1(a408)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[1334, 3083])).
% 1.97/1.61 tff(3085,plain,
% 1.97/1.61 (c3_1(a408)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[1345, 3083])).
% 1.97/1.61 tff(3086,plain,
% 1.97/1.61 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | c1_1(a477))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | c1_1(a477))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3087,plain,
% 1.97/1.61 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | c0_1(a477)) <=> (hskp2 | hskp1 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | c1_1(a477))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3088,plain,
% 1.97/1.61 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | c0_1(a477))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | c1_1(a477)))),
% 1.97/1.61 inference(monotonicity,[status(thm)],[3087])).
% 1.97/1.61 tff(3089,plain,
% 1.97/1.61 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | c0_1(a477))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | c1_1(a477))),
% 1.97/1.61 inference(transitivity,[status(thm)],[3088, 3086])).
% 1.97/1.61 tff(3090,plain,
% 1.97/1.61 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | c0_1(a477))),
% 1.97/1.61 inference(quant_inst,[status(thm)],[])).
% 1.97/1.61 tff(3091,plain,
% 1.97/1.61 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | c1_1(a477)),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3090, 3089])).
% 1.97/1.61 tff(3092,plain,
% 1.97/1.61 (hskp2 | hskp1 | c1_1(a477)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3091, 150, 3064, 3058, 33])).
% 1.97/1.61 tff(3093,plain,
% 1.97/1.61 (c1_1(a477)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3092, 23, 12])).
% 1.97/1.61 tff(3094,plain,
% 1.97/1.61 (((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | c0_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | hskp3 | c0_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3095,plain,
% 1.97/1.61 ((hskp16 | hskp3 | (~ndr1_0) | c0_1(a477) | (~c1_1(a477)) | (~c3_1(a477))) <=> (hskp16 | hskp3 | c0_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3096,plain,
% 1.97/1.61 (((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | (~ndr1_0) | c0_1(a477) | (~c1_1(a477)) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | c0_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477))))),
% 1.97/1.61 inference(monotonicity,[status(thm)],[3095])).
% 1.97/1.61 tff(3097,plain,
% 1.97/1.61 (((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | (~ndr1_0) | c0_1(a477) | (~c1_1(a477)) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | hskp3 | c0_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.61 inference(transitivity,[status(thm)],[3096, 3094])).
% 1.97/1.61 tff(3098,plain,
% 1.97/1.61 ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | hskp3 | (~ndr1_0) | c0_1(a477) | (~c1_1(a477)) | (~c3_1(a477)))),
% 1.97/1.61 inference(quant_inst,[status(thm)],[])).
% 1.97/1.61 tff(3099,plain,
% 1.97/1.61 ((~![U: $i] : (hskp16 | hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | hskp3 | c0_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477))),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3098, 3097])).
% 1.97/1.61 tff(3100,plain,
% 1.97/1.61 (hskp16 | hskp3 | (~c1_1(a477))),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3099, 150, 3075, 3064, 1396])).
% 1.97/1.61 tff(3101,plain,
% 1.97/1.61 (hskp16),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3100, 3093, 44])).
% 1.97/1.61 tff(3102,plain,
% 1.97/1.61 (~c3_1(a434)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[1016, 3101])).
% 1.97/1.61 tff(3103,plain,
% 1.97/1.61 (c1_1(a434)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[1044, 3101])).
% 1.97/1.61 tff(3104,plain,
% 1.97/1.61 (~c0_1(a434)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[1022, 3101])).
% 1.97/1.61 tff(3105,plain,
% 1.97/1.61 (~hskp7),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[2653, 3104, 12, 23, 3103, 3102])).
% 1.97/1.61 tff(3106,plain,
% 1.97/1.61 (c2_1(a434)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[1032, 150, 3105, 23, 3103, 3102, 118])).
% 1.97/1.61 tff(3107,plain,
% 1.97/1.61 (c2_1(a408)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[1356, 3083])).
% 1.97/1.61 tff(3108,plain,
% 1.97/1.61 ($false),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[2224, 150, 12, 3107, 3085, 3104, 3102, 3084, 1595, 3106])).
% 1.97/1.61 tff(3109,plain,(hskp2 | hskp1 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.97/1.61 tff(3110,plain,
% 1.97/1.61 (hskp2),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3109, 12, 44])).
% 1.97/1.61 tff(3111,plain,
% 1.97/1.61 (~c1_1(a402)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[2623, 3110])).
% 1.97/1.61 tff(3112,plain,
% 1.97/1.61 (c0_1(a402)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[520, 3110])).
% 1.97/1.61 tff(3113,assumption,(c1_1(a408)), introduced(assumption)).
% 1.97/1.61 tff(3114,assumption,(~c0_1(a408)), introduced(assumption)).
% 1.97/1.61 tff(3115,assumption,(c3_1(a408)), introduced(assumption)).
% 1.97/1.61 tff(3116,plain,
% 1.97/1.61 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a408) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a408)) | (~c1_1(a408)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a408) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a408)) | (~c1_1(a408)))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3117,plain,
% 1.97/1.61 (((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a408) | (~c3_1(a408)) | (~c1_1(a408))) <=> (c0_1(a408) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a408)) | (~c1_1(a408)))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3118,plain,
% 1.97/1.61 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a408) | (~c3_1(a408)) | (~c1_1(a408)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a408) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a408)) | (~c1_1(a408))))),
% 1.97/1.61 inference(monotonicity,[status(thm)],[3117])).
% 1.97/1.61 tff(3119,plain,
% 1.97/1.61 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a408) | (~c3_1(a408)) | (~c1_1(a408)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a408) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a408)) | (~c1_1(a408)))),
% 1.97/1.61 inference(transitivity,[status(thm)],[3118, 3116])).
% 1.97/1.61 tff(3120,plain,
% 1.97/1.61 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a408) | (~c3_1(a408)) | (~c1_1(a408)))),
% 1.97/1.61 inference(quant_inst,[status(thm)],[])).
% 1.97/1.61 tff(3121,plain,
% 1.97/1.61 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a408) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a408)) | (~c1_1(a408))),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3120, 3119])).
% 1.97/1.61 tff(3122,plain,
% 1.97/1.61 ((~c3_1(a402)) | (~c1_1(a408))),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3121, 150, 3115, 1439, 3114, 105, 531])).
% 1.97/1.61 tff(3123,plain,
% 1.97/1.61 (~c3_1(a402)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3122, 3113])).
% 1.97/1.61 tff(3124,assumption,(c2_1(a408)), introduced(assumption)).
% 1.97/1.61 tff(3125,plain,
% 1.97/1.61 (c3_1(a402) | (~c1_1(a408))),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[1457, 150, 12, 3124, 1439, 3114, 105, 22])).
% 1.97/1.61 tff(3126,plain,
% 1.97/1.61 ($false),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3125, 3123, 3113])).
% 1.97/1.61 tff(3127,plain,((~c1_1(a408)) | hskp1 | (~c2_1(a408)) | (~c0_1(a402)) | c0_1(a408) | c1_1(a402) | (~c3_1(a408))), inference(lemma,lemma(discharge,[]))).
% 1.97/1.61 tff(3128,plain,
% 1.97/1.61 (~c1_1(a408)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3127, 12, 3107, 3112, 3084, 3111, 3085])).
% 1.97/1.61 tff(3129,plain,
% 1.97/1.61 (~c2_1(a402)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[509, 3110])).
% 1.97/1.61 tff(3130,plain,
% 1.97/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3131,plain,
% 1.97/1.61 (((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408))) <=> (c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3132,plain,
% 1.97/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408)))),
% 1.97/1.61 inference(monotonicity,[status(thm)],[3131])).
% 1.97/1.61 tff(3133,plain,
% 1.97/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408))),
% 1.97/1.61 inference(transitivity,[status(thm)],[3132, 3130])).
% 1.97/1.61 tff(3134,plain,
% 1.97/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)))),
% 1.97/1.61 inference(quant_inst,[status(thm)],[])).
% 1.97/1.61 tff(3135,plain,
% 1.97/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408)),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3134, 3133])).
% 1.97/1.61 tff(3136,plain,
% 1.97/1.61 (~c3_1(a402)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3135, 150, 3107, 3112, 3084, 3111, 3129, 2891, 3128])).
% 1.97/1.61 tff(3137,assumption,(~c1_1(a408)), introduced(assumption)).
% 1.97/1.61 tff(3138,plain,
% 1.97/1.61 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | c2_1(a477) | (~ndr1_0) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp18 | hskp3 | c2_1(a477) | (~ndr1_0) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3139,plain,
% 1.97/1.61 ((hskp18 | hskp3 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477))) <=> (hskp18 | hskp3 | c2_1(a477) | (~ndr1_0) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3140,plain,
% 1.97/1.61 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | c2_1(a477) | (~ndr1_0) | c1_1(a477) | (~c3_1(a477))))),
% 1.97/1.61 inference(monotonicity,[status(thm)],[3139])).
% 1.97/1.61 tff(3141,plain,
% 1.97/1.61 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp18 | hskp3 | c2_1(a477) | (~ndr1_0) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.61 inference(transitivity,[status(thm)],[3140, 3138])).
% 1.97/1.61 tff(3142,plain,
% 1.97/1.61 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.61 inference(quant_inst,[status(thm)],[])).
% 1.97/1.61 tff(3143,plain,
% 1.97/1.61 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp18 | hskp3 | c2_1(a477) | (~ndr1_0) | c1_1(a477) | (~c3_1(a477))),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3142, 3141])).
% 1.97/1.61 tff(3144,plain,
% 1.97/1.61 (hskp18 | hskp3 | c1_1(a477)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3143, 150, 3075, 3058, 1507])).
% 1.97/1.61 tff(3145,plain,
% 1.97/1.61 (hskp18),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3144, 1, 44])).
% 1.97/1.61 tff(3146,plain,
% 1.97/1.61 (~c3_1(a440)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[1521, 3145])).
% 1.97/1.61 tff(3147,plain,
% 1.97/1.61 (~c2_1(a440)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[1527, 3145])).
% 1.97/1.61 tff(3148,plain,
% 1.97/1.61 (c0_1(a440)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[1539, 3145])).
% 1.97/1.61 tff(3149,plain,
% 1.97/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a477) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | (~c0_1(a440)) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a477) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | (~c0_1(a440)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3150,plain,
% 1.97/1.61 (((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a477) | c2_1(a477) | (~c3_1(a477))) <=> (c2_1(a477) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | (~c0_1(a440)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3151,plain,
% 1.97/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a477) | c2_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a477) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | (~c0_1(a440)) | c1_1(a477) | (~c3_1(a477))))),
% 1.97/1.61 inference(monotonicity,[status(thm)],[3150])).
% 1.97/1.61 tff(3152,plain,
% 1.97/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a477) | c2_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a477) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | (~c0_1(a440)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.61 inference(transitivity,[status(thm)],[3151, 3149])).
% 1.97/1.61 tff(3153,plain,
% 1.97/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a440) | c3_1(a440) | (~c0_1(a440)) | c1_1(a408) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a477) | c2_1(a477) | (~c3_1(a477)))),
% 1.97/1.61 inference(quant_inst,[status(thm)],[])).
% 1.97/1.61 tff(3154,plain,
% 1.97/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a477) | c2_1(a440) | c3_1(a440) | (~ndr1_0) | (~c2_1(a408)) | (~c3_1(a408)) | c1_1(a408) | (~c0_1(a440)) | c1_1(a477) | (~c3_1(a477))),
% 1.97/1.61 inference(modus_ponens,[status(thm)],[3153, 3152])).
% 1.97/1.61 tff(3155,plain,
% 1.97/1.61 ($false),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3154, 150, 3075, 3148, 3107, 3085, 3058, 3147, 3146, 1497, 1, 3137])).
% 1.97/1.61 tff(3156,plain,(c1_1(a477) | c1_1(a408) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.97/1.61 tff(3157,plain,
% 1.97/1.61 (c1_1(a477)),
% 1.97/1.61 inference(unit_resolution,[status(thm)],[3156, 3128, 44])).
% 1.97/1.61 tff(3158,plain,
% 1.97/1.61 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a477) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a477) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3159,plain,
% 1.97/1.61 ((hskp22 | (~ndr1_0) | c2_1(a477) | (~c1_1(a477)) | (~c3_1(a477)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402))) <=> (hskp22 | c2_1(a477) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.61 inference(rewrite,[status(thm)],[])).
% 1.97/1.61 tff(3160,plain,
% 1.97/1.61 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a477) | (~c1_1(a477)) | (~c3_1(a477)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a477) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477))))),
% 1.97/1.61 inference(monotonicity,[status(thm)],[3159])).
% 1.97/1.61 tff(3161,plain,
% 1.97/1.61 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a477) | (~c1_1(a477)) | (~c3_1(a477)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a477) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.61 inference(transitivity,[status(thm)],[3160, 3158])).
% 1.97/1.61 tff(3162,plain,
% 1.97/1.61 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a477) | (~c1_1(a477)) | (~c3_1(a477)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))),
% 1.97/1.62 inference(quant_inst,[status(thm)],[])).
% 1.97/1.62 tff(3163,plain,
% 1.97/1.62 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a477) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477))),
% 1.97/1.62 inference(modus_ponens,[status(thm)],[3162, 3161])).
% 1.97/1.62 tff(3164,plain,
% 1.97/1.62 (hskp22 | c3_1(a402) | (~c1_1(a477))),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3163, 150, 3075, 3112, 3058, 3129, 929])).
% 1.97/1.62 tff(3165,plain,
% 1.97/1.62 (hskp22),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3164, 3157, 3136])).
% 1.97/1.62 tff(3166,plain,
% 1.97/1.62 (~c1_1(a451)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[844, 3165])).
% 1.97/1.62 tff(3167,plain,
% 1.97/1.62 (c0_1(a451)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[866, 3165])).
% 1.97/1.62 tff(3168,plain,
% 1.97/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a451) | c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408) | (~c3_1(a451)) | (~c0_1(a451)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a451) | c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.97/1.62 inference(rewrite,[status(thm)],[])).
% 1.97/1.62 tff(3169,plain,
% 1.97/1.62 (((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408))) <=> (c1_1(a451) | c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.97/1.62 inference(rewrite,[status(thm)],[])).
% 1.97/1.62 tff(3170,plain,
% 1.97/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a451) | c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408) | (~c3_1(a451)) | (~c0_1(a451))))),
% 1.97/1.62 inference(monotonicity,[status(thm)],[3169])).
% 1.97/1.62 tff(3171,plain,
% 1.97/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a451) | c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.97/1.62 inference(transitivity,[status(thm)],[3170, 3168])).
% 1.97/1.62 tff(3172,plain,
% 1.97/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c2_1(a402) | c1_1(a402) | (~c0_1(a402)) | c1_1(a408) | c0_1(a408) | (~c2_1(a408)))),
% 1.97/1.62 inference(quant_inst,[status(thm)],[])).
% 1.97/1.62 tff(3173,plain,
% 1.97/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a451) | c0_1(a408) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c2_1(a408)) | c1_1(a408) | (~c3_1(a451)) | (~c0_1(a451))),
% 1.97/1.62 inference(modus_ponens,[status(thm)],[3172, 3171])).
% 1.97/1.62 tff(3174,plain,
% 1.97/1.62 (~c3_1(a451)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3173, 150, 3167, 3107, 3112, 3166, 3084, 3111, 3129, 2891, 3128])).
% 1.97/1.62 tff(3175,plain,
% 1.97/1.62 (hskp16),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3100, 3157, 44])).
% 1.97/1.62 tff(3176,plain,
% 1.97/1.62 (~c0_1(a434)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[1022, 3175])).
% 1.97/1.62 tff(3177,plain,
% 1.97/1.62 (c1_1(a434)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[1044, 3175])).
% 1.97/1.62 tff(3178,plain,
% 1.97/1.62 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c1_1(a451) | c0_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c1_1(a434)) | c3_1(a451) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c1_1(a451) | c0_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c1_1(a434)) | c3_1(a451) | (~c0_1(a451)))),
% 1.97/1.62 inference(rewrite,[status(thm)],[])).
% 1.97/1.62 tff(3179,plain,
% 1.97/1.62 ((hskp1 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434))) <=> (hskp1 | c1_1(a451) | c0_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c1_1(a434)) | c3_1(a451) | (~c0_1(a451)))),
% 1.97/1.62 inference(rewrite,[status(thm)],[])).
