TSTP Solution File: SYN470-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN470-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:55:42 EDT 2022
% Result : Unsatisfiable 1.80s 1.44s
% Output : Proof 2.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN470-1 : TPTP v8.1.0. Released v2.1.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 04:10:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 1.80/1.44 % SZS status Unsatisfiable
% 1.80/1.44 % SZS output start Proof
% 1.80/1.44 tff(c2_1_type, type, (
% 1.80/1.44 c2_1: $i > $o)).
% 1.80/1.44 tff(a496_type, type, (
% 1.80/1.44 a496: $i)).
% 1.80/1.44 tff(hskp2_type, type, (
% 1.80/1.44 hskp2: $o)).
% 1.80/1.44 tff(a509_type, type, (
% 1.80/1.44 a509: $i)).
% 1.80/1.44 tff(hskp10_type, type, (
% 1.80/1.44 hskp10: $o)).
% 1.80/1.44 tff(a528_type, type, (
% 1.80/1.44 a528: $i)).
% 1.80/1.44 tff(a510_type, type, (
% 1.80/1.44 a510: $i)).
% 1.80/1.44 tff(hskp11_type, type, (
% 1.80/1.44 hskp11: $o)).
% 1.80/1.44 tff(c0_1_type, type, (
% 1.80/1.44 c0_1: $i > $o)).
% 1.80/1.44 tff(c3_1_type, type, (
% 1.80/1.44 c3_1: $i > $o)).
% 1.80/1.44 tff(ndr1_0_type, type, (
% 1.80/1.44 ndr1_0: $o)).
% 1.80/1.44 tff(a559_type, type, (
% 1.80/1.44 a559: $i)).
% 1.80/1.44 tff(hskp26_type, type, (
% 1.80/1.44 hskp26: $o)).
% 1.80/1.44 tff(c1_1_type, type, (
% 1.80/1.44 c1_1: $i > $o)).
% 1.80/1.44 tff(a494_type, type, (
% 1.80/1.44 a494: $i)).
% 1.80/1.44 tff(hskp0_type, type, (
% 1.80/1.44 hskp0: $o)).
% 1.80/1.44 tff(a520_type, type, (
% 1.80/1.44 a520: $i)).
% 1.80/1.44 tff(hskp22_type, type, (
% 1.80/1.44 hskp22: $o)).
% 1.80/1.44 tff(hskp15_type, type, (
% 1.80/1.44 hskp15: $o)).
% 1.80/1.44 tff(a532_type, type, (
% 1.80/1.44 a532: $i)).
% 1.80/1.44 tff(hskp17_type, type, (
% 1.80/1.44 hskp17: $o)).
% 1.80/1.44 tff(a540_type, type, (
% 1.80/1.44 a540: $i)).
% 1.80/1.44 tff(hskp27_type, type, (
% 1.80/1.44 hskp27: $o)).
% 1.80/1.44 tff(a568_type, type, (
% 1.80/1.44 a568: $i)).
% 1.80/1.44 tff(hskp7_type, type, (
% 1.80/1.44 hskp7: $o)).
% 1.80/1.44 tff(a502_type, type, (
% 1.80/1.44 a502: $i)).
% 1.80/1.44 tff(a500_type, type, (
% 1.80/1.44 a500: $i)).
% 1.80/1.44 tff(hskp28_type, type, (
% 1.80/1.44 hskp28: $o)).
% 1.80/1.44 tff(a498_type, type, (
% 1.80/1.44 a498: $i)).
% 1.80/1.44 tff(a504_type, type, (
% 1.80/1.44 a504: $i)).
% 1.80/1.44 tff(hskp29_type, type, (
% 1.80/1.44 hskp29: $o)).
% 1.80/1.44 tff(hskp4_type, type, (
% 1.80/1.44 hskp4: $o)).
% 1.80/1.44 tff(hskp13_type, type, (
% 1.80/1.44 hskp13: $o)).
% 1.80/1.44 tff(a507_type, type, (
% 1.80/1.44 a507: $i)).
% 1.80/1.44 tff(a495_type, type, (
% 1.80/1.44 a495: $i)).
% 1.80/1.44 tff(hskp1_type, type, (
% 1.80/1.44 hskp1: $o)).
% 1.80/1.44 tff(a536_type, type, (
% 1.80/1.44 a536: $i)).