% 1.97/1.62 tff(3180,plain,
% 1.97/1.62 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | c1_1(a451) | c0_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c1_1(a434)) | c3_1(a451) | (~c0_1(a451))))),
% 1.97/1.62 inference(monotonicity,[status(thm)],[3179])).
% 1.97/1.62 tff(3181,plain,
% 1.97/1.62 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c1_1(a451) | c0_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c1_1(a434)) | c3_1(a451) | (~c0_1(a451)))),
% 1.97/1.62 inference(transitivity,[status(thm)],[3180, 3178])).
% 1.97/1.62 tff(3182,plain,
% 1.97/1.62 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c0_1(a451)) | c0_1(a434) | (~c2_1(a434)) | (~c1_1(a434)))),
% 1.97/1.62 inference(quant_inst,[status(thm)],[])).
% 1.97/1.62 tff(3183,plain,
% 1.97/1.62 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp1 | c1_1(a451) | c0_1(a434) | (~ndr1_0) | (~c2_1(a434)) | (~c1_1(a434)) | c3_1(a451) | (~c0_1(a451))),
% 1.97/1.62 inference(modus_ponens,[status(thm)],[3182, 3181])).
% 1.97/1.62 tff(3184,plain,
% 1.97/1.62 (~c2_1(a434)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3183, 150, 12, 3167, 3177, 3166, 3176, 22, 3174])).
% 1.97/1.62 tff(3185,plain,
% 1.97/1.62 (~c3_1(a434)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[1016, 3175])).
% 1.97/1.62 tff(3186,plain,
% 1.97/1.62 ($false),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[2273, 150, 3177, 3107, 3176, 3185, 3084, 346, 3184, 3128])).
% 1.97/1.62 tff(3187,plain,(hskp1 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.97/1.62 tff(3188,plain,
% 1.97/1.62 (hskp1),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3187, 44])).
% 1.97/1.62 tff(3189,plain,
% 1.97/1.62 (~c3_1(a401)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[794, 3188])).
% 1.97/1.62 tff(3190,plain,
% 1.97/1.62 (c1_1(a401)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[805, 3188])).
% 1.97/1.62 tff(3191,plain,
% 1.97/1.62 (c0_1(a401)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[816, 3188])).
% 1.97/1.62 tff(3192,plain,
% 1.97/1.62 (hskp20),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[823, 150, 3191, 3190, 3189, 483])).
% 1.97/1.62 tff(3193,plain,
% 1.97/1.62 (~c2_1(a449)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[914, 3192])).
% 1.97/1.62 tff(3194,plain,
% 1.97/1.62 (c3_1(a449)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[908, 3192])).
% 1.97/1.62 tff(3195,plain,
% 1.97/1.62 (c1_1(a449)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[834, 3192])).
% 1.97/1.62 tff(3196,plain,
% 1.97/1.62 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)) | (~c3_1(a477)))),
% 1.97/1.62 inference(rewrite,[status(thm)],[])).
% 1.97/1.62 tff(3197,plain,
% 1.97/1.62 ((hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a477) | c0_1(a477) | (~c3_1(a477))) <=> (hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)) | (~c3_1(a477)))),
% 1.97/1.62 inference(rewrite,[status(thm)],[])).
% 1.97/1.62 tff(3198,plain,
% 1.97/1.62 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)) | (~c3_1(a477))))),
% 1.97/1.62 inference(monotonicity,[status(thm)],[3197])).
% 1.97/1.62 tff(3199,plain,
% 1.97/1.62 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)) | (~c3_1(a477)))),
% 1.97/1.62 inference(transitivity,[status(thm)],[3198, 3196])).
% 1.97/1.62 tff(3200,plain,
% 1.97/1.62 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a477) | c0_1(a477) | (~c3_1(a477)))),
% 1.97/1.62 inference(quant_inst,[status(thm)],[])).
% 1.97/1.62 tff(3201,plain,
% 1.97/1.62 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a449) | (~ndr1_0) | (~c3_1(a449)) | (~c1_1(a449)) | (~c3_1(a477))),
% 1.97/1.62 inference(modus_ponens,[status(thm)],[3200, 3199])).
% 1.97/1.62 tff(3202,plain,
% 1.97/1.62 (hskp10),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3201, 150, 3075, 3195, 3194, 3064, 3058, 3193, 2169])).
% 1.97/1.62 tff(3203,plain,
% 1.97/1.62 (~c2_1(a418)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[2181, 3202])).
% 1.97/1.62 tff(3204,plain,
% 1.97/1.62 (~c0_1(a418)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[2187, 3202])).
% 1.97/1.62 tff(3205,plain,
% 1.97/1.62 (hskp11),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[2331, 150, 3107, 3085, 3191, 3190, 3084, 3189, 1117])).
% 1.97/1.62 tff(3206,plain,
% 1.97/1.62 (~c2_1(a420)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[1223, 3205])).
% 1.97/1.62 tff(3207,plain,
% 1.97/1.62 (~c1_1(a420)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[1106, 3205])).
% 1.97/1.62 tff(3208,plain,
% 1.97/1.62 (c1_1(a418)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[2200, 3202])).
% 1.97/1.62 tff(3209,plain,
% 1.97/1.62 (~c3_1(a420)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[2341, 150, 3208, 3107, 3085, 3207, 3206, 3204, 3203, 3084, 43])).
% 1.97/1.62 tff(3210,plain,
% 1.97/1.62 (~c0_1(a420)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[1100, 3205])).
% 1.97/1.62 tff(3211,plain,
% 1.97/1.62 (hskp0),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[2349, 150, 3107, 3085, 3210, 3207, 3206, 3084, 2150])).
% 1.97/1.62 tff(3212,plain,
% 1.97/1.62 (~c3_1(a400)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[405, 3211])).
% 1.97/1.62 tff(3213,plain,
% 1.97/1.62 (c2_1(a400)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[374, 3211])).
% 1.97/1.62 tff(3214,plain,
% 1.97/1.62 (c1_1(a400)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[385, 3211])).
% 1.97/1.62 tff(3215,plain,
% 1.97/1.62 ($false),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[2359, 150, 44, 3214, 3213, 3210, 3207, 3212, 1426, 3209])).
% 1.97/1.62 tff(3216,plain,(hskp3), inference(lemma,lemma(discharge,[]))).
% 1.97/1.62 tff(3217,plain,
% 1.97/1.62 (~c2_1(a403)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[1644, 3216])).
% 1.97/1.62 tff(3218,plain,
% 1.97/1.62 (~c0_1(a403)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[1272, 3216])).
% 1.97/1.62 tff(3219,plain,
% 1.97/1.62 (hskp2 | hskp1 | c1_1(a403)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[502, 150, 3218, 3217, 33])).
% 1.97/1.62 tff(3220,plain,
% 1.97/1.62 (c1_1(a403)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3219, 23, 12])).
% 1.97/1.62 tff(3221,plain,
% 1.97/1.62 (~c3_1(a403)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[1994, 3216])).
% 1.97/1.62 tff(3222,plain,
% 1.97/1.62 (hskp7 | hskp2 | (~c1_1(a403))),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[646, 150, 3217, 3221, 118])).
% 1.97/1.62 tff(3223,plain,
% 1.97/1.62 (hskp7),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3222, 23, 3220])).
% 1.97/1.62 tff(3224,plain,
% 1.97/1.62 (~c3_1(a410)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[254, 3223])).
% 1.97/1.62 tff(3225,plain,
% 1.97/1.62 (~c1_1(a410)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[260, 3223])).
% 1.97/1.62 tff(3226,plain,
% 1.97/1.62 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.62 inference(rewrite,[status(thm)],[])).
% 1.97/1.62 tff(3227,plain,
% 1.97/1.62 ((hskp13 | hskp2 | (~ndr1_0) | c2_1(a477) | (~c1_1(a477)) | (~c3_1(a477))) <=> (hskp13 | hskp2 | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.62 inference(rewrite,[status(thm)],[])).
% 1.97/1.62 tff(3228,plain,
% 1.97/1.62 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a477) | (~c1_1(a477)) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477))))),
% 1.97/1.62 inference(monotonicity,[status(thm)],[3227])).
% 1.97/1.62 tff(3229,plain,
% 1.97/1.62 (((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a477) | (~c1_1(a477)) | (~c3_1(a477)))) <=> ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.62 inference(transitivity,[status(thm)],[3228, 3226])).
% 1.97/1.62 tff(3230,plain,
% 1.97/1.62 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp13 | hskp2 | (~ndr1_0) | c2_1(a477) | (~c1_1(a477)) | (~c3_1(a477)))),
% 1.97/1.62 inference(quant_inst,[status(thm)],[])).
% 1.97/1.62 tff(3231,plain,
% 1.97/1.62 ((~![U: $i] : (hskp13 | hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp13 | hskp2 | c2_1(a477) | (~ndr1_0) | (~c3_1(a477)) | (~c1_1(a477))),
% 1.97/1.62 inference(modus_ponens,[status(thm)],[3230, 3229])).
% 1.97/1.62 tff(3232,plain,
% 1.97/1.62 (hskp13 | hskp2 | (~c1_1(a477))),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3231, 150, 3075, 3058, 271])).
% 1.97/1.62 tff(3233,plain,
% 1.97/1.62 (hskp13),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3232, 23, 3093])).
% 1.97/1.62 tff(3234,plain,
% 1.97/1.62 (~c0_1(a427)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[284, 3233])).
% 1.97/1.62 tff(3235,plain,
% 1.97/1.62 (c0_1(a410)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[295, 3223])).
% 1.97/1.62 tff(3236,plain,
% 1.97/1.62 (c2_1(a427)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[306, 3233])).
% 1.97/1.62 tff(3237,plain,
% 1.97/1.62 (c1_1(a427)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[317, 3233])).
% 1.97/1.62 tff(3238,plain,
% 1.97/1.62 ($false),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[324, 150, 12, 3237, 3236, 3235, 3234, 3225, 3224, 22])).
% 1.97/1.62 tff(3239,plain,(hskp2 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.97/1.62 tff(3240,plain,
% 1.97/1.62 (hskp2),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3239, 12])).
% 1.97/1.62 tff(3241,plain,
% 1.97/1.62 (~c1_1(a402)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[2623, 3240])).
% 1.97/1.62 tff(3242,plain,
% 1.97/1.62 (c0_1(a402)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[520, 3240])).
% 1.97/1.62 tff(3243,assumption,(hskp19), introduced(assumption)).
% 1.97/1.62 tff(3244,plain,
% 1.97/1.62 (c1_1(a445)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[458, 3243])).
% 1.97/1.62 tff(3245,plain,
% 1.97/1.62 (~c0_1(a445)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[332, 3243])).
% 1.97/1.62 tff(3246,plain,
% 1.97/1.62 (c3_1(a445)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[470, 3243])).
% 1.97/1.62 tff(3247,plain,
% 1.97/1.62 (hskp11),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[788, 3246, 12, 3241, 3217, 3218, 3221, 3245, 3244])).
% 1.97/1.62 tff(3248,plain,
% 1.97/1.62 (~c2_1(a420)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[1223, 3247])).
% 1.97/1.62 tff(3249,plain,
% 1.97/1.62 (~c0_1(a420)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[1100, 3247])).
% 1.97/1.62 tff(3250,plain,
% 1.97/1.62 (~c1_1(a420)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[1106, 3247])).
% 1.97/1.62 tff(3251,plain,
% 1.97/1.62 ($false),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[1169, 3250, 3249, 3218, 3241, 3244, 3245, 3246, 12, 3248, 3217, 3221])).
% 1.97/1.62 tff(3252,plain,((~hskp19) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.97/1.62 tff(3253,plain,
% 1.97/1.62 (~hskp19),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3252, 12])).
% 1.97/1.62 tff(3254,plain,
% 1.97/1.62 (~c2_1(a402)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[509, 3240])).
% 1.97/1.62 tff(3255,assumption,(~hskp16), introduced(assumption)).
% 1.97/1.62 tff(3256,plain,
% 1.97/1.62 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)))),
% 1.97/1.62 inference(rewrite,[status(thm)],[])).
% 1.97/1.62 tff(3257,plain,
% 1.97/1.62 ((hskp16 | hskp7 | (~ndr1_0) | c2_1(a402) | (~c3_1(a402)) | (~c0_1(a402))) <=> (hskp16 | hskp7 | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)))),
% 1.97/1.62 inference(rewrite,[status(thm)],[])).
% 1.97/1.62 tff(3258,plain,
% 1.97/1.62 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a402) | (~c3_1(a402)) | (~c0_1(a402)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402))))),
% 1.97/1.62 inference(monotonicity,[status(thm)],[3257])).
% 1.97/1.62 tff(3259,plain,
% 1.97/1.62 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a402) | (~c3_1(a402)) | (~c0_1(a402)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)))),
% 1.97/1.62 inference(transitivity,[status(thm)],[3258, 3256])).
% 1.97/1.62 tff(3260,plain,
% 1.97/1.62 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a402) | (~c3_1(a402)) | (~c0_1(a402)))),
% 1.97/1.62 inference(quant_inst,[status(thm)],[])).
% 1.97/1.62 tff(3261,plain,
% 1.97/1.62 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402))),
% 1.97/1.62 inference(modus_ponens,[status(thm)],[3260, 3259])).
% 1.97/1.62 tff(3262,plain,
% 1.97/1.62 (hskp16 | hskp7 | (~c3_1(a402))),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3261, 150, 3242, 3254, 1003])).
% 1.97/1.62 tff(3263,plain,
% 1.97/1.62 (~c3_1(a402)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3262, 3255, 1025])).
% 1.97/1.62 tff(3264,plain,
% 1.97/1.62 (hskp12 | c3_1(a402)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[555, 150, 12, 3242, 3241, 549])).
% 1.97/1.62 tff(3265,plain,
% 1.97/1.62 (hskp12),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3264, 3263])).
% 1.97/1.62 tff(3266,plain,
% 1.97/1.62 (~c2_1(a426)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[562, 3265])).
% 1.97/1.62 tff(3267,plain,
% 1.97/1.62 (c0_1(a426)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[612, 3265])).
% 1.97/1.62 tff(3268,plain,
% 1.97/1.62 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | c2_1(a426) | (~ndr1_0) | (~c0_1(a426)) | (~c3_1(a426)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c2_1(a426) | (~ndr1_0) | (~c0_1(a426)) | (~c3_1(a426)))),
% 1.97/1.62 inference(rewrite,[status(thm)],[])).
% 1.97/1.62 tff(3269,plain,
% 1.97/1.62 ((hskp16 | hskp7 | (~ndr1_0) | c2_1(a426) | (~c3_1(a426)) | (~c0_1(a426))) <=> (hskp16 | hskp7 | c2_1(a426) | (~ndr1_0) | (~c0_1(a426)) | (~c3_1(a426)))),
% 1.97/1.62 inference(rewrite,[status(thm)],[])).
% 1.97/1.62 tff(3270,plain,
% 1.97/1.62 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a426) | (~c3_1(a426)) | (~c0_1(a426)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | c2_1(a426) | (~ndr1_0) | (~c0_1(a426)) | (~c3_1(a426))))),
% 1.97/1.62 inference(monotonicity,[status(thm)],[3269])).
% 1.97/1.62 tff(3271,plain,
% 1.97/1.62 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a426) | (~c3_1(a426)) | (~c0_1(a426)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c2_1(a426) | (~ndr1_0) | (~c0_1(a426)) | (~c3_1(a426)))),
% 1.97/1.62 inference(transitivity,[status(thm)],[3270, 3268])).
% 1.97/1.62 tff(3272,plain,
% 1.97/1.62 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a426) | (~c3_1(a426)) | (~c0_1(a426)))),
% 1.97/1.62 inference(quant_inst,[status(thm)],[])).
% 1.97/1.62 tff(3273,plain,
% 1.97/1.62 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c2_1(a426) | (~ndr1_0) | (~c0_1(a426)) | (~c3_1(a426))),
% 1.97/1.62 inference(modus_ponens,[status(thm)],[3272, 3271])).
% 1.97/1.62 tff(3274,plain,
% 1.97/1.62 (~c3_1(a426)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3273, 150, 3255, 1025, 3267, 3266, 1003])).
% 1.97/1.62 tff(3275,plain,
% 1.97/1.62 (hskp22 | c3_1(a402) | (~c1_1(a477))),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3163, 150, 3075, 3242, 3058, 3254, 929])).