% 1.80/1.44 tff(hskp20_type, type, (
% 1.80/1.44 hskp20: $o)).
% 1.80/1.44 tff(a514_type, type, (
% 1.80/1.44 a514: $i)).
% 1.80/1.44 tff(hskp12_type, type, (
% 1.80/1.44 hskp12: $o)).
% 1.80/1.44 tff(a527_type, type, (
% 1.80/1.44 a527: $i)).
% 1.80/1.44 tff(hskp14_type, type, (
% 1.80/1.44 hskp14: $o)).
% 1.80/1.44 tff(hskp6_type, type, (
% 1.80/1.44 hskp6: $o)).
% 1.80/1.44 tff(a501_type, type, (
% 1.80/1.44 a501: $i)).
% 1.80/1.44 tff(a522_type, type, (
% 1.80/1.44 a522: $i)).
% 1.80/1.44 tff(hskp31_type, type, (
% 1.80/1.44 hskp31: $o)).
% 1.80/1.44 tff(hskp9_type, type, (
% 1.80/1.44 hskp9: $o)).
% 1.80/1.44 tff(a505_type, type, (
% 1.80/1.44 a505: $i)).
% 1.80/1.44 tff(hskp8_type, type, (
% 1.80/1.44 hskp8: $o)).
% 1.80/1.44 tff(a499_type, type, (
% 1.80/1.44 a499: $i)).
% 1.80/1.44 tff(hskp5_type, type, (
% 1.80/1.44 hskp5: $o)).
% 1.80/1.44 tff(a554_type, type, (
% 1.80/1.44 a554: $i)).
% 1.80/1.44 tff(hskp24_type, type, (
% 1.80/1.44 hskp24: $o)).
% 1.80/1.44 tff(a541_type, type, (
% 1.80/1.44 a541: $i)).
% 1.80/1.44 tff(hskp23_type, type, (
% 1.80/1.44 hskp23: $o)).
% 1.80/1.44 tff(a538_type, type, (
% 1.80/1.44 a538: $i)).
% 1.80/1.44 tff(hskp21_type, type, (
% 1.80/1.44 hskp21: $o)).
% 1.80/1.44 tff(a497_type, type, (
% 1.80/1.44 a497: $i)).
% 1.80/1.44 tff(hskp3_type, type, (
% 1.80/1.44 hskp3: $o)).
% 1.80/1.44 tff(a534_type, type, (
% 1.80/1.44 a534: $i)).
% 1.80/1.44 tff(hskp19_type, type, (
% 1.80/1.44 hskp19: $o)).
% 1.80/1.44 tff(a533_type, type, (
% 1.80/1.44 a533: $i)).
% 1.80/1.44 tff(hskp18_type, type, (
% 1.80/1.44 hskp18: $o)).
% 1.80/1.44 tff(a558_type, type, (
% 1.80/1.44 a558: $i)).
% 1.80/1.44 tff(hskp25_type, type, (
% 1.80/1.44 hskp25: $o)).
% 1.80/1.44 tff(1,plain,
% 1.80/1.44 (^[U: $i] : refl((hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))),
% 1.80/1.44 inference(bind,[status(th)],[])).
% 1.80/1.44 tff(2,plain,
% 1.80/1.44 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.80/1.44 inference(quant_intro,[status(thm)],[1])).
% 1.80/1.44 tff(3,plain,
% 1.80/1.44 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.80/1.44 inference(rewrite,[status(thm)],[])).
% 1.80/1.44 tff(4,plain,
% 1.80/1.44 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp10) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp10))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp10) | hskp11) <=> ((hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp11))), rewrite(((hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp11) <=> (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp10) | hskp11) <=> (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))))),
% 1.80/1.44 inference(bind,[status(th)],[])).
% 1.80/1.44 tff(5,plain,
% 1.80/1.44 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp10) | hskp11) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.80/1.44 inference(quant_intro,[status(thm)],[4])).
% 1.80/1.44 tff(6,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp10) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 1.80/1.44 tff(7,plain,
% 1.80/1.44 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.80/1.44 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.80/1.44 tff(8,plain,
% 1.80/1.44 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.80/1.44 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.80/1.44 tff(9,plain,(
% 1.80/1.44 ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.80/1.44 inference(skolemize,[status(sab)],[8])).
% 1.80/1.44 tff(10,plain,
% 1.80/1.44 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.80/1.44 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.80/1.44 tff(11,assumption,(~hskp10), introduced(assumption)).
% 1.80/1.44 tff(12,plain,
% 1.80/1.44 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W)))),
% 1.80/1.44 inference(bind,[status(th)],[])).
% 1.80/1.44 tff(13,plain,
% 1.80/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))),
% 1.80/1.44 inference(quant_intro,[status(thm)],[12])).
% 1.80/1.44 tff(14,plain,
% 1.80/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))),
% 1.80/1.44 inference(rewrite,[status(thm)],[])).
% 1.80/1.44 tff(15,plain,
% 1.80/1.44 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))))),
% 1.80/1.44 inference(bind,[status(th)],[])).
% 1.80/1.44 tff(16,plain,
% 1.80/1.44 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))),
% 1.80/1.44 inference(quant_intro,[status(thm)],[15])).
% 1.80/1.44 tff(17,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 1.80/1.44 tff(18,plain,
% 1.80/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))),
% 1.80/1.44 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.80/1.44 tff(19,plain,
% 1.80/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))),
% 1.80/1.44 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.80/1.44 tff(20,plain,(
% 1.80/1.44 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))),
% 1.80/1.44 inference(skolemize,[status(sab)],[19])).
% 1.80/1.44 tff(21,plain,
% 1.80/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))),
% 1.80/1.44 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.80/1.44 tff(22,plain,
% 1.80/1.44 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.80/1.44 inference(bind,[status(th)],[])).
% 1.80/1.44 tff(23,plain,
% 1.80/1.44 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.80/1.44 inference(quant_intro,[status(thm)],[22])).
% 1.80/1.44 tff(24,plain,
% 1.80/1.44 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.80/1.44 inference(rewrite,[status(thm)],[])).
% 1.80/1.44 tff(25,plain,
% 1.80/1.44 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.80/1.44 inference(bind,[status(th)],[])).
% 1.80/1.44 tff(26,plain,
% 1.80/1.44 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.80/1.44 inference(quant_intro,[status(thm)],[25])).
% 1.80/1.44 tff(27,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 1.87/1.44 tff(28,plain,
% 1.87/1.44 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.87/1.44 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.87/1.44 tff(29,plain,
% 1.87/1.44 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.87/1.44 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.87/1.44 tff(30,plain,(
% 1.87/1.44 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.87/1.44 inference(skolemize,[status(sab)],[29])).
% 1.87/1.44 tff(31,plain,
% 1.87/1.44 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.87/1.44 inference(modus_ponens,[status(thm)],[30, 23])).
% 1.87/1.44 tff(32,assumption,(~hskp26), introduced(assumption)).
% 1.87/1.44 tff(33,plain,
% 1.87/1.44 (^[U: $i] : refl((hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.87/1.44 inference(bind,[status(th)],[])).
% 1.87/1.44 tff(34,plain,
% 1.87/1.44 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.87/1.44 inference(quant_intro,[status(thm)],[33])).
% 1.87/1.44 tff(35,plain,
% 1.87/1.44 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.87/1.44 inference(rewrite,[status(thm)],[])).
% 1.87/1.44 tff(36,plain,
% 1.87/1.44 (^[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)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp10) <=> ((hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp10) <=> (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.87/1.44 inference(bind,[status(th)],[])).
% 1.87/1.44 tff(37,plain,
% 1.87/1.44 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp10) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.87/1.44 inference(quant_intro,[status(thm)],[36])).
% 1.87/1.44 tff(38,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 1.87/1.44 tff(39,plain,
% 1.87/1.44 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.87/1.44 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.87/1.44 tff(40,plain,
% 1.87/1.44 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.87/1.44 inference(modus_ponens,[status(thm)],[39, 35])).
% 1.87/1.44 tff(41,plain,(
% 1.87/1.44 ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.87/1.44 inference(skolemize,[status(sab)],[40])).
% 1.87/1.44 tff(42,plain,
% 1.87/1.44 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.87/1.44 inference(modus_ponens,[status(thm)],[41, 34])).
% 1.87/1.44 tff(43,assumption,(~hskp15), introduced(assumption)).
% 1.87/1.44 tff(44,plain,
% 1.87/1.44 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 1.87/1.44 inference(bind,[status(th)],[])).