% 1.97/1.62 tff(3276,plain,
% 1.97/1.62 (~c1_1(a477)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3275, 3263, 934])).
% 1.97/1.62 tff(3277,plain,
% 1.97/1.62 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.97/1.62 inference(bind,[status(th)],[])).
% 1.97/1.62 tff(3278,plain,
% 1.97/1.62 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.97/1.62 inference(quant_intro,[status(thm)],[3277])).
% 1.97/1.62 tff(3279,plain,
% 1.97/1.62 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.97/1.62 inference(rewrite,[status(thm)],[])).
% 1.97/1.62 tff(3280,plain,
% 1.97/1.62 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.97/1.62 inference(bind,[status(th)],[])).
% 1.97/1.62 tff(3281,plain,
% 1.97/1.62 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.97/1.62 inference(quant_intro,[status(thm)],[3280])).
% 1.97/1.62 tff(3282,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 1.97/1.62 tff(3283,plain,
% 1.97/1.62 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.97/1.62 inference(modus_ponens,[status(thm)],[3282, 3281])).
% 1.97/1.62 tff(3284,plain,
% 1.97/1.62 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.97/1.62 inference(modus_ponens,[status(thm)],[3283, 3279])).
% 1.97/1.62 tff(3285,plain,(
% 1.97/1.62 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.97/1.62 inference(skolemize,[status(sab)],[3284])).
% 1.97/1.62 tff(3286,plain,
% 1.97/1.62 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.97/1.62 inference(modus_ponens,[status(thm)],[3285, 3278])).
% 1.97/1.62 tff(3287,plain,
% 1.97/1.62 (c1_1(a426)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[601, 3265])).
% 1.97/1.62 tff(3288,plain,
% 1.97/1.62 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a477) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a477) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.62 inference(rewrite,[status(thm)],[])).
% 1.97/1.62 tff(3289,plain,
% 1.97/1.62 ((hskp7 | (~ndr1_0) | c2_1(a426) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477))) <=> (hskp7 | c0_1(a477) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.62 inference(rewrite,[status(thm)],[])).
% 1.97/1.62 tff(3290,plain,
% 1.97/1.62 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a426) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a477) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | (~c3_1(a477))))),
% 1.97/1.62 inference(monotonicity,[status(thm)],[3289])).
% 1.97/1.62 tff(3291,plain,
% 1.97/1.62 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a426) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a477) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.62 inference(transitivity,[status(thm)],[3290, 3288])).
% 1.97/1.62 tff(3292,plain,
% 1.97/1.62 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a426) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)))),
% 1.97/1.62 inference(quant_inst,[status(thm)],[])).
% 1.97/1.62 tff(3293,plain,
% 1.97/1.62 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a477) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | c1_1(a477) | (~c3_1(a477))),
% 1.97/1.62 inference(modus_ponens,[status(thm)],[3292, 3291])).
% 1.97/1.62 tff(3294,plain,
% 1.97/1.62 ($false),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3293, 150, 1025, 3075, 3287, 3064, 3266, 3286, 3276, 3274])).
% 1.97/1.62 tff(3295,plain,(hskp16 | hskp7 | hskp22 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.97/1.62 tff(3296,plain,
% 1.97/1.62 (hskp16),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3295, 1025, 934, 12])).
% 1.97/1.62 tff(3297,plain,
% 1.97/1.62 (~c0_1(a434)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[1022, 3296])).
% 1.97/1.62 tff(3298,assumption,(c1_1(a477)), introduced(assumption)).
% 1.97/1.62 tff(3299,plain,
% 1.97/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a477) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a477) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.62 inference(rewrite,[status(thm)],[])).
% 1.97/1.62 tff(3300,plain,
% 1.97/1.62 (((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477))) <=> (c0_1(a477) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.62 inference(rewrite,[status(thm)],[])).
% 1.97/1.62 tff(3301,plain,
% 1.97/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a477) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477))))),
% 1.97/1.62 inference(monotonicity,[status(thm)],[3300])).
% 1.97/1.62 tff(3302,plain,
% 1.97/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a477) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.62 inference(transitivity,[status(thm)],[3301, 3299])).
% 1.97/1.62 tff(3303,plain,
% 1.97/1.62 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.62 inference(quant_inst,[status(thm)],[])).
% 1.97/1.62 tff(3304,plain,
% 1.97/1.62 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a477) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a477)) | (~c1_1(a477))),
% 1.97/1.62 inference(modus_ponens,[status(thm)],[3303, 3302])).
% 1.97/1.62 tff(3305,plain,
% 1.97/1.62 ((~c3_1(a402)) | (~c1_1(a477))),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3304, 150, 3075, 1439, 3064, 105, 531])).
% 1.97/1.62 tff(3306,plain,
% 1.97/1.62 (~c3_1(a402)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3305, 3298])).
% 1.97/1.62 tff(3307,plain,
% 1.97/1.62 (hskp22 | c3_1(a402) | (~c1_1(a477))),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3163, 150, 3075, 1439, 3058, 2054, 929])).
% 1.97/1.62 tff(3308,plain,
% 1.97/1.62 ($false),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3307, 3306, 3298, 934])).
% 1.97/1.62 tff(3309,plain,((~c1_1(a477)) | hskp22 | (~c0_1(a402)) | c2_1(a402) | c1_1(a402)), inference(lemma,lemma(discharge,[]))).
% 1.97/1.62 tff(3310,plain,
% 1.97/1.62 (~c1_1(a477)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[3309, 934, 3242, 3254, 3241])).
% 1.97/1.62 tff(3311,plain,
% 1.97/1.62 (c1_1(a434)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[1044, 3296])).
% 1.97/1.62 tff(3312,plain,
% 1.97/1.62 (~c3_1(a434)),
% 1.97/1.62 inference(unit_resolution,[status(thm)],[1016, 3296])).
% 1.97/1.62 tff(3313,plain,
% 1.97/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a477) | c2_1(a477) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a477) | c2_1(a477) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.63 inference(rewrite,[status(thm)],[])).
% 1.97/1.63 tff(3314,plain,
% 1.97/1.63 (((~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477))) <=> (c0_1(a477) | c2_1(a477) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.63 inference(rewrite,[status(thm)],[])).
% 1.97/1.63 tff(3315,plain,
% 1.97/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a477) | c2_1(a477) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | c1_1(a477) | (~c3_1(a477))))),
% 1.97/1.63 inference(monotonicity,[status(thm)],[3314])).
% 1.97/1.63 tff(3316,plain,
% 1.97/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a477) | c2_1(a477) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.63 inference(transitivity,[status(thm)],[3315, 3313])).
% 1.97/1.63 tff(3317,plain,
% 1.97/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c0_1(a434) | c3_1(a434) | (~c2_1(a434)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)))),
% 1.97/1.63 inference(quant_inst,[status(thm)],[])).
% 1.97/1.63 tff(3318,plain,
% 1.97/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a477) | c2_1(a477) | c0_1(a434) | c3_1(a434) | (~ndr1_0) | (~c2_1(a434)) | c1_1(a477) | (~c3_1(a477))),
% 1.97/1.63 inference(modus_ponens,[status(thm)],[3317, 3316])).
% 1.97/1.63 tff(3319,plain,
% 1.97/1.63 (~c2_1(a434)),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[3318, 150, 3075, 3064, 3058, 1047, 1026, 778, 1])).
% 1.97/1.63 tff(3320,plain,
% 1.97/1.63 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a477) | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a477) | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.63 inference(rewrite,[status(thm)],[])).
% 1.97/1.63 tff(3321,plain,
% 1.97/1.63 ((hskp7 | (~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477))) <=> (hskp7 | c0_1(a477) | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.63 inference(rewrite,[status(thm)],[])).
% 1.97/1.63 tff(3322,plain,
% 1.97/1.63 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a477) | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)) | c1_1(a477) | (~c3_1(a477))))),
% 1.97/1.63 inference(monotonicity,[status(thm)],[3321])).
% 1.97/1.63 tff(3323,plain,
% 1.97/1.63 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a477) | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.63 inference(transitivity,[status(thm)],[3322, 3320])).
% 1.97/1.63 tff(3324,plain,
% 1.97/1.63 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a434) | c3_1(a434) | (~c1_1(a434)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)))),
% 1.97/1.63 inference(quant_inst,[status(thm)],[])).
% 1.97/1.63 tff(3325,plain,
% 1.97/1.63 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a477) | c3_1(a434) | (~ndr1_0) | c2_1(a434) | (~c1_1(a434)) | c1_1(a477) | (~c3_1(a477))),
% 1.97/1.63 inference(modus_ponens,[status(thm)],[3324, 3323])).
% 1.97/1.63 tff(3326,plain,
% 1.97/1.63 ($false),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[3325, 150, 1025, 3075, 2634, 3064, 1026, 3286, 3319, 1])).
% 1.97/1.63 tff(3327,plain,(c1_1(a477) | hskp7 | (~c1_1(a434)) | c3_1(a434) | c0_1(a434)), inference(lemma,lemma(discharge,[]))).
% 1.97/1.63 tff(3328,plain,
% 1.97/1.63 ($false),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[3327, 3312, 3311, 3310, 1025, 3297])).
% 1.97/1.63 tff(3329,plain,(hskp7 | hskp22 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.97/1.63 tff(3330,plain,
% 1.97/1.63 (hskp7),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[3329, 934, 12])).
% 1.97/1.63 tff(3331,plain,
% 1.97/1.63 (~c3_1(a410)),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[254, 3330])).
% 1.97/1.63 tff(3332,plain,
% 1.97/1.63 (~c1_1(a410)),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[260, 3330])).
% 1.97/1.63 tff(3333,plain,
% 1.97/1.63 (c0_1(a410)),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[295, 3330])).
% 1.97/1.63 tff(3334,plain,
% 1.97/1.63 (((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)))) <=> ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | hskp1 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)))),
% 1.97/1.63 inference(rewrite,[status(thm)],[])).
% 1.97/1.63 tff(3335,plain,
% 1.97/1.63 ((hskp12 | hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410))) <=> (hskp12 | hskp1 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)))),
% 1.97/1.63 inference(rewrite,[status(thm)],[])).
% 1.97/1.63 tff(3336,plain,
% 1.97/1.63 (((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)))) <=> ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410))))),
% 1.97/1.63 inference(monotonicity,[status(thm)],[3335])).
% 1.97/1.63 tff(3337,plain,
% 1.97/1.63 (((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)))) <=> ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | hskp1 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)))),
% 1.97/1.63 inference(transitivity,[status(thm)],[3336, 3334])).
% 1.97/1.63 tff(3338,plain,
% 1.97/1.63 ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp12 | hskp1 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)))),
% 1.97/1.63 inference(quant_inst,[status(thm)],[])).
% 1.97/1.63 tff(3339,plain,
% 1.97/1.63 ((~![U: $i] : (hskp12 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp12 | hskp1 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410))),
% 1.97/1.63 inference(modus_ponens,[status(thm)],[3338, 3337])).
% 1.97/1.63 tff(3340,plain,
% 1.97/1.63 (hskp12),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[3339, 150, 12, 3333, 3332, 3331, 549])).
% 1.97/1.63 tff(3341,plain,
% 1.97/1.63 (~c2_1(a426)),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[562, 3340])).
% 1.97/1.63 tff(3342,plain,
% 1.97/1.63 (c1_1(a426)),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[601, 3340])).
% 1.97/1.63 tff(3343,plain,
% 1.97/1.63 (c0_1(a426)),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[612, 3340])).
% 1.97/1.63 tff(3344,plain,
% 1.97/1.63 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.97/1.63 inference(bind,[status(th)],[])).
% 1.97/1.63 tff(3345,plain,
% 1.97/1.63 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.97/1.63 inference(quant_intro,[status(thm)],[3344])).
% 1.97/1.63 tff(3346,plain,
% 1.97/1.63 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.97/1.63 inference(rewrite,[status(thm)],[])).
% 1.97/1.63 tff(3347,plain,
% 1.97/1.63 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.97/1.63 inference(bind,[status(th)],[])).
% 1.97/1.63 tff(3348,plain,
% 1.97/1.63 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.97/1.63 inference(quant_intro,[status(thm)],[3347])).
% 1.97/1.63 tff(3349,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 1.97/1.63 tff(3350,plain,
% 1.97/1.63 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.97/1.63 inference(modus_ponens,[status(thm)],[3349, 3348])).
% 1.97/1.63 tff(3351,plain,
% 1.97/1.63 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.97/1.63 inference(modus_ponens,[status(thm)],[3350, 3346])).
% 1.97/1.63 tff(3352,plain,(
% 1.97/1.63 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.97/1.63 inference(skolemize,[status(sab)],[3351])).
% 1.97/1.63 tff(3353,plain,
% 1.97/1.63 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.97/1.63 inference(modus_ponens,[status(thm)],[3352, 3345])).
% 1.97/1.63 tff(3354,assumption,(~c3_1(a426)), introduced(assumption)).
% 1.97/1.63 tff(3355,assumption,(c1_1(a426)), introduced(assumption)).
% 1.97/1.63 tff(3356,assumption,(c0_1(a426)), introduced(assumption)).
% 1.97/1.63 tff(3357,plain,
% 1.97/1.63 (((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c1_1(a426)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c1_1(a426)))),
% 1.97/1.63 inference(rewrite,[status(thm)],[])).
% 1.97/1.63 tff(3358,plain,
% 1.97/1.63 ((hskp20 | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | (~c0_1(a426))) <=> (hskp20 | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c1_1(a426)))),
% 1.97/1.63 inference(rewrite,[status(thm)],[])).
% 1.97/1.63 tff(3359,plain,
% 1.97/1.63 (((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | (~c0_1(a426)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c1_1(a426))))),
% 1.97/1.63 inference(monotonicity,[status(thm)],[3358])).
% 1.97/1.63 tff(3360,plain,
% 1.97/1.63 (((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | (~c0_1(a426)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c1_1(a426)))),
% 1.97/1.63 inference(transitivity,[status(thm)],[3359, 3357])).
% 1.97/1.63 tff(3361,plain,
% 1.97/1.63 ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a426) | (~c1_1(a426)) | (~c0_1(a426)))),
% 1.97/1.63 inference(quant_inst,[status(thm)],[])).
% 1.97/1.63 tff(3362,plain,
% 1.97/1.63 ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c1_1(a426))),
% 1.97/1.63 inference(modus_ponens,[status(thm)],[3361, 3360])).
% 1.97/1.63 tff(3363,plain,
% 1.97/1.63 (hskp20 | c3_1(a426)),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[3362, 150, 3356, 3355, 483])).
% 1.97/1.63 tff(3364,plain,
% 1.97/1.63 (hskp20),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[3363, 3354])).
% 1.97/1.63 tff(3365,plain,
% 1.97/1.63 (~c2_1(a449)),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[914, 3364])).
% 1.97/1.63 tff(3366,plain,
% 1.97/1.63 (c3_1(a449)),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[908, 3364])).
% 1.97/1.63 tff(3367,plain,
% 1.97/1.63 (c1_1(a449)),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[834, 3364])).
% 1.97/1.63 tff(3368,plain,
% 1.97/1.63 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a449) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c3_1(a449)) | (~c1_1(a449)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.97/1.63 inference(rewrite,[status(thm)],[])).
% 1.97/1.63 tff(3369,plain,
% 1.97/1.63 ((hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a426) | c3_1(a426) | (~c0_1(a426))) <=> (hskp22 | c2_1(a449) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.97/1.63 inference(rewrite,[status(thm)],[])).
% 1.97/1.63 tff(3370,plain,
% 1.97/1.63 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a426) | c3_1(a426) | (~c0_1(a426)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a449) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c3_1(a449)) | (~c1_1(a449))))),
% 1.97/1.63 inference(monotonicity,[status(thm)],[3369])).
% 1.97/1.63 tff(3371,plain,
% 1.97/1.63 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a426) | c3_1(a426) | (~c0_1(a426)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c3_1(a449)) | (~c1_1(a449)))),
% 1.97/1.63 inference(transitivity,[status(thm)],[3370, 3368])).
% 1.97/1.63 tff(3372,plain,
% 1.97/1.63 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a449) | (~c1_1(a449)) | (~c3_1(a449)) | c2_1(a426) | c3_1(a426) | (~c0_1(a426)))),
% 1.97/1.63 inference(quant_inst,[status(thm)],[])).