% 1.87/1.44 tff(45,plain,
% 1.87/1.44 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.87/1.44 inference(quant_intro,[status(thm)],[44])).
% 1.87/1.44 tff(46,plain,
% 1.87/1.44 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.87/1.44 inference(rewrite,[status(thm)],[])).
% 1.87/1.44 tff(47,plain,
% 1.87/1.44 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 1.87/1.44 inference(bind,[status(th)],[])).
% 1.87/1.44 tff(48,plain,
% 1.87/1.44 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.87/1.44 inference(quant_intro,[status(thm)],[47])).
% 1.87/1.44 tff(49,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 1.87/1.45 tff(50,plain,
% 1.87/1.45 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.87/1.45 tff(51,plain,
% 1.87/1.45 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[50, 46])).
% 1.87/1.45 tff(52,plain,(
% 1.87/1.45 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.87/1.45 inference(skolemize,[status(sab)],[51])).
% 1.87/1.45 tff(53,plain,
% 1.87/1.45 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[52, 45])).
% 1.87/1.45 tff(54,assumption,(hskp11), introduced(assumption)).
% 1.87/1.45 tff(55,plain,
% 1.87/1.45 (((~hskp11) | (~c2_1(a510))) <=> ((~hskp11) | (~c2_1(a510)))),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(56,plain,
% 1.87/1.45 (((~c2_1(a510)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a510)))),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(57,axiom,((~c2_1(a510)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 1.87/1.45 tff(58,plain,
% 1.87/1.45 ((~hskp11) | (~c2_1(a510))),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[57, 56])).
% 1.87/1.45 tff(59,plain,
% 1.87/1.45 ((~hskp11) | (~c2_1(a510))),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[58, 55])).
% 1.87/1.45 tff(60,plain,
% 1.87/1.45 (~c2_1(a510)),
% 1.87/1.45 inference(unit_resolution,[status(thm)],[59, 54])).
% 1.87/1.45 tff(61,plain,
% 1.87/1.45 (((~hskp11) | (~c1_1(a510))) <=> ((~hskp11) | (~c1_1(a510)))),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(62,plain,
% 1.87/1.45 (((~c1_1(a510)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a510)))),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(63,axiom,((~c1_1(a510)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 1.87/1.45 tff(64,plain,
% 1.87/1.45 ((~hskp11) | (~c1_1(a510))),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.87/1.45 tff(65,plain,
% 1.87/1.45 ((~hskp11) | (~c1_1(a510))),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[64, 61])).
% 1.87/1.45 tff(66,plain,
% 1.87/1.45 (~c1_1(a510)),
% 1.87/1.45 inference(unit_resolution,[status(thm)],[65, 54])).
% 1.87/1.45 tff(67,plain,
% 1.87/1.45 (((~hskp11) | c0_1(a510)) <=> ((~hskp11) | c0_1(a510))),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(68,axiom,((~hskp11) | c0_1(a510)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 1.87/1.45 tff(69,plain,
% 1.87/1.45 ((~hskp11) | c0_1(a510)),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[68, 67])).
% 1.87/1.45 tff(70,plain,
% 1.87/1.45 ((~hskp11) | c0_1(a510)),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[69, 67])).
% 1.87/1.45 tff(71,plain,
% 1.87/1.45 ((~hskp11) | c0_1(a510)),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[70, 67])).
% 1.87/1.45 tff(72,plain,
% 1.87/1.45 ((~hskp11) | c0_1(a510)),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[71, 67])).
% 1.87/1.45 tff(73,plain,
% 1.87/1.45 ((~hskp11) | c0_1(a510)),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[72, 67])).
% 1.87/1.45 tff(74,plain,
% 1.87/1.45 ((~hskp11) | c0_1(a510)),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[73, 67])).
% 1.87/1.45 tff(75,plain,
% 1.87/1.45 ((~hskp11) | c0_1(a510)),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[74, 67])).
% 1.87/1.45 tff(76,plain,
% 1.87/1.45 ((~hskp11) | c0_1(a510)),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[75, 67])).
% 1.87/1.45 tff(77,plain,
% 1.87/1.45 (c0_1(a510)),
% 1.87/1.45 inference(unit_resolution,[status(thm)],[76, 54])).
% 1.87/1.45 tff(78,assumption,(~ndr1_0), introduced(assumption)).