% 1.97/1.63 tff(3373,plain,
% 1.97/1.63 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a449) | c2_1(a426) | (~ndr1_0) | c3_1(a426) | (~c0_1(a426)) | (~c3_1(a449)) | (~c1_1(a449))),
% 1.97/1.63 inference(modus_ponens,[status(thm)],[3372, 3371])).
% 1.97/1.63 tff(3374,plain,
% 1.97/1.63 ($false),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[3373, 150, 934, 3367, 3366, 3356, 3365, 1130, 929, 3354])).
% 1.97/1.63 tff(3375,plain,(c3_1(a426) | hskp22 | (~c0_1(a426)) | c2_1(a426) | (~c1_1(a426))), inference(lemma,lemma(discharge,[]))).
% 1.97/1.63 tff(3376,plain,
% 1.97/1.63 (c3_1(a426)),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[3375, 3342, 3343, 3341, 934])).
% 1.97/1.63 tff(3377,plain,
% 1.97/1.63 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a426) | (~ndr1_0) | (~c3_1(a426)) | (~c1_1(a426)) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a426) | (~ndr1_0) | (~c3_1(a426)) | (~c1_1(a426)) | (~c3_1(a477)))),
% 1.97/1.63 inference(rewrite,[status(thm)],[])).
% 1.97/1.63 tff(3378,plain,
% 1.97/1.63 ((hskp10 | (~ndr1_0) | c2_1(a426) | (~c1_1(a426)) | (~c3_1(a426)) | c2_1(a477) | c0_1(a477) | (~c3_1(a477))) <=> (hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a426) | (~ndr1_0) | (~c3_1(a426)) | (~c1_1(a426)) | (~c3_1(a477)))),
% 1.97/1.63 inference(rewrite,[status(thm)],[])).
% 1.97/1.63 tff(3379,plain,
% 1.97/1.63 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a426) | (~c1_1(a426)) | (~c3_1(a426)) | c2_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a426) | (~ndr1_0) | (~c3_1(a426)) | (~c1_1(a426)) | (~c3_1(a477))))),
% 1.97/1.63 inference(monotonicity,[status(thm)],[3378])).
% 1.97/1.63 tff(3380,plain,
% 1.97/1.63 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a426) | (~c1_1(a426)) | (~c3_1(a426)) | c2_1(a477) | c0_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a426) | (~ndr1_0) | (~c3_1(a426)) | (~c1_1(a426)) | (~c3_1(a477)))),
% 1.97/1.63 inference(transitivity,[status(thm)],[3379, 3377])).
% 1.97/1.63 tff(3381,plain,
% 1.97/1.63 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a426) | (~c1_1(a426)) | (~c3_1(a426)) | c2_1(a477) | c0_1(a477) | (~c3_1(a477)))),
% 1.97/1.63 inference(quant_inst,[status(thm)],[])).
% 1.97/1.63 tff(3382,plain,
% 1.97/1.63 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a477) | c2_1(a477) | c2_1(a426) | (~ndr1_0) | (~c3_1(a426)) | (~c1_1(a426)) | (~c3_1(a477))),
% 1.97/1.63 inference(modus_ponens,[status(thm)],[3381, 3380])).
% 1.97/1.63 tff(3383,plain,
% 1.97/1.63 (hskp10),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[3382, 150, 3075, 3342, 3064, 3058, 3341, 2169, 3376])).
% 1.97/1.63 tff(3384,plain,
% 1.97/1.63 (~c2_1(a418)),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[2181, 3383])).
% 1.97/1.63 tff(3385,plain,
% 1.97/1.63 (~c0_1(a418)),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[2187, 3383])).
% 1.97/1.63 tff(3386,plain,
% 1.97/1.63 (c1_1(a418)),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[2200, 3383])).
% 1.97/1.63 tff(3387,plain,
% 1.97/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a477) | c0_1(a418) | c2_1(a418) | (~ndr1_0) | (~c1_1(a418)) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a477) | c0_1(a418) | c2_1(a418) | (~ndr1_0) | (~c1_1(a418)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.63 inference(rewrite,[status(thm)],[])).
% 1.97/1.63 tff(3388,plain,
% 1.97/1.63 ((hskp28 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c2_1(a418) | c0_1(a418) | (~c1_1(a418))) <=> (hskp28 | c2_1(a477) | c0_1(a418) | c2_1(a418) | (~ndr1_0) | (~c1_1(a418)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.63 inference(rewrite,[status(thm)],[])).
% 1.97/1.63 tff(3389,plain,
% 1.97/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c2_1(a418) | c0_1(a418) | (~c1_1(a418)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a477) | c0_1(a418) | c2_1(a418) | (~ndr1_0) | (~c1_1(a418)) | c1_1(a477) | (~c3_1(a477))))),
% 1.97/1.63 inference(monotonicity,[status(thm)],[3388])).
% 1.97/1.63 tff(3390,plain,
% 1.97/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c2_1(a418) | c0_1(a418) | (~c1_1(a418)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a477) | c0_1(a418) | c2_1(a418) | (~ndr1_0) | (~c1_1(a418)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.63 inference(transitivity,[status(thm)],[3389, 3387])).
% 1.97/1.63 tff(3391,plain,
% 1.97/1.63 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c2_1(a418) | c0_1(a418) | (~c1_1(a418)))),
% 1.97/1.63 inference(quant_inst,[status(thm)],[])).
% 1.97/1.63 tff(3392,plain,
% 1.97/1.63 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a477) | c0_1(a418) | c2_1(a418) | (~ndr1_0) | (~c1_1(a418)) | c1_1(a477) | (~c3_1(a477))),
% 1.97/1.63 inference(modus_ponens,[status(thm)],[3391, 3390])).
% 1.97/1.63 tff(3393,plain,
% 1.97/1.63 (hskp28),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[3392, 150, 3075, 3386, 3058, 3385, 3384, 3353, 1])).
% 1.97/1.63 tff(3394,plain,
% 1.97/1.63 (c2_1(a414)),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[2951, 3393])).
% 1.97/1.63 tff(3395,plain,
% 1.97/1.63 (c0_1(a414)),
% 1.97/1.63 inference(unit_resolution,[status(thm)],[2962, 3393])).
% 1.97/1.63 tff(3396,plain,
% 1.97/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414)))),
% 1.97/1.63 inference(rewrite,[status(thm)],[])).
% 1.97/1.63 tff(3397,plain,
% 1.97/1.63 (((~ndr1_0) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402))) <=> (c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414)))),
% 1.97/1.64 inference(rewrite,[status(thm)],[])).
% 1.97/1.64 tff(3398,plain,
% 1.97/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414))))),
% 1.97/1.64 inference(monotonicity,[status(thm)],[3397])).
% 1.97/1.64 tff(3399,plain,
% 1.97/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414)))),
% 1.97/1.64 inference(transitivity,[status(thm)],[3398, 3396])).
% 1.97/1.64 tff(3400,plain,
% 1.97/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414)) | c2_1(a426) | (~c1_1(a426)) | (~c0_1(a426)) | c1_1(a402) | c2_1(a402) | (~c0_1(a402)))),
% 1.97/1.64 inference(quant_inst,[status(thm)],[])).
% 1.97/1.64 tff(3401,plain,
% 1.97/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a426) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c0_1(a402)) | (~c0_1(a426)) | (~c1_1(a426)) | (~c2_1(a414)) | (~c1_1(a414)) | (~c0_1(a414))),
% 1.97/1.64 inference(modus_ponens,[status(thm)],[3400, 3399])).
% 1.97/1.64 tff(3402,plain,
% 1.97/1.64 (~c1_1(a414)),
% 1.97/1.64 inference(unit_resolution,[status(thm)],[3401, 150, 3395, 3394, 3343, 3342, 3242, 3341, 3241, 3254, 495])).
% 1.97/1.64 tff(3403,plain,
% 1.97/1.64 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a426) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a426)) | (~c1_1(a426)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a426) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a426)) | (~c1_1(a426)))),
% 1.97/1.64 inference(rewrite,[status(thm)],[])).
% 1.97/1.64 tff(3404,plain,
% 1.97/1.64 ((hskp22 | (~ndr1_0) | c2_1(a426) | (~c1_1(a426)) | (~c3_1(a426)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402))) <=> (hskp22 | c2_1(a426) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a426)) | (~c1_1(a426)))),
% 1.97/1.64 inference(rewrite,[status(thm)],[])).
% 1.97/1.64 tff(3405,plain,
% 1.97/1.64 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a426) | (~c1_1(a426)) | (~c3_1(a426)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a426) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a426)) | (~c1_1(a426))))),
% 1.97/1.64 inference(monotonicity,[status(thm)],[3404])).
% 1.97/1.64 tff(3406,plain,
% 1.97/1.64 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a426) | (~c1_1(a426)) | (~c3_1(a426)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a426) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a426)) | (~c1_1(a426)))),
% 1.97/1.64 inference(transitivity,[status(thm)],[3405, 3403])).
% 1.97/1.64 tff(3407,plain,
% 1.97/1.64 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a426) | (~c1_1(a426)) | (~c3_1(a426)) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)))),
% 1.97/1.64 inference(quant_inst,[status(thm)],[])).
% 1.97/1.64 tff(3408,plain,
% 1.97/1.64 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a426) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c3_1(a426)) | (~c1_1(a426))),
% 1.97/1.64 inference(modus_ponens,[status(thm)],[3407, 3406])).
% 1.97/1.64 tff(3409,plain,
% 1.97/1.64 (c3_1(a402)),
% 1.97/1.64 inference(unit_resolution,[status(thm)],[3408, 150, 934, 3342, 3242, 3341, 3254, 929, 3376])).
% 1.97/1.64 tff(3410,plain,
% 1.97/1.64 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a418) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a418)) | (~c1_1(a418)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a418) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a418)) | (~c1_1(a418)))),
% 1.97/1.64 inference(rewrite,[status(thm)],[])).
% 1.97/1.64 tff(3411,plain,
% 1.97/1.64 (((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a418) | (~c3_1(a418)) | (~c1_1(a418))) <=> (c0_1(a418) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a418)) | (~c1_1(a418)))),
% 1.97/1.64 inference(rewrite,[status(thm)],[])).
% 1.97/1.64 tff(3412,plain,
% 1.97/1.64 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a418) | (~c3_1(a418)) | (~c1_1(a418)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a418) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a418)) | (~c1_1(a418))))),
% 1.97/1.64 inference(monotonicity,[status(thm)],[3411])).
% 1.97/1.64 tff(3413,plain,
% 1.97/1.64 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a418) | (~c3_1(a418)) | (~c1_1(a418)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a418) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a418)) | (~c1_1(a418)))),
% 1.97/1.64 inference(transitivity,[status(thm)],[3412, 3410])).
% 1.97/1.64 tff(3414,plain,
% 1.97/1.64 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a402) | (~c3_1(a402)) | (~c0_1(a402)) | c0_1(a418) | (~c3_1(a418)) | (~c1_1(a418)))),
% 1.97/1.64 inference(quant_inst,[status(thm)],[])).
% 1.97/1.64 tff(3415,plain,
% 1.97/1.64 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a418) | c1_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a402)) | (~c3_1(a418)) | (~c1_1(a418))),
% 1.97/1.64 inference(modus_ponens,[status(thm)],[3414, 3413])).
% 1.97/1.64 tff(3416,plain,
% 1.97/1.64 (~c3_1(a418)),
% 1.97/1.64 inference(unit_resolution,[status(thm)],[3415, 150, 3386, 3242, 3385, 3241, 531, 3409])).
% 1.97/1.64 tff(3417,plain,
% 1.97/1.64 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a418) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c3_1(a418) | (~c1_1(a418)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a418) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c3_1(a418) | (~c1_1(a418)))),
% 1.97/1.64 inference(rewrite,[status(thm)],[])).
% 1.97/1.64 tff(3418,plain,
% 1.97/1.64 ((hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a418) | c3_1(a418) | (~c1_1(a418))) <=> (hskp9 | c0_1(a418) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c3_1(a418) | (~c1_1(a418)))),
% 1.97/1.64 inference(rewrite,[status(thm)],[])).
% 1.97/1.64 tff(3419,plain,
% 1.97/1.64 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a418) | c3_1(a418) | (~c1_1(a418)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a418) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c3_1(a418) | (~c1_1(a418))))),
% 1.97/1.64 inference(monotonicity,[status(thm)],[3418])).
% 1.97/1.64 tff(3420,plain,
% 1.97/1.64 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a418) | c3_1(a418) | (~c1_1(a418)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a418) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c3_1(a418) | (~c1_1(a418)))),
% 1.97/1.64 inference(transitivity,[status(thm)],[3419, 3417])).
% 1.97/1.64 tff(3421,plain,
% 1.97/1.64 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a410) | c3_1(a410) | (~c0_1(a410)) | c0_1(a418) | c3_1(a418) | (~c1_1(a418)))),
% 1.97/1.64 inference(quant_inst,[status(thm)],[])).
% 1.97/1.64 tff(3422,plain,
% 1.97/1.64 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a418) | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c3_1(a418) | (~c1_1(a418))),
% 1.97/1.64 inference(modus_ponens,[status(thm)],[3421, 3420])).
% 1.97/1.64 tff(3423,plain,
% 1.97/1.64 (hskp9),
% 1.97/1.64 inference(unit_resolution,[status(thm)],[3422, 150, 3386, 3333, 3385, 3332, 3331, 640, 3416])).
% 1.97/1.64 tff(3424,plain,
% 1.97/1.64 (~c1_1(a416)),
% 1.97/1.64 inference(unit_resolution,[status(thm)],[663, 3423])).
% 1.97/1.64 tff(3425,plain,
% 1.97/1.64 (~c0_1(a416)),
% 1.97/1.64 inference(unit_resolution,[status(thm)],[669, 3423])).
% 1.97/1.64 tff(3426,plain,
% 1.97/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a418) | c2_1(a418) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c3_1(a418) | (~c1_1(a418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a418) | c2_1(a418) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c3_1(a418) | (~c1_1(a418)))),
% 1.97/1.64 inference(rewrite,[status(thm)],[])).
% 1.97/1.64 tff(3427,plain,
% 1.97/1.64 (((~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c1_1(a418)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a418) | c0_1(a418) | c2_1(a418)) <=> (c0_1(a418) | c2_1(a418) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c3_1(a418) | (~c1_1(a418)))),
% 1.97/1.64 inference(rewrite,[status(thm)],[])).
% 1.97/1.64 tff(3428,plain,
% 1.97/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c1_1(a418)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a418) | c0_1(a418) | c2_1(a418))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a418) | c2_1(a418) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c3_1(a418) | (~c1_1(a418))))),
% 1.97/1.64 inference(monotonicity,[status(thm)],[3427])).
% 1.97/1.64 tff(3429,plain,
% 1.97/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c1_1(a418)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a418) | c0_1(a418) | c2_1(a418))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a418) | c2_1(a418) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c3_1(a418) | (~c1_1(a418)))),
% 1.97/1.64 inference(transitivity,[status(thm)],[3428, 3426])).
% 1.97/1.64 tff(3430,plain,
% 1.97/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a418) | c3_1(a418) | (~c1_1(a418)) | c1_1(a416) | c0_1(a416) | (~c2_1(a416)) | c3_1(a418) | c0_1(a418) | c2_1(a418))),
% 1.97/1.64 inference(quant_inst,[status(thm)],[])).
% 1.97/1.64 tff(3431,plain,
% 1.97/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a418) | c2_1(a418) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | (~c2_1(a416)) | c3_1(a418) | (~c1_1(a418))),
% 1.97/1.64 inference(modus_ponens,[status(thm)],[3430, 3429])).
% 1.97/1.64 tff(3432,plain,
% 1.97/1.64 (~c2_1(a416)),
% 1.97/1.64 inference(unit_resolution,[status(thm)],[3431, 150, 3386, 3385, 3384, 3425, 3424, 346, 3416])).
% 1.97/1.64 tff(3433,plain,
% 1.97/1.64 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.97/1.64 inference(bind,[status(th)],[])).
% 1.97/1.64 tff(3434,plain,
% 1.97/1.64 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.97/1.64 inference(quant_intro,[status(thm)],[3433])).
% 1.97/1.64 tff(3435,plain,
% 1.97/1.64 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.97/1.64 inference(rewrite,[status(thm)],[])).
% 1.97/1.64 tff(3436,plain,
% 1.97/1.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp19) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp19))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.97/1.64 inference(bind,[status(th)],[])).
% 1.97/1.64 tff(3437,plain,
% 1.97/1.64 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.97/1.64 inference(quant_intro,[status(thm)],[3436])).
% 1.97/1.64 tff(3438,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 1.97/1.64 tff(3439,plain,
% 1.97/1.64 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.97/1.64 inference(modus_ponens,[status(thm)],[3438, 3437])).
% 1.97/1.64 tff(3440,plain,
% 1.97/1.64 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.97/1.64 inference(modus_ponens,[status(thm)],[3439, 3435])).
% 1.97/1.64 tff(3441,plain,(
% 1.97/1.64 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.97/1.64 inference(skolemize,[status(sab)],[3440])).
% 1.97/1.64 tff(3442,plain,
% 1.97/1.64 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.97/1.64 inference(modus_ponens,[status(thm)],[3441, 3434])).
% 1.97/1.64 tff(3443,plain,
% 1.97/1.64 (c3_1(a414)),
% 1.97/1.64 inference(unit_resolution,[status(thm)],[2940, 3393])).
% 1.97/1.64 tff(3444,plain,
% 1.97/1.64 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)))),
% 1.97/1.64 inference(rewrite,[status(thm)],[])).
% 1.97/1.64 tff(3445,plain,
% 1.97/1.64 ((hskp19 | (~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410))) <=> (hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)))),
% 1.97/1.64 inference(rewrite,[status(thm)],[])).
% 1.97/1.64 tff(3446,plain,
% 1.97/1.64 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414))))),
% 1.97/1.64 inference(monotonicity,[status(thm)],[3445])).
% 1.97/1.64 tff(3447,plain,
% 1.97/1.64 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)))),
% 1.97/1.64 inference(transitivity,[status(thm)],[3446, 3444])).
% 1.97/1.64 tff(3448,plain,
% 1.97/1.64 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410)))),
% 1.97/1.64 inference(quant_inst,[status(thm)],[])).
% 1.97/1.64 tff(3449,plain,
% 1.97/1.64 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414))),
% 1.97/1.64 inference(modus_ponens,[status(thm)],[3448, 3447])).
% 1.97/1.64 tff(3450,plain,
% 1.97/1.64 (~c2_1(a410)),
% 1.97/1.64 inference(unit_resolution,[status(thm)],[3449, 150, 3253, 3395, 3394, 3443, 3332, 3331, 3442])).
% 1.97/1.64 tff(3451,plain,
% 1.97/1.64 (c3_1(a416)),
% 1.97/1.64 inference(unit_resolution,[status(thm)],[727, 3423])).
% 1.97/1.64 tff(3452,plain,
% 1.97/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | c2_1(a416) | (~c3_1(a416)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | c2_1(a416) | (~c3_1(a416)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414)))),
% 1.97/1.64 inference(rewrite,[status(thm)],[])).
% 1.97/1.64 tff(3453,plain,
% 1.97/1.64 (((~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414)) | c1_1(a416) | c2_1(a416) | (~c3_1(a416))) <=> (c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | c2_1(a416) | (~c3_1(a416)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414)))),
% 1.97/1.64 inference(rewrite,[status(thm)],[])).
% 1.97/1.64 tff(3454,plain,
% 1.97/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414)) | c1_1(a416) | c2_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | c2_1(a416) | (~c3_1(a416)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414))))),
% 1.97/1.64 inference(monotonicity,[status(thm)],[3453])).
% 1.97/1.64 tff(3455,plain,
% 1.97/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414)) | c1_1(a416) | c2_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | c2_1(a416) | (~c3_1(a416)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414)))),
% 1.97/1.64 inference(transitivity,[status(thm)],[3454, 3452])).
% 1.97/1.64 tff(3456,plain,
% 1.97/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414)) | c1_1(a416) | c2_1(a416) | (~c3_1(a416)))),
% 1.97/1.64 inference(quant_inst,[status(thm)],[])).
% 1.97/1.64 tff(3457,plain,
% 1.97/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a416) | c3_1(a410) | (~ndr1_0) | (~c0_1(a410)) | c2_1(a410) | c2_1(a416) | (~c3_1(a416)) | c1_1(a414) | (~c2_1(a414)) | (~c3_1(a414))),
% 1.97/1.64 inference(modus_ponens,[status(thm)],[3456, 3455])).
% 1.97/1.64 tff(3458,plain,
% 1.97/1.64 ($false),
% 1.97/1.64 inference(unit_resolution,[status(thm)],[3457, 150, 3394, 3443, 3451, 3333, 3424, 3331, 1497, 3450, 3432, 3402])).
% 1.97/1.64 tff(3459,plain,(hskp22 | c1_1(a477) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.97/1.64 tff(3460,plain,
% 1.97/1.64 (hskp22),
% 1.97/1.64 inference(unit_resolution,[status(thm)],[3459, 1, 12])).
% 1.97/1.64 tff(3461,plain,
% 1.97/1.64 (~c1_1(a451)),
% 1.97/1.64 inference(unit_resolution,[status(thm)],[844, 3460])).
% 1.97/1.64 tff(3462,plain,
% 1.97/1.64 (c2_1(a451)),
% 1.97/1.64 inference(unit_resolution,[status(thm)],[855, 3460])).
% 1.97/1.64 tff(3463,assumption,(~c3_1(a451)), introduced(assumption)).
% 1.97/1.64 tff(3464,assumption,(c2_1(a451)), introduced(assumption)).
% 1.97/1.64 tff(3465,plain,
% 1.97/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a477) | c1_1(a451) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c2_1(a451)) | c3_1(a451) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a477) | c1_1(a451) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c2_1(a451)) | c3_1(a451) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.64 inference(rewrite,[status(thm)],[])).
% 1.97/1.64 tff(3466,plain,
% 1.97/1.64 (((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)) | c3_1(a403) | c1_1(a403) | c0_1(a403)) <=> (c0_1(a477) | c1_1(a451) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c2_1(a451)) | c3_1(a451) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.64 inference(rewrite,[status(thm)],[])).
% 1.97/1.64 tff(3467,plain,
% 1.97/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)) | c3_1(a403) | c1_1(a403) | c0_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a477) | c1_1(a451) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c2_1(a451)) | c3_1(a451) | c1_1(a477) | (~c3_1(a477))))),
% 1.97/1.64 inference(monotonicity,[status(thm)],[3466])).
% 1.97/1.64 tff(3468,plain,
% 1.97/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)) | c3_1(a403) | c1_1(a403) | c0_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a477) | c1_1(a451) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c2_1(a451)) | c3_1(a451) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.64 inference(transitivity,[status(thm)],[3467, 3465])).
% 1.97/1.64 tff(3469,plain,
% 1.97/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a477) | c0_1(a477) | (~c3_1(a477)) | c3_1(a403) | c1_1(a403) | c0_1(a403))),
% 1.97/1.64 inference(quant_inst,[status(thm)],[])).
% 1.97/1.64 tff(3470,plain,
% 1.97/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a477) | c1_1(a451) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c2_1(a451)) | c3_1(a451) | c1_1(a477) | (~c3_1(a477))),
% 1.97/1.64 inference(modus_ponens,[status(thm)],[3469, 3468])).
% 1.97/1.64 tff(3471,plain,
% 1.97/1.64 (c1_1(a403) | c3_1(a451)),
% 1.97/1.64 inference(unit_resolution,[status(thm)],[3470, 150, 3075, 3464, 3064, 868, 3218, 3221, 1824, 1])).
% 1.97/1.64 tff(3472,plain,
% 1.97/1.64 (c1_1(a403)),
% 1.97/1.64 inference(unit_resolution,[status(thm)],[3471, 3463])).
% 1.97/1.64 tff(3473,plain,
% 1.97/1.64 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a477) | c0_1(a403) | c2_1(a403) | (~ndr1_0) | (~c1_1(a403)) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a477) | c0_1(a403) | c2_1(a403) | (~ndr1_0) | (~c1_1(a403)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.64 inference(rewrite,[status(thm)],[])).
% 1.97/1.64 tff(3474,plain,
% 1.97/1.64 ((hskp28 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c2_1(a403) | c0_1(a403) | (~c1_1(a403))) <=> (hskp28 | c2_1(a477) | c0_1(a403) | c2_1(a403) | (~ndr1_0) | (~c1_1(a403)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.64 inference(rewrite,[status(thm)],[])).
% 1.97/1.64 tff(3475,plain,
% 1.97/1.64 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c2_1(a403) | c0_1(a403) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a477) | c0_1(a403) | c2_1(a403) | (~ndr1_0) | (~c1_1(a403)) | c1_1(a477) | (~c3_1(a477))))),
% 1.97/1.65 inference(monotonicity,[status(thm)],[3474])).
% 1.97/1.65 tff(3476,plain,
% 1.97/1.65 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c2_1(a403) | c0_1(a403) | (~c1_1(a403)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a477) | c0_1(a403) | c2_1(a403) | (~ndr1_0) | (~c1_1(a403)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.65 inference(transitivity,[status(thm)],[3475, 3473])).
% 1.97/1.65 tff(3477,plain,
% 1.97/1.65 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)) | c2_1(a403) | c0_1(a403) | (~c1_1(a403)))),
% 1.97/1.65 inference(quant_inst,[status(thm)],[])).
% 1.97/1.65 tff(3478,plain,
% 1.97/1.65 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a477) | c0_1(a403) | c2_1(a403) | (~ndr1_0) | (~c1_1(a403)) | c1_1(a477) | (~c3_1(a477))),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3477, 3476])).
% 1.97/1.65 tff(3479,plain,
% 1.97/1.65 (hskp28 | (~c1_1(a403)) | c1_1(a477)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[3478, 150, 3075, 3058, 3218, 3217, 3353])).
% 1.97/1.65 tff(3480,plain,
% 1.97/1.65 (hskp28),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[3479, 3472, 1])).
% 1.97/1.65 tff(3481,plain,
% 1.97/1.65 (c3_1(a414)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[2940, 3480])).
% 1.97/1.65 tff(3482,plain,
% 1.97/1.65 (c2_1(a414)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[2951, 3480])).
% 1.97/1.65 tff(3483,plain,
% 1.97/1.65 (c0_1(a414)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[2962, 3480])).
% 1.97/1.65 tff(3484,plain,
% 1.97/1.65 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | c1_1(a451) | (~ndr1_0) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | (~c2_1(a451)) | c3_1(a451))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a451) | (~ndr1_0) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | (~c2_1(a451)) | c3_1(a451))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3485,plain,
% 1.97/1.65 ((hskp19 | (~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451))) <=> (hskp19 | c1_1(a451) | (~ndr1_0) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | (~c2_1(a451)) | c3_1(a451))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3486,plain,
% 1.97/1.65 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | c1_1(a451) | (~ndr1_0) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | (~c2_1(a451)) | c3_1(a451)))),
% 1.97/1.65 inference(monotonicity,[status(thm)],[3485])).
% 1.97/1.65 tff(3487,plain,
% 1.97/1.65 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a451) | (~ndr1_0) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | (~c2_1(a451)) | c3_1(a451))),
% 1.97/1.65 inference(transitivity,[status(thm)],[3486, 3484])).
% 1.97/1.65 tff(3488,plain,
% 1.97/1.65 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)))),
% 1.97/1.65 inference(quant_inst,[status(thm)],[])).
% 1.97/1.65 tff(3489,plain,
% 1.97/1.65 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a451) | (~ndr1_0) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | (~c2_1(a451)) | c3_1(a451)),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3488, 3487])).
% 1.97/1.65 tff(3490,plain,
% 1.97/1.65 ($false),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[3489, 150, 119, 3483, 3482, 3481, 3464, 868, 3442, 3463])).
% 1.97/1.65 tff(3491,plain,(c3_1(a451) | hskp19 | (~c2_1(a451)) | c1_1(a451) | c1_1(a477)), inference(lemma,lemma(discharge,[]))).
% 1.97/1.65 tff(3492,plain,
% 1.97/1.65 (c3_1(a451)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[3491, 3462, 1, 3461, 3253])).
% 1.97/1.65 tff(3493,plain,
% 1.97/1.65 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.97/1.65 inference(bind,[status(th)],[])).
% 1.97/1.65 tff(3494,plain,
% 1.97/1.65 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.97/1.65 inference(quant_intro,[status(thm)],[3493])).
% 1.97/1.65 tff(3495,plain,
% 1.97/1.65 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3496,plain,
% 1.97/1.65 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.97/1.65 inference(bind,[status(th)],[])).
% 1.97/1.65 tff(3497,plain,
% 1.97/1.65 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.97/1.65 inference(quant_intro,[status(thm)],[3496])).
% 1.97/1.65 tff(3498,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 1.97/1.65 tff(3499,plain,
% 1.97/1.65 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3498, 3497])).
% 1.97/1.65 tff(3500,plain,
% 1.97/1.65 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3499, 3495])).
% 1.97/1.65 tff(3501,plain,(
% 1.97/1.65 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.97/1.65 inference(skolemize,[status(sab)],[3500])).
% 1.97/1.65 tff(3502,plain,
% 1.97/1.65 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3501, 3494])).
% 1.97/1.65 tff(3503,plain,
% 1.97/1.65 (c0_1(a451)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[866, 3460])).
% 1.97/1.65 tff(3504,plain,
% 1.97/1.65 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | c2_1(a477) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a477) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3505,plain,
% 1.97/1.65 ((hskp4 | (~ndr1_0) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)) | c2_1(a477) | c1_1(a477) | (~c3_1(a477))) <=> (hskp4 | c2_1(a477) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3506,plain,
% 1.97/1.65 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | c2_1(a477) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a477) | (~c3_1(a477))))),
% 1.97/1.65 inference(monotonicity,[status(thm)],[3505])).
% 1.97/1.65 tff(3507,plain,
% 1.97/1.65 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a477) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.65 inference(transitivity,[status(thm)],[3506, 3504])).
% 1.97/1.65 tff(3508,plain,
% 1.97/1.65 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a451) | (~c2_1(a451)) | (~c0_1(a451)) | c2_1(a477) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.65 inference(quant_inst,[status(thm)],[])).
% 1.97/1.65 tff(3509,plain,
% 1.97/1.65 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp4 | c2_1(a477) | c1_1(a451) | (~ndr1_0) | (~c2_1(a451)) | (~c0_1(a451)) | c1_1(a477) | (~c3_1(a477))),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3508, 3507])).
% 1.97/1.65 tff(3510,plain,
% 1.97/1.65 (hskp4),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[3509, 150, 3075, 3503, 3462, 3058, 3461, 3502, 1])).
% 1.97/1.65 tff(3511,plain,
% 1.97/1.65 (((~hskp4) | (~c2_1(a404))) <=> ((~hskp4) | (~c2_1(a404)))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3512,plain,
% 1.97/1.65 (((~c2_1(a404)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a404)))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3513,axiom,((~c2_1(a404)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 1.97/1.65 tff(3514,plain,
% 1.97/1.65 ((~hskp4) | (~c2_1(a404))),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3513, 3512])).
% 1.97/1.65 tff(3515,plain,
% 1.97/1.65 ((~hskp4) | (~c2_1(a404))),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3514, 3511])).
% 1.97/1.65 tff(3516,plain,
% 1.97/1.65 (~c2_1(a404)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[3515, 3510])).
% 1.97/1.65 tff(3517,plain,
% 1.97/1.65 (((~hskp4) | c3_1(a404)) <=> ((~hskp4) | c3_1(a404))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3518,axiom,((~hskp4) | c3_1(a404)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.97/1.65 tff(3519,plain,
% 1.97/1.65 ((~hskp4) | c3_1(a404)),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3518, 3517])).
% 1.97/1.65 tff(3520,plain,
% 1.97/1.65 ((~hskp4) | c3_1(a404)),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3519, 3517])).
% 1.97/1.65 tff(3521,plain,
% 1.97/1.65 ((~hskp4) | c3_1(a404)),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3520, 3517])).
% 1.97/1.65 tff(3522,plain,
% 1.97/1.65 ((~hskp4) | c3_1(a404)),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3521, 3517])).
% 1.97/1.65 tff(3523,plain,
% 1.97/1.65 ((~hskp4) | c3_1(a404)),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3522, 3517])).
% 1.97/1.65 tff(3524,plain,
% 1.97/1.65 ((~hskp4) | c3_1(a404)),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3523, 3517])).
% 1.97/1.65 tff(3525,plain,
% 1.97/1.65 ((~hskp4) | c3_1(a404)),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3524, 3517])).