% 1.87/1.45 tff(79,plain,
% 1.87/1.45 ((ndr1_0 | (~hskp10)) <=> (ndr1_0 | (~hskp10))),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(80,plain,
% 1.87/1.45 (((~hskp10) | ndr1_0) <=> (ndr1_0 | (~hskp10))),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(81,axiom,((~hskp10) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause22')).
% 1.87/1.45 tff(82,plain,
% 1.87/1.45 (ndr1_0 | (~hskp10)),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.87/1.45 tff(83,plain,
% 1.87/1.45 (ndr1_0 | (~hskp10)),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[82, 79])).
% 1.87/1.45 tff(84,plain,
% 1.87/1.45 (~hskp10),
% 1.87/1.45 inference(unit_resolution,[status(thm)],[83, 78])).
% 1.87/1.45 tff(85,plain,
% 1.87/1.45 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(86,plain,
% 1.87/1.45 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(87,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause5')).
% 1.87/1.45 tff(88,plain,
% 1.87/1.45 (ndr1_0 | (~hskp27)),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[87, 86])).
% 1.87/1.45 tff(89,plain,
% 1.87/1.45 (ndr1_0 | (~hskp27)),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[88, 85])).
% 1.87/1.45 tff(90,plain,
% 1.87/1.45 (~hskp27),
% 1.87/1.45 inference(unit_resolution,[status(thm)],[89, 78])).
% 1.87/1.45 tff(91,plain,
% 1.87/1.45 ((ndr1_0 | (~hskp26)) <=> (ndr1_0 | (~hskp26))),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(92,plain,
% 1.87/1.45 (((~hskp26) | ndr1_0) <=> (ndr1_0 | (~hskp26))),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(93,axiom,((~hskp26) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause6')).
% 1.87/1.45 tff(94,plain,
% 1.87/1.45 (ndr1_0 | (~hskp26)),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.87/1.45 tff(95,plain,
% 1.87/1.45 (ndr1_0 | (~hskp26)),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[94, 91])).
% 1.87/1.45 tff(96,plain,
% 1.87/1.45 (~hskp26),
% 1.87/1.45 inference(unit_resolution,[status(thm)],[95, 78])).
% 1.87/1.45 tff(97,plain,
% 1.87/1.45 ((hskp27 | hskp26 | hskp10) <=> (hskp27 | hskp26 | hskp10)),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(98,plain,
% 1.87/1.45 (((hskp27 | hskp10) | hskp26) <=> (hskp27 | hskp26 | hskp10)),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(99,plain,
% 1.87/1.45 ((hskp27 | hskp10) <=> (hskp27 | hskp10)),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(100,plain,
% 1.87/1.45 (((hskp27 | hskp10) | hskp26) <=> ((hskp27 | hskp10) | hskp26)),
% 1.87/1.45 inference(monotonicity,[status(thm)],[99])).
% 1.87/1.45 tff(101,plain,
% 1.87/1.45 (((hskp27 | hskp10) | hskp26) <=> (hskp27 | hskp26 | hskp10)),
% 1.87/1.45 inference(transitivity,[status(thm)],[100, 98])).
% 1.87/1.45 tff(102,axiom,((hskp27 | hskp10) | hskp26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 1.87/1.45 tff(103,plain,
% 1.87/1.45 (hskp27 | hskp26 | hskp10),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.87/1.45 tff(104,plain,
% 1.87/1.45 (hskp27 | hskp26 | hskp10),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[103, 97])).
% 1.87/1.45 tff(105,plain,
% 1.87/1.45 (hskp27 | hskp26 | hskp10),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[104, 97])).
% 1.87/1.45 tff(106,plain,
% 1.87/1.45 (hskp27 | hskp26 | hskp10),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[105, 97])).
% 1.87/1.45 tff(107,plain,
% 1.87/1.45 (hskp27 | hskp26 | hskp10),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[106, 97])).
% 1.87/1.45 tff(108,plain,
% 1.87/1.45 (hskp27 | hskp26 | hskp10),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[107, 97])).
% 1.87/1.45 tff(109,plain,
% 1.87/1.45 (hskp27 | hskp26 | hskp10),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[108, 97])).
% 1.87/1.45 tff(110,plain,
% 1.87/1.45 (hskp27 | hskp26 | hskp10),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[109, 97])).