% 1.97/1.65 tff(3526,plain,
% 1.97/1.65 ((~hskp4) | c3_1(a404)),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3525, 3517])).
% 1.97/1.65 tff(3527,plain,
% 1.97/1.65 (c3_1(a404)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[3526, 3510])).
% 1.97/1.65 tff(3528,plain,
% 1.97/1.65 (((~hskp4) | c0_1(a404)) <=> ((~hskp4) | c0_1(a404))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3529,axiom,((~hskp4) | c0_1(a404)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 1.97/1.65 tff(3530,plain,
% 1.97/1.65 ((~hskp4) | c0_1(a404)),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3529, 3528])).
% 1.97/1.65 tff(3531,plain,
% 1.97/1.65 ((~hskp4) | c0_1(a404)),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3530, 3528])).
% 1.97/1.65 tff(3532,plain,
% 1.97/1.65 ((~hskp4) | c0_1(a404)),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3531, 3528])).
% 1.97/1.65 tff(3533,plain,
% 1.97/1.65 ((~hskp4) | c0_1(a404)),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3532, 3528])).
% 1.97/1.65 tff(3534,plain,
% 1.97/1.65 ((~hskp4) | c0_1(a404)),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3533, 3528])).
% 1.97/1.65 tff(3535,plain,
% 1.97/1.65 ((~hskp4) | c0_1(a404)),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3534, 3528])).
% 1.97/1.65 tff(3536,plain,
% 1.97/1.65 ((~hskp4) | c0_1(a404)),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3535, 3528])).
% 1.97/1.65 tff(3537,plain,
% 1.97/1.65 ((~hskp4) | c0_1(a404)),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3536, 3528])).
% 1.97/1.65 tff(3538,plain,
% 1.97/1.65 (c0_1(a404)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[3537, 3510])).
% 1.97/1.65 tff(3539,assumption,(~c2_1(a404)), introduced(assumption)).
% 1.97/1.65 tff(3540,assumption,(c3_1(a404)), introduced(assumption)).
% 1.97/1.65 tff(3541,assumption,(c0_1(a404)), introduced(assumption)).
% 1.97/1.65 tff(3542,plain,
% 1.97/1.65 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | c2_1(a404) | (~ndr1_0) | (~c3_1(a404)) | (~c0_1(a404)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c2_1(a404) | (~ndr1_0) | (~c3_1(a404)) | (~c0_1(a404)))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3543,plain,
% 1.97/1.65 ((hskp16 | hskp7 | (~ndr1_0) | c2_1(a404) | (~c3_1(a404)) | (~c0_1(a404))) <=> (hskp16 | hskp7 | c2_1(a404) | (~ndr1_0) | (~c3_1(a404)) | (~c0_1(a404)))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3544,plain,
% 1.97/1.65 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a404) | (~c3_1(a404)) | (~c0_1(a404)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | c2_1(a404) | (~ndr1_0) | (~c3_1(a404)) | (~c0_1(a404))))),
% 1.97/1.65 inference(monotonicity,[status(thm)],[3543])).
% 1.97/1.65 tff(3545,plain,
% 1.97/1.65 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a404) | (~c3_1(a404)) | (~c0_1(a404)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c2_1(a404) | (~ndr1_0) | (~c3_1(a404)) | (~c0_1(a404)))),
% 1.97/1.65 inference(transitivity,[status(thm)],[3544, 3542])).
% 1.97/1.65 tff(3546,plain,
% 1.97/1.65 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c2_1(a404) | (~c3_1(a404)) | (~c0_1(a404)))),
% 1.97/1.65 inference(quant_inst,[status(thm)],[])).
% 1.97/1.65 tff(3547,plain,
% 1.97/1.65 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c2_1(a404) | (~ndr1_0) | (~c3_1(a404)) | (~c0_1(a404))),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3546, 3545])).
% 1.97/1.65 tff(3548,plain,
% 1.97/1.65 (hskp16 | hskp7),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[3547, 150, 3541, 3540, 3539, 1003])).
% 1.97/1.65 tff(3549,plain,
% 1.97/1.65 (hskp16),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[3548, 1025])).
% 1.97/1.65 tff(3550,plain,
% 1.97/1.65 (~c0_1(a434)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[1022, 3549])).
% 1.97/1.65 tff(3551,plain,
% 1.97/1.65 (c1_1(a434)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[1044, 3549])).
% 1.97/1.65 tff(3552,plain,
% 1.97/1.65 (~c3_1(a434)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[1016, 3549])).
% 1.97/1.65 tff(3553,plain,
% 1.97/1.65 ($false),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[3327, 3552, 3551, 1, 1025, 3550])).
% 1.97/1.65 tff(3554,plain,(hskp7 | c1_1(a477) | (~c0_1(a404)) | (~c3_1(a404)) | c2_1(a404)), inference(lemma,lemma(discharge,[]))).
% 1.97/1.65 tff(3555,plain,
% 1.97/1.65 (hskp7),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[3554, 3538, 1, 3527, 3516])).
% 1.97/1.65 tff(3556,plain,
% 1.97/1.65 (~c3_1(a410)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[254, 3555])).
% 1.97/1.65 tff(3557,plain,
% 1.97/1.65 (~c1_1(a410)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[260, 3555])).
% 1.97/1.65 tff(3558,plain,
% 1.97/1.65 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3559,plain,
% 1.97/1.65 ((hskp19 | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410))) <=> (hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3560,plain,
% 1.97/1.65 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451))))),
% 1.97/1.65 inference(monotonicity,[status(thm)],[3559])).
% 1.97/1.65 tff(3561,plain,
% 1.97/1.65 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)))),
% 1.97/1.65 inference(transitivity,[status(thm)],[3560, 3558])).
% 1.97/1.65 tff(3562,plain,
% 1.97/1.65 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451)) | c1_1(a410) | c3_1(a410) | (~c2_1(a410)))),
% 1.97/1.65 inference(quant_inst,[status(thm)],[])).
% 1.97/1.65 tff(3563,plain,
% 1.97/1.65 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp19 | c1_1(a410) | c3_1(a410) | (~ndr1_0) | (~c2_1(a410)) | (~c2_1(a451)) | (~c3_1(a451)) | (~c0_1(a451))),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3562, 3561])).
% 1.97/1.65 tff(3564,plain,
% 1.97/1.65 (~c2_1(a410)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[3563, 150, 3253, 3503, 3462, 3557, 3556, 3442, 3492])).
% 1.97/1.65 tff(3565,plain,
% 1.97/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a477) | c1_1(a451) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a477) | c1_1(a451) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3566,plain,
% 1.97/1.65 (((~ndr1_0) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)) | c1_1(a451) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | c2_1(a477) | (~c3_1(a477))) <=> (c2_1(a477) | c1_1(a451) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3567,plain,
% 1.97/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)) | c1_1(a451) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | c2_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a477) | c1_1(a451) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | (~c3_1(a477))))),
% 1.97/1.65 inference(monotonicity,[status(thm)],[3566])).
% 1.97/1.65 tff(3568,plain,
% 1.97/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)) | c1_1(a451) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | c2_1(a477) | (~c3_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a477) | c1_1(a451) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | (~c3_1(a477)))),
% 1.97/1.65 inference(transitivity,[status(thm)],[3567, 3565])).
% 1.97/1.65 tff(3569,plain,
% 1.97/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a402) | c3_1(a402) | (~c0_1(a402)) | c1_1(a451) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | c2_1(a477) | (~c3_1(a477)))),
% 1.97/1.65 inference(quant_inst,[status(thm)],[])).
% 1.97/1.65 tff(3570,plain,
% 1.97/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a477) | c1_1(a451) | c2_1(a402) | (~ndr1_0) | c3_1(a402) | (~c0_1(a402)) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a477) | (~c3_1(a477))),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3569, 3568])).
% 1.97/1.65 tff(3571,plain,
% 1.97/1.65 (c3_1(a402)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[3570, 150, 3075, 3462, 3242, 3058, 3461, 3254, 1497, 1, 3492])).
% 1.97/1.65 tff(3572,plain,
% 1.97/1.65 (c0_1(a410)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[295, 3555])).
% 1.97/1.65 tff(3573,plain,
% 1.97/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a451) | c3_1(a410) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a410)) | c2_1(a410) | (~c2_1(a451)) | (~c3_1(a451)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a451) | c3_1(a410) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a410)) | c2_1(a410) | (~c2_1(a451)) | (~c3_1(a451)))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3574,plain,
% 1.97/1.65 (((~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)) | c1_1(a451) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a402) | c2_1(a402) | (~c3_1(a402))) <=> (c1_1(a451) | c3_1(a410) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a410)) | c2_1(a410) | (~c2_1(a451)) | (~c3_1(a451)))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3575,plain,
% 1.97/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)) | c1_1(a451) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a402) | c2_1(a402) | (~c3_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a451) | c3_1(a410) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a410)) | c2_1(a410) | (~c2_1(a451)) | (~c3_1(a451))))),
% 1.97/1.65 inference(monotonicity,[status(thm)],[3574])).
% 1.97/1.65 tff(3576,plain,
% 1.97/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)) | c1_1(a451) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a402) | c2_1(a402) | (~c3_1(a402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a451) | c3_1(a410) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a410)) | c2_1(a410) | (~c2_1(a451)) | (~c3_1(a451)))),
% 1.97/1.65 inference(transitivity,[status(thm)],[3575, 3573])).
% 1.97/1.65 tff(3577,plain,
% 1.97/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a410) | c3_1(a410) | (~c0_1(a410)) | c1_1(a451) | (~c2_1(a451)) | (~c3_1(a451)) | c1_1(a402) | c2_1(a402) | (~c3_1(a402)))),
% 1.97/1.65 inference(quant_inst,[status(thm)],[])).
% 1.97/1.65 tff(3578,plain,
% 1.97/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a451) | c3_1(a410) | c1_1(a402) | c2_1(a402) | (~ndr1_0) | (~c3_1(a402)) | (~c0_1(a410)) | c2_1(a410) | (~c2_1(a451)) | (~c3_1(a451))),
% 1.97/1.65 inference(modus_ponens,[status(thm)],[3577, 3576])).
% 1.97/1.65 tff(3579,plain,
% 1.97/1.65 ($false),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[3578, 150, 3462, 3572, 3461, 3556, 3241, 3254, 1497, 3571, 3492, 3564])).
% 1.97/1.65 tff(3580,plain,(c1_1(a477) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.97/1.65 tff(3581,plain,
% 1.97/1.65 (c1_1(a477)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[3580, 12])).
% 1.97/1.65 tff(3582,plain,
% 1.97/1.65 (hskp22),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[3309, 3581, 3242, 3254, 3241])).
% 1.97/1.65 tff(3583,plain,
% 1.97/1.65 (~c1_1(a451)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[844, 3582])).
% 1.97/1.65 tff(3584,plain,
% 1.97/1.65 (c0_1(a451)),
% 1.97/1.65 inference(unit_resolution,[status(thm)],[866, 3582])).
% 1.97/1.65 tff(3585,plain,
% 1.97/1.65 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a477) | c1_1(a451) | (~ndr1_0) | (~c3_1(a451)) | (~c0_1(a451)) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a477) | c1_1(a451) | (~ndr1_0) | (~c3_1(a451)) | (~c0_1(a451)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3586,plain,
% 1.97/1.65 (((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477))) <=> (c0_1(a477) | c1_1(a451) | (~ndr1_0) | (~c3_1(a451)) | (~c0_1(a451)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.65 inference(rewrite,[status(thm)],[])).
% 1.97/1.65 tff(3587,plain,
% 1.97/1.65 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a477) | c1_1(a451) | (~ndr1_0) | (~c3_1(a451)) | (~c0_1(a451)) | (~c3_1(a477)) | (~c1_1(a477))))),
% 1.97/1.66 inference(monotonicity,[status(thm)],[3586])).
% 1.97/1.66 tff(3588,plain,
% 1.97/1.66 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a477) | c1_1(a451) | (~ndr1_0) | (~c3_1(a451)) | (~c0_1(a451)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.66 inference(transitivity,[status(thm)],[3587, 3585])).
% 1.97/1.66 tff(3589,plain,
% 1.97/1.66 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a451) | (~c3_1(a451)) | (~c0_1(a451)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.66 inference(quant_inst,[status(thm)],[])).
% 1.97/1.66 tff(3590,plain,
% 1.97/1.66 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a477) | c1_1(a451) | (~ndr1_0) | (~c3_1(a451)) | (~c0_1(a451)) | (~c3_1(a477)) | (~c1_1(a477))),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3589, 3588])).
% 1.97/1.66 tff(3591,plain,
% 1.97/1.66 (~c3_1(a451)),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3590, 150, 3075, 3584, 3064, 3583, 531, 3581])).
% 1.97/1.66 tff(3592,plain,
% 1.97/1.66 (c2_1(a451)),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[855, 3582])).
% 1.97/1.66 tff(3593,plain,
% 1.97/1.66 ($false),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3489, 150, 119, 2963, 2952, 2941, 3464, 868, 3442, 3463])).
% 1.97/1.66 tff(3594,plain,((~hskp28) | hskp19 | (~c2_1(a451)) | c1_1(a451) | c3_1(a451)), inference(lemma,lemma(discharge,[]))).
% 1.97/1.66 tff(3595,plain,
% 1.97/1.66 (~hskp28),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3594, 3253, 3592, 3583, 3591])).
% 1.97/1.66 tff(3596,assumption,(~hskp9), introduced(assumption)).
% 1.97/1.66 tff(3597,plain,
% 1.97/1.66 (hskp9 | c3_1(a402) | (~c1_1(a403))),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[747, 150, 1439, 3218, 3221, 105, 640])).
% 1.97/1.66 tff(3598,plain,
% 1.97/1.66 (~c1_1(a403)),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3597, 3596, 3306])).
% 1.97/1.66 tff(3599,plain,
% 1.97/1.66 (^[U: $i] : refl((hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 1.97/1.66 inference(bind,[status(th)],[])).
% 1.97/1.66 tff(3600,plain,
% 1.97/1.66 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.97/1.66 inference(quant_intro,[status(thm)],[3599])).
% 1.97/1.66 tff(3601,plain,
% 1.97/1.66 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.97/1.66 inference(rewrite,[status(thm)],[])).
% 1.97/1.66 tff(3602,plain,
% 1.97/1.66 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp9) <=> ((hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp9))), rewrite(((hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 1.97/1.66 inference(bind,[status(th)],[])).
% 1.97/1.66 tff(3603,plain,
% 1.97/1.66 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp9) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.97/1.66 inference(quant_intro,[status(thm)],[3602])).
% 1.97/1.66 tff(3604,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp8) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 1.97/1.66 tff(3605,plain,
% 1.97/1.66 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3604, 3603])).
% 1.97/1.66 tff(3606,plain,
% 1.97/1.66 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3605, 3601])).
% 1.97/1.66 tff(3607,plain,(
% 1.97/1.66 ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.97/1.66 inference(skolemize,[status(sab)],[3606])).
% 1.97/1.66 tff(3608,plain,
% 1.97/1.66 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3607, 3600])).
% 1.97/1.66 tff(3609,plain,
% 1.97/1.66 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c1_1(a477)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c1_1(a477)))),
% 1.97/1.66 inference(rewrite,[status(thm)],[])).
% 1.97/1.66 tff(3610,plain,
% 1.97/1.66 ((hskp9 | hskp8 | (~ndr1_0) | c2_1(a477) | c0_1(a477) | (~c1_1(a477))) <=> (hskp9 | hskp8 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c1_1(a477)))),
% 1.97/1.66 inference(rewrite,[status(thm)],[])).
% 1.97/1.66 tff(3611,plain,
% 1.97/1.66 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c2_1(a477) | c0_1(a477) | (~c1_1(a477)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c1_1(a477))))),
% 1.97/1.66 inference(monotonicity,[status(thm)],[3610])).
% 1.97/1.66 tff(3612,plain,
% 1.97/1.66 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c2_1(a477) | c0_1(a477) | (~c1_1(a477)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c1_1(a477)))),
% 1.97/1.66 inference(transitivity,[status(thm)],[3611, 3609])).
% 1.97/1.66 tff(3613,plain,
% 1.97/1.66 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c2_1(a477) | c0_1(a477) | (~c1_1(a477)))),
% 1.97/1.66 inference(quant_inst,[status(thm)],[])).
% 1.97/1.66 tff(3614,plain,
% 1.97/1.66 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp8 | c0_1(a477) | c2_1(a477) | (~ndr1_0) | (~c1_1(a477))),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3613, 3612])).
% 1.97/1.66 tff(3615,plain,
% 1.97/1.66 (hskp9 | hskp8 | (~c1_1(a477))),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3614, 150, 3064, 3058, 3608])).
% 1.97/1.66 tff(3616,plain,
% 1.97/1.66 (hskp8),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3615, 3596, 3298])).
% 1.97/1.66 tff(3617,plain,
% 1.97/1.66 (((~hskp8) | (~c1_1(a415))) <=> ((~hskp8) | (~c1_1(a415)))),
% 1.97/1.66 inference(rewrite,[status(thm)],[])).
% 1.97/1.66 tff(3618,plain,
% 1.97/1.66 (((~c1_1(a415)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a415)))),
% 1.97/1.66 inference(rewrite,[status(thm)],[])).
% 1.97/1.66 tff(3619,axiom,((~c1_1(a415)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 1.97/1.66 tff(3620,plain,
% 1.97/1.66 ((~hskp8) | (~c1_1(a415))),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3619, 3618])).
% 1.97/1.66 tff(3621,plain,
% 1.97/1.66 ((~hskp8) | (~c1_1(a415))),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3620, 3617])).
% 1.97/1.66 tff(3622,plain,
% 1.97/1.66 (~c1_1(a415)),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3621, 3616])).
% 1.97/1.66 tff(3623,plain,
% 1.97/1.66 (((~hskp8) | c3_1(a415)) <=> ((~hskp8) | c3_1(a415))),
% 1.97/1.66 inference(rewrite,[status(thm)],[])).
% 1.97/1.66 tff(3624,axiom,((~hskp8) | c3_1(a415)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 1.97/1.66 tff(3625,plain,
% 1.97/1.66 ((~hskp8) | c3_1(a415)),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3624, 3623])).
% 1.97/1.66 tff(3626,plain,
% 1.97/1.66 ((~hskp8) | c3_1(a415)),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3625, 3623])).
% 1.97/1.66 tff(3627,plain,
% 1.97/1.66 ((~hskp8) | c3_1(a415)),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3626, 3623])).
% 1.97/1.66 tff(3628,plain,
% 1.97/1.66 ((~hskp8) | c3_1(a415)),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3627, 3623])).
% 1.97/1.66 tff(3629,plain,
% 1.97/1.66 ((~hskp8) | c3_1(a415)),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3628, 3623])).
% 1.97/1.66 tff(3630,plain,
% 1.97/1.66 ((~hskp8) | c3_1(a415)),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3629, 3623])).
% 1.97/1.66 tff(3631,plain,
% 1.97/1.66 ((~hskp8) | c3_1(a415)),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3630, 3623])).
% 1.97/1.66 tff(3632,plain,
% 1.97/1.66 ((~hskp8) | c3_1(a415)),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3631, 3623])).
% 1.97/1.66 tff(3633,plain,
% 1.97/1.66 (c3_1(a415)),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3632, 3616])).
% 1.97/1.66 tff(3634,plain,
% 1.97/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a451) | c1_1(a415) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a451) | c1_1(a415) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451))),
% 1.97/1.66 inference(rewrite,[status(thm)],[])).
% 1.97/1.66 tff(3635,plain,
% 1.97/1.66 (((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a415) | c0_1(a415) | (~c3_1(a415)) | c3_1(a403) | c1_1(a403) | c0_1(a403)) <=> (c1_1(a451) | c1_1(a415) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451))),
% 1.97/1.66 inference(rewrite,[status(thm)],[])).
% 1.97/1.66 tff(3636,plain,
% 1.97/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a415) | c0_1(a415) | (~c3_1(a415)) | c3_1(a403) | c1_1(a403) | c0_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a451) | c1_1(a415) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451)))),
% 1.97/1.66 inference(monotonicity,[status(thm)],[3635])).
% 1.97/1.66 tff(3637,plain,
% 1.97/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a415) | c0_1(a415) | (~c3_1(a415)) | c3_1(a403) | c1_1(a403) | c0_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a451) | c1_1(a415) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451))),
% 1.97/1.66 inference(transitivity,[status(thm)],[3636, 3634])).
% 1.97/1.66 tff(3638,plain,
% 1.97/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a415) | c0_1(a415) | (~c3_1(a415)) | c3_1(a403) | c1_1(a403) | c0_1(a403))),
% 1.97/1.66 inference(quant_inst,[status(thm)],[])).
% 1.97/1.66 tff(3639,plain,
% 1.97/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a451) | c1_1(a415) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451)),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3638, 3637])).
% 1.97/1.66 tff(3640,plain,
% 1.97/1.66 (c0_1(a415)),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3639, 150, 3464, 3633, 868, 3622, 3218, 3221, 1824, 3598, 3463])).
% 1.97/1.66 tff(3641,plain,
% 1.97/1.66 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a477) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | (~c0_1(a415)) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a477) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | (~c0_1(a415)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.66 inference(rewrite,[status(thm)],[])).
% 1.97/1.66 tff(3642,plain,
% 1.97/1.66 (((~ndr1_0) | c1_1(a415) | (~c3_1(a415)) | (~c0_1(a415)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477))) <=> (c0_1(a477) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | (~c0_1(a415)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.66 inference(rewrite,[status(thm)],[])).
% 1.97/1.66 tff(3643,plain,
% 1.97/1.66 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a415) | (~c3_1(a415)) | (~c0_1(a415)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (c0_1(a477) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | (~c0_1(a415)) | (~c3_1(a477)) | (~c1_1(a477))))),
% 1.97/1.66 inference(monotonicity,[status(thm)],[3642])).
% 1.97/1.66 tff(3644,plain,
% 1.97/1.66 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a415) | (~c3_1(a415)) | (~c0_1(a415)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a477) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | (~c0_1(a415)) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.66 inference(transitivity,[status(thm)],[3643, 3641])).
% 1.97/1.66 tff(3645,plain,
% 1.97/1.66 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c1_1(a415) | (~c3_1(a415)) | (~c0_1(a415)) | c0_1(a477) | (~c3_1(a477)) | (~c1_1(a477)))),
% 1.97/1.66 inference(quant_inst,[status(thm)],[])).
% 1.97/1.66 tff(3646,plain,
% 1.97/1.66 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | c0_1(a477) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | (~c0_1(a415)) | (~c3_1(a477)) | (~c1_1(a477))),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3645, 3644])).
% 1.97/1.66 tff(3647,plain,
% 1.97/1.66 ($false),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3646, 150, 3075, 3633, 3064, 3622, 531, 3298, 3640])).
% 1.97/1.66 tff(3648,plain,(hskp9 | (~c1_1(a477)) | (~c2_1(a451)) | c1_1(a451) | c3_1(a451) | (~c0_1(a402)) | c1_1(a402)), inference(lemma,lemma(discharge,[]))).
% 1.97/1.66 tff(3649,plain,
% 1.97/1.66 (hskp9),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3648, 3581, 3592, 3583, 3591, 3242, 3241])).
% 1.97/1.66 tff(3650,plain,
% 1.97/1.66 (~c0_1(a416)),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[669, 3649])).
% 1.97/1.66 tff(3651,plain,
% 1.97/1.66 (~c1_1(a416)),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[663, 3649])).
% 1.97/1.66 tff(3652,assumption,(~c0_1(a416)), introduced(assumption)).
% 1.97/1.66 tff(3653,assumption,(~c1_1(a416)), introduced(assumption)).
% 1.97/1.66 tff(3654,plain,
% 1.97/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a451) | c0_1(a416) | c1_1(a416) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451))),
% 1.97/1.66 inference(rewrite,[status(thm)],[])).
% 1.97/1.66 tff(3655,plain,
% 1.97/1.66 (((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)) | c3_1(a403) | c1_1(a403) | c0_1(a403)) <=> (c1_1(a451) | c0_1(a416) | c1_1(a416) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451))),
% 1.97/1.66 inference(rewrite,[status(thm)],[])).
% 1.97/1.66 tff(3656,plain,
% 1.97/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)) | c3_1(a403) | c1_1(a403) | c0_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a451) | c0_1(a416) | c1_1(a416) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451)))),
% 1.97/1.66 inference(monotonicity,[status(thm)],[3655])).
% 1.97/1.66 tff(3657,plain,
% 1.97/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)) | c3_1(a403) | c1_1(a403) | c0_1(a403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451))),
% 1.97/1.66 inference(transitivity,[status(thm)],[3656, 3654])).
% 1.97/1.66 tff(3658,plain,
% 1.97/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)) | c3_1(a403) | c1_1(a403) | c0_1(a403))),
% 1.97/1.66 inference(quant_inst,[status(thm)],[])).
% 1.97/1.66 tff(3659,plain,
% 1.97/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c0_1(a403) | c3_1(a403) | (~ndr1_0) | c1_1(a403) | (~c3_1(a416)) | (~c2_1(a451)) | c3_1(a451)),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3658, 3657])).
% 1.97/1.66 tff(3660,plain,
% 1.97/1.66 (c1_1(a403) | (~c3_1(a416))),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3659, 150, 3464, 868, 3652, 3653, 3218, 3221, 1824, 3463])).
% 1.97/1.66 tff(3661,plain,
% 1.97/1.66 (~c3_1(a416)),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3660, 3598])).
% 1.97/1.66 tff(3662,plain,
% 1.97/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a416) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a416) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451))),
% 1.97/1.66 inference(rewrite,[status(thm)],[])).
% 1.97/1.66 tff(3663,plain,
% 1.97/1.66 (((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a415) | c0_1(a415) | (~c3_1(a415)) | c3_1(a416) | c1_1(a416) | c0_1(a416)) <=> (c3_1(a416) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451))),
% 1.97/1.66 inference(rewrite,[status(thm)],[])).
% 1.97/1.66 tff(3664,plain,
% 1.97/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a415) | c0_1(a415) | (~c3_1(a415)) | c3_1(a416) | c1_1(a416) | c0_1(a416))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a416) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451)))),
% 1.97/1.66 inference(monotonicity,[status(thm)],[3663])).
% 1.97/1.66 tff(3665,plain,
% 1.97/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a415) | c0_1(a415) | (~c3_1(a415)) | c3_1(a416) | c1_1(a416) | c0_1(a416))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a416) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451))),
% 1.97/1.66 inference(transitivity,[status(thm)],[3664, 3662])).
% 1.97/1.66 tff(3666,plain,
% 1.97/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a451) | c3_1(a451) | (~c2_1(a451)) | c1_1(a415) | c0_1(a415) | (~c3_1(a415)) | c3_1(a416) | c1_1(a416) | c0_1(a416))),
% 1.97/1.66 inference(quant_inst,[status(thm)],[])).
% 1.97/1.66 tff(3667,plain,
% 1.97/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a416) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c1_1(a415) | (~ndr1_0) | (~c3_1(a415)) | c0_1(a415) | (~c2_1(a451)) | c3_1(a451)),
% 1.97/1.66 inference(modus_ponens,[status(thm)],[3666, 3665])).
% 1.97/1.66 tff(3668,plain,
% 1.97/1.66 (c0_1(a415)),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3667, 150, 3464, 3661, 3633, 868, 3652, 3653, 3622, 1824, 3463])).
% 1.97/1.66 tff(3669,plain,
% 1.97/1.66 ($false),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3646, 150, 3075, 3633, 3064, 3622, 531, 3298, 3668])).
% 1.97/1.66 tff(3670,plain,(hskp9 | (~c1_1(a477)) | (~c2_1(a451)) | c1_1(a451) | c0_1(a416) | c1_1(a416) | c3_1(a451) | (~c0_1(a402)) | c1_1(a402)), inference(lemma,lemma(discharge,[]))).
% 1.97/1.66 tff(3671,plain,
% 1.97/1.66 (hskp9),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3670, 3652, 3464, 868, 3653, 3298, 3463, 1439, 105])).
% 1.97/1.66 tff(3672,plain,
% 1.97/1.66 (c3_1(a416)),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[727, 3671])).
% 1.97/1.66 tff(3673,plain,
% 1.97/1.66 (c0_1(a416) | c1_1(a403) | (~c3_1(a416))),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3659, 150, 3464, 868, 3653, 3218, 3221, 1824, 3463])).
% 1.97/1.66 tff(3674,plain,
% 1.97/1.66 (c1_1(a403)),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3673, 3672, 3652])).
% 1.97/1.66 tff(3675,plain,
% 1.97/1.66 (c0_1(a416) | (~c1_1(a403)) | (~c2_1(a416))),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[757, 150, 3653, 3218, 3217, 3221, 346])).
% 1.97/1.66 tff(3676,plain,
% 1.97/1.66 (~c2_1(a416)),
% 1.97/1.66 inference(unit_resolution,[status(thm)],[3675, 3674, 3652])).
% 1.97/1.66 tff(3677,assumption,(~hskp28), introduced(assumption)).
% 1.97/1.66 tff(3678,plain,
% 1.97/1.66 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c0_1(a477) | c2_1(a477) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a477) | c2_1(a477) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c1_1(a477)))),
% 1.97/1.66 inference(rewrite,[status(thm)],[])).
% 1.97/1.66 tff(3679,plain,
% 1.97/1.66 ((hskp28 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c2_1(a477) | c0_1(a477) | (~c1_1(a477))) <=> (hskp28 | c0_1(a477) | c2_1(a477) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c1_1(a477)))),
% 1.97/1.66 inference(rewrite,[status(thm)],[])).
% 1.97/1.66 tff(3680,plain,
% 1.97/1.66 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c2_1(a477) | c0_1(a477) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c0_1(a477) | c2_1(a477) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c1_1(a477))))),
% 1.97/1.66 inference(monotonicity,[status(thm)],[3679])).
% 1.97/1.66 tff(3681,plain,
% 1.97/1.66 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c2_1(a477) | c0_1(a477) | (~c1_1(a477)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a477) | c2_1(a477) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c1_1(a477)))),
% 1.97/1.66 inference(transitivity,[status(thm)],[3680, 3678])).
% 1.97/1.66 tff(3682,plain,
% 1.97/1.66 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c2_1(a477) | c0_1(a477) | (~c1_1(a477)))),
% 1.97/1.66 inference(quant_inst,[status(thm)],[])).
% 1.97/1.66 tff(3683,plain,
% 1.97/1.66 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a477) | c2_1(a477) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c1_1(a477))),
% 2.06/1.67 inference(modus_ponens,[status(thm)],[3682, 3681])).
% 2.06/1.67 tff(3684,plain,
% 2.06/1.67 ($false),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[3683, 3677, 150, 3672, 3064, 3058, 3653, 3353, 3298, 3676])).
% 2.06/1.67 tff(3685,plain,(c0_1(a416) | hskp28 | c1_1(a416) | (~c1_1(a477)) | (~c2_1(a451)) | c1_1(a451) | c3_1(a451) | (~c0_1(a402)) | c1_1(a402)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.67 tff(3686,plain,
% 2.06/1.67 ($false),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[3685, 3651, 3650, 3595, 3581, 3592, 3583, 3591, 3242, 3241])).
% 2.06/1.67 tff(3687,plain,(hskp1), inference(lemma,lemma(discharge,[]))).
% 2.06/1.67 tff(3688,plain,
% 2.06/1.67 (~c3_1(a401)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[794, 3687])).
% 2.06/1.67 tff(3689,plain,
% 2.06/1.67 (c1_1(a401)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[805, 3687])).
% 2.06/1.67 tff(3690,plain,
% 2.06/1.67 (c0_1(a401)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[816, 3687])).
% 2.06/1.67 tff(3691,plain,
% 2.06/1.67 (hskp20),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[823, 150, 3690, 3689, 3688, 483])).
% 2.06/1.67 tff(3692,plain,
% 2.06/1.67 (~c2_1(a449)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[914, 3691])).
% 2.06/1.67 tff(3693,plain,
% 2.06/1.67 (c3_1(a449)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[908, 3691])).
% 2.06/1.67 tff(3694,plain,
% 2.06/1.67 (c1_1(a449)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[834, 3691])).
% 2.06/1.67 tff(3695,plain,
% 2.06/1.67 (hskp10),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[3201, 150, 3075, 3694, 3693, 3064, 3058, 3692, 2169])).
% 2.06/1.67 tff(3696,plain,
% 2.06/1.67 (~c2_1(a418)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[2181, 3695])).