% 1.87/1.45 tff(111,plain,
% 1.87/1.45 ($false),
% 1.87/1.45 inference(unit_resolution,[status(thm)],[110, 96, 90, 84])).
% 1.87/1.45 tff(112,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.87/1.45 tff(113,plain,
% 1.87/1.45 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | c2_1(a510) | (~ndr1_0) | (~c3_1(a510)) | (~c0_1(a510)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | c2_1(a510) | (~ndr1_0) | (~c3_1(a510)) | (~c0_1(a510)))),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(114,plain,
% 1.87/1.45 ((hskp15 | hskp10 | (~ndr1_0) | c2_1(a510) | (~c3_1(a510)) | (~c0_1(a510))) <=> (hskp15 | hskp10 | c2_1(a510) | (~ndr1_0) | (~c3_1(a510)) | (~c0_1(a510)))),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(115,plain,
% 1.87/1.45 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a510) | (~c3_1(a510)) | (~c0_1(a510)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | c2_1(a510) | (~ndr1_0) | (~c3_1(a510)) | (~c0_1(a510))))),
% 1.87/1.45 inference(monotonicity,[status(thm)],[114])).
% 1.87/1.45 tff(116,plain,
% 1.87/1.45 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a510) | (~c3_1(a510)) | (~c0_1(a510)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | c2_1(a510) | (~ndr1_0) | (~c3_1(a510)) | (~c0_1(a510)))),
% 1.87/1.45 inference(transitivity,[status(thm)],[115, 113])).
% 1.87/1.45 tff(117,plain,
% 1.87/1.45 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a510) | (~c3_1(a510)) | (~c0_1(a510)))),
% 1.87/1.45 inference(quant_inst,[status(thm)],[])).
% 1.87/1.45 tff(118,plain,
% 1.87/1.45 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | c2_1(a510) | (~ndr1_0) | (~c3_1(a510)) | (~c0_1(a510))),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.87/1.45 tff(119,plain,
% 1.87/1.45 (~c3_1(a510)),
% 1.87/1.45 inference(unit_resolution,[status(thm)],[118, 112, 43, 11, 77, 60, 42])).
% 1.87/1.45 tff(120,plain,
% 1.87/1.45 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | c3_1(a510) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | c3_1(a510) | (~c0_1(a510)))),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(121,plain,
% 1.87/1.45 ((hskp22 | (~ndr1_0) | c3_1(a510) | c2_1(a510) | (~c0_1(a510)) | c1_1(a510) | c3_1(a510) | (~c0_1(a510))) <=> (hskp22 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | c3_1(a510) | (~c0_1(a510)))),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(122,plain,
% 1.87/1.45 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a510) | c2_1(a510) | (~c0_1(a510)) | c1_1(a510) | c3_1(a510) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | c3_1(a510) | (~c0_1(a510))))),
% 1.87/1.45 inference(monotonicity,[status(thm)],[121])).
% 1.87/1.45 tff(123,plain,
% 1.87/1.45 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a510) | c2_1(a510) | (~c0_1(a510)) | c1_1(a510) | c3_1(a510) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | c3_1(a510) | (~c0_1(a510)))),
% 1.87/1.45 inference(transitivity,[status(thm)],[122, 120])).
% 1.87/1.45 tff(124,plain,
% 1.87/1.45 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a510) | c2_1(a510) | (~c0_1(a510)) | c1_1(a510) | c3_1(a510) | (~c0_1(a510)))),
% 1.87/1.45 inference(quant_inst,[status(thm)],[])).
% 1.87/1.45 tff(125,plain,
% 1.87/1.45 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | c3_1(a510) | (~c0_1(a510))),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[124, 123])).
% 1.87/1.45 tff(126,plain,
% 1.87/1.45 (hskp22),
% 1.87/1.45 inference(unit_resolution,[status(thm)],[125, 112, 77, 66, 60, 31, 119])).
% 1.87/1.45 tff(127,plain,
% 1.87/1.45 (((~hskp22) | (~c0_1(a540))) <=> ((~hskp22) | (~c0_1(a540)))),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(128,plain,
% 1.87/1.45 (((~c0_1(a540)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a540)))),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(129,axiom,((~c0_1(a540)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 1.87/1.45 tff(130,plain,
% 1.87/1.45 ((~hskp22) | (~c0_1(a540))),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[129, 128])).