% 2.06/1.67 tff(3697,plain,
% 2.06/1.67 (~c0_1(a418)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[2187, 3695])).
% 2.06/1.67 tff(3698,plain,
% 2.06/1.67 (c1_1(a418)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[2200, 3695])).
% 2.06/1.67 tff(3699,plain,
% 2.06/1.67 (hskp28 | c1_1(a477)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[3392, 150, 3075, 3698, 3058, 3697, 3696, 3353])).
% 2.06/1.67 tff(3700,plain,
% 2.06/1.67 (hskp28),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[3699, 1])).
% 2.06/1.67 tff(3701,plain,
% 2.06/1.67 (c3_1(a414)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[2940, 3700])).
% 2.06/1.67 tff(3702,plain,
% 2.06/1.67 (c2_1(a414)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[2951, 3700])).
% 2.06/1.67 tff(3703,plain,
% 2.06/1.67 (c0_1(a414)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[2962, 3700])).
% 2.06/1.67 tff(3704,plain,
% 2.06/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a477) | c2_1(a477) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c1_1(a477))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a477) | c2_1(a477) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c1_1(a477))),
% 2.06/1.67 inference(rewrite,[status(thm)],[])).
% 2.06/1.67 tff(3705,plain,
% 2.06/1.67 (((~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a477) | c0_1(a477) | c2_1(a477)) <=> (c0_1(a477) | c2_1(a477) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c1_1(a477))),
% 2.06/1.67 inference(rewrite,[status(thm)],[])).
% 2.06/1.67 tff(3706,plain,
% 2.06/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a477) | c0_1(a477) | c2_1(a477))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a477) | c2_1(a477) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c1_1(a477)))),
% 2.06/1.67 inference(monotonicity,[status(thm)],[3705])).
% 2.06/1.67 tff(3707,plain,
% 2.06/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a477) | c0_1(a477) | c2_1(a477))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a477) | c2_1(a477) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c1_1(a477))),
% 2.06/1.67 inference(transitivity,[status(thm)],[3706, 3704])).
% 2.06/1.67 tff(3708,plain,
% 2.06/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a414)) | (~c3_1(a414)) | (~c0_1(a414)) | c3_1(a401) | (~c1_1(a401)) | (~c0_1(a401)) | c1_1(a477) | c0_1(a477) | c2_1(a477))),
% 2.06/1.67 inference(quant_inst,[status(thm)],[])).
% 2.06/1.67 tff(3709,plain,
% 2.06/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a477) | c2_1(a477) | c3_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a401)) | (~c2_1(a414)) | (~c0_1(a414)) | (~c3_1(a414)) | c1_1(a477)),
% 2.06/1.67 inference(modus_ponens,[status(thm)],[3708, 3707])).
% 2.06/1.67 tff(3710,plain,
% 2.06/1.67 ($false),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[3709, 150, 3703, 3702, 3701, 3690, 3689, 3064, 3058, 3688, 11, 1])).
% 2.06/1.67 tff(3711,plain,(c1_1(a477)), inference(lemma,lemma(discharge,[]))).
% 2.06/1.67 tff(3712,plain,
% 2.06/1.67 (c2_1(a401)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[2543, 23, 3689, 3688, 3690])).
% 2.06/1.67 tff(3713,plain,
% 2.06/1.67 (hskp13),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[3232, 23, 3711])).
% 2.06/1.67 tff(3714,plain,
% 2.06/1.67 (~c0_1(a427)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[284, 3713])).
% 2.06/1.67 tff(3715,plain,
% 2.06/1.67 (c2_1(a427)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[306, 3713])).
% 2.06/1.67 tff(3716,plain,
% 2.06/1.67 (c1_1(a427)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[317, 3713])).
% 2.06/1.67 tff(3717,assumption,(c2_1(a401)), introduced(assumption)).
% 2.06/1.67 tff(3718,assumption,(hskp8), introduced(assumption)).
% 2.06/1.67 tff(3719,plain,
% 2.06/1.67 (~c1_1(a415)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[3621, 3718])).
% 2.06/1.67 tff(3720,assumption,(~c0_1(a427)), introduced(assumption)).
% 2.06/1.67 tff(3721,plain,
% 2.06/1.67 (c3_1(a415)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[3632, 3718])).
% 2.06/1.67 tff(3722,plain,
% 2.06/1.67 (((~hskp8) | c2_1(a415)) <=> ((~hskp8) | c2_1(a415))),
% 2.06/1.67 inference(rewrite,[status(thm)],[])).
% 2.06/1.67 tff(3723,axiom,((~hskp8) | c2_1(a415)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 2.06/1.67 tff(3724,plain,
% 2.06/1.67 ((~hskp8) | c2_1(a415)),
% 2.06/1.67 inference(modus_ponens,[status(thm)],[3723, 3722])).
% 2.06/1.67 tff(3725,plain,
% 2.06/1.67 ((~hskp8) | c2_1(a415)),
% 2.06/1.67 inference(modus_ponens,[status(thm)],[3724, 3722])).
% 2.06/1.67 tff(3726,plain,
% 2.06/1.67 ((~hskp8) | c2_1(a415)),
% 2.06/1.67 inference(modus_ponens,[status(thm)],[3725, 3722])).
% 2.06/1.67 tff(3727,plain,
% 2.06/1.67 ((~hskp8) | c2_1(a415)),
% 2.06/1.67 inference(modus_ponens,[status(thm)],[3726, 3722])).
% 2.06/1.67 tff(3728,plain,
% 2.06/1.67 ((~hskp8) | c2_1(a415)),
% 2.06/1.67 inference(modus_ponens,[status(thm)],[3727, 3722])).
% 2.06/1.67 tff(3729,plain,
% 2.06/1.67 ((~hskp8) | c2_1(a415)),
% 2.06/1.67 inference(modus_ponens,[status(thm)],[3728, 3722])).
% 2.06/1.67 tff(3730,plain,
% 2.06/1.67 ((~hskp8) | c2_1(a415)),
% 2.06/1.67 inference(modus_ponens,[status(thm)],[3729, 3722])).
% 2.06/1.67 tff(3731,plain,
% 2.06/1.67 ((~hskp8) | c2_1(a415)),
% 2.06/1.67 inference(modus_ponens,[status(thm)],[3730, 3722])).
% 2.06/1.67 tff(3732,plain,
% 2.06/1.67 (c2_1(a415)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[3731, 3718])).
% 2.06/1.67 tff(3733,assumption,(c2_1(a427)), introduced(assumption)).
% 2.06/1.67 tff(3734,assumption,(c1_1(a427)), introduced(assumption)).
% 2.06/1.67 tff(3735,plain,
% 2.06/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | c1_1(a415) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a415)) | (~c3_1(a415)) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a415) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a415)) | (~c3_1(a415)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 2.06/1.67 inference(rewrite,[status(thm)],[])).
% 2.06/1.67 tff(3736,plain,
% 2.06/1.67 (((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a415) | (~c2_1(a415)) | (~c3_1(a415)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427))) <=> (c0_1(a427) | c1_1(a415) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a415)) | (~c3_1(a415)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 2.06/1.67 inference(rewrite,[status(thm)],[])).
% 2.06/1.67 tff(3737,plain,
% 2.06/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a415) | (~c2_1(a415)) | (~c3_1(a415)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | c1_1(a415) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a415)) | (~c3_1(a415)) | (~c2_1(a427)) | (~c1_1(a427))))),
% 2.06/1.67 inference(monotonicity,[status(thm)],[3736])).
% 2.06/1.67 tff(3738,plain,
% 2.06/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a415) | (~c2_1(a415)) | (~c3_1(a415)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a415) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a415)) | (~c3_1(a415)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 2.06/1.67 inference(transitivity,[status(thm)],[3737, 3735])).
% 2.06/1.67 tff(3739,plain,
% 2.06/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a415) | (~c2_1(a415)) | (~c3_1(a415)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))),
% 2.06/1.67 inference(quant_inst,[status(thm)],[])).
% 2.06/1.67 tff(3740,plain,
% 2.06/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a415) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a415)) | (~c3_1(a415)) | (~c2_1(a427)) | (~c1_1(a427))),
% 2.06/1.67 inference(modus_ponens,[status(thm)],[3739, 3738])).
% 2.06/1.67 tff(3741,plain,
% 2.06/1.67 ($false),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[3740, 150, 3734, 3733, 3732, 3721, 3690, 3720, 3719, 3688, 704, 3717])).
% 2.06/1.67 tff(3742,plain,((~hskp8) | (~c1_1(a427)) | (~c2_1(a427)) | c0_1(a427) | (~c2_1(a401))), inference(lemma,lemma(discharge,[]))).
% 2.06/1.67 tff(3743,plain,
% 2.06/1.67 (~hskp8),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[3742, 3716, 3715, 3714, 3712])).
% 2.06/1.67 tff(3744,plain,
% 2.06/1.67 (hskp9),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[3615, 3743, 3711])).
% 2.06/1.67 tff(3745,plain,
% 2.06/1.67 (~c1_1(a416)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[663, 3744])).
% 2.06/1.67 tff(3746,plain,
% 2.06/1.67 (c3_1(a416)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[727, 3744])).
% 2.06/1.67 tff(3747,plain,
% 2.06/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | c1_1(a416) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a416) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 2.06/1.67 inference(rewrite,[status(thm)],[])).
% 2.06/1.67 tff(3748,plain,
% 2.06/1.67 (((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427))) <=> (c0_1(a427) | c1_1(a416) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 2.06/1.67 inference(rewrite,[status(thm)],[])).
% 2.06/1.67 tff(3749,plain,
% 2.06/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a427) | c1_1(a416) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427))))),
% 2.06/1.67 inference(monotonicity,[status(thm)],[3748])).
% 2.06/1.67 tff(3750,plain,
% 2.06/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a416) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427)))),
% 2.06/1.67 inference(transitivity,[status(thm)],[3749, 3747])).
% 2.06/1.67 tff(3751,plain,
% 2.06/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a401) | (~c2_1(a401)) | (~c0_1(a401)) | c1_1(a416) | (~c2_1(a416)) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c1_1(a427)))),
% 2.06/1.67 inference(quant_inst,[status(thm)],[])).
% 2.06/1.67 tff(3752,plain,
% 2.06/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a427) | c1_1(a416) | c3_1(a401) | (~ndr1_0) | (~c2_1(a401)) | (~c0_1(a401)) | (~c2_1(a416)) | (~c3_1(a416)) | (~c2_1(a427)) | (~c1_1(a427))),
% 2.06/1.67 inference(modus_ponens,[status(thm)],[3751, 3750])).
% 2.06/1.67 tff(3753,plain,
% 2.06/1.67 (~c2_1(a416)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[3752, 150, 3716, 3715, 3746, 3690, 3714, 3745, 3688, 704, 3712])).
% 2.06/1.67 tff(3754,plain,
% 2.06/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a477) | c2_1(a477) | c0_1(a427) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | (~c3_1(a427)) | (~c1_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a477) | c2_1(a477) | c0_1(a427) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | (~c3_1(a427)) | (~c1_1(a477)))),
% 2.06/1.67 inference(rewrite,[status(thm)],[])).
% 2.06/1.67 tff(3755,plain,
% 2.06/1.67 (((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a477) | c2_1(a477) | (~c1_1(a477))) <=> (c0_1(a477) | c2_1(a477) | c0_1(a427) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | (~c3_1(a427)) | (~c1_1(a477)))),
% 2.06/1.67 inference(rewrite,[status(thm)],[])).
% 2.06/1.67 tff(3756,plain,
% 2.06/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a477) | c2_1(a477) | (~c1_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a477) | c2_1(a477) | c0_1(a427) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | (~c3_1(a427)) | (~c1_1(a477))))),
% 2.06/1.67 inference(monotonicity,[status(thm)],[3755])).
% 2.06/1.67 tff(3757,plain,
% 2.06/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a477) | c2_1(a477) | (~c1_1(a477)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a477) | c2_1(a477) | c0_1(a427) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | (~c3_1(a427)) | (~c1_1(a477)))),
% 2.06/1.67 inference(transitivity,[status(thm)],[3756, 3754])).
% 2.06/1.67 tff(3758,plain,
% 2.06/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a427) | (~c2_1(a427)) | (~c3_1(a427)) | c0_1(a477) | c2_1(a477) | (~c1_1(a477)))),
% 2.06/1.67 inference(quant_inst,[status(thm)],[])).
% 2.06/1.67 tff(3759,plain,
% 2.06/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a477) | c2_1(a477) | c0_1(a427) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | (~c3_1(a427)) | (~c1_1(a477))),
% 2.06/1.67 inference(modus_ponens,[status(thm)],[3758, 3757])).
% 2.06/1.67 tff(3760,plain,
% 2.06/1.67 (~c3_1(a427)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[3759, 150, 3715, 3746, 3064, 3058, 3714, 3745, 43, 3711, 3753])).
% 2.06/1.67 tff(3761,plain,
% 2.06/1.67 (~c0_1(a416)),
% 2.06/1.67 inference(unit_resolution,[status(thm)],[669, 3744])).
% 2.06/1.67 tff(3762,plain,
% 2.06/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a427) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | c3_1(a427))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a427) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | c3_1(a427))),
% 2.06/1.67 inference(rewrite,[status(thm)],[])).
% 2.06/1.67 tff(3763,plain,
% 2.06/1.67 (((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a427) | c3_1(a427) | (~c2_1(a427)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416))) <=> (c0_1(a427) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | c3_1(a427))),
% 2.06/1.67 inference(rewrite,[status(thm)],[])).
% 2.06/1.67 tff(3764,plain,
% 2.06/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a427) | c3_1(a427) | (~c2_1(a427)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a427) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | c3_1(a427)))),
% 2.06/1.67 inference(monotonicity,[status(thm)],[3763])).
% 2.06/1.67 tff(3765,plain,
% 2.06/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a427) | c3_1(a427) | (~c2_1(a427)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a427) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | c3_1(a427))),
% 2.06/1.67 inference(transitivity,[status(thm)],[3764, 3762])).
% 2.06/1.67 tff(3766,plain,
% 2.06/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a416) | c1_1(a416) | (~c3_1(a416)) | c0_1(a427) | c3_1(a427) | (~c2_1(a427)) | c1_1(a416) | c0_1(a416) | (~c3_1(a416)))),
% 2.06/1.67 inference(quant_inst,[status(thm)],[])).
% 2.06/1.68 tff(3767,plain,
% 2.06/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a427) | c0_1(a416) | c1_1(a416) | (~ndr1_0) | c2_1(a416) | (~c3_1(a416)) | (~c2_1(a427)) | c3_1(a427)),
% 2.06/1.68 inference(modus_ponens,[status(thm)],[3766, 3765])).
% 2.06/1.68 tff(3768,plain,
% 2.06/1.68 ($false),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[3767, 150, 3715, 3746, 3714, 3761, 3745, 778, 3760, 3753])).
% 2.06/1.68 tff(3769,plain,(hskp2), inference(lemma,lemma(discharge,[]))).
% 2.06/1.68 tff(3770,plain,
% 2.06/1.68 (~c1_1(a402)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[2623, 3769])).
% 2.06/1.68 tff(3771,plain,
% 2.06/1.68 (c0_1(a402)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[520, 3769])).
% 2.06/1.68 tff(3772,plain,
% 2.06/1.68 (~c2_1(a402)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[509, 3769])).
% 2.06/1.68 tff(3773,plain,
% 2.06/1.68 (hskp22),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[3309, 3772, 3711, 3771, 3770])).
% 2.06/1.68 tff(3774,plain,
% 2.06/1.68 (~c1_1(a451)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[844, 3773])).
% 2.06/1.68 tff(3775,plain,
% 2.06/1.68 (c0_1(a451)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[866, 3773])).
% 2.06/1.68 tff(3776,plain,
% 2.06/1.68 (~c3_1(a451)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[3590, 150, 3075, 3775, 3064, 3774, 531, 3711])).
% 2.06/1.68 tff(3777,plain,
% 2.06/1.68 (c2_1(a451)),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[855, 3773])).
% 2.06/1.68 tff(3778,plain,
% 2.06/1.68 ($false),
% 2.06/1.68 inference(unit_resolution,[status(thm)],[892, 150, 3777, 3690, 3689, 3774, 3688, 886, 3776])).
% 2.06/1.68 % SZS output end Proof
%------------------------------------------------------------------------------