% 1.87/1.45 tff(131,plain,
% 1.87/1.45 ((~hskp22) | (~c0_1(a540))),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[130, 127])).
% 1.87/1.45 tff(132,plain,
% 1.87/1.45 (~c0_1(a540)),
% 1.87/1.45 inference(unit_resolution,[status(thm)],[131, 126])).
% 1.87/1.45 tff(133,plain,
% 1.87/1.45 (((~hskp22) | c3_1(a540)) <=> ((~hskp22) | c3_1(a540))),
% 1.87/1.45 inference(rewrite,[status(thm)],[])).
% 1.87/1.45 tff(134,axiom,((~hskp22) | c3_1(a540)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 1.87/1.45 tff(135,plain,
% 1.87/1.45 ((~hskp22) | c3_1(a540)),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.87/1.45 tff(136,plain,
% 1.87/1.45 ((~hskp22) | c3_1(a540)),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[135, 133])).
% 1.87/1.45 tff(137,plain,
% 1.87/1.45 ((~hskp22) | c3_1(a540)),
% 1.87/1.45 inference(modus_ponens,[status(thm)],[136, 133])).
% 1.87/1.45 tff(138,plain,
% 1.87/1.45 ((~hskp22) | c3_1(a540)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[137, 133])).
% 1.88/1.45 tff(139,plain,
% 1.88/1.45 ((~hskp22) | c3_1(a540)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[138, 133])).
% 1.88/1.45 tff(140,plain,
% 1.88/1.45 ((~hskp22) | c3_1(a540)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[139, 133])).
% 1.88/1.45 tff(141,plain,
% 1.88/1.45 ((~hskp22) | c3_1(a540)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[140, 133])).
% 1.88/1.45 tff(142,plain,
% 1.88/1.45 ((~hskp22) | c3_1(a540)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[141, 133])).
% 1.88/1.45 tff(143,plain,
% 1.88/1.45 (c3_1(a540)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[142, 126])).
% 1.88/1.45 tff(144,plain,
% 1.88/1.45 (((~hskp22) | c1_1(a540)) <=> ((~hskp22) | c1_1(a540))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(145,axiom,((~hskp22) | c1_1(a540)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 1.88/1.45 tff(146,plain,
% 1.88/1.45 ((~hskp22) | c1_1(a540)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[145, 144])).
% 1.88/1.45 tff(147,plain,
% 1.88/1.45 ((~hskp22) | c1_1(a540)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[146, 144])).
% 1.88/1.45 tff(148,plain,
% 1.88/1.45 ((~hskp22) | c1_1(a540)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[147, 144])).
% 1.88/1.45 tff(149,plain,
% 1.88/1.45 ((~hskp22) | c1_1(a540)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[148, 144])).
% 1.88/1.45 tff(150,plain,
% 1.88/1.45 ((~hskp22) | c1_1(a540)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[149, 144])).
% 1.88/1.45 tff(151,plain,
% 1.88/1.45 ((~hskp22) | c1_1(a540)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[150, 144])).
% 1.88/1.45 tff(152,plain,
% 1.88/1.45 ((~hskp22) | c1_1(a540)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[151, 144])).
% 1.88/1.45 tff(153,plain,
% 1.88/1.45 ((~hskp22) | c1_1(a540)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[152, 144])).
% 1.88/1.45 tff(154,plain,
% 1.88/1.45 (c1_1(a540)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[153, 126])).
% 1.88/1.45 tff(155,plain,
% 1.88/1.45 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c0_1(a540) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a540) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(156,plain,
% 1.88/1.45 ((hskp10 | (~ndr1_0) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a540))) <=> (hskp10 | c0_1(a540) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(157,plain,
% 1.88/1.45 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c0_1(a540) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c3_1(a540)) | (~c1_1(a540))))),
% 1.88/1.45 inference(monotonicity,[status(thm)],[156])).
% 1.88/1.45 tff(158,plain,
% 1.88/1.45 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a540) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.88/1.45 inference(transitivity,[status(thm)],[157, 155])).
% 1.88/1.45 tff(159,plain,
% 1.88/1.45 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a540)))),
% 1.88/1.45 inference(quant_inst,[status(thm)],[])).
% 1.88/1.45 tff(160,plain,
% 1.88/1.45 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a540) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c3_1(a540)) | (~c1_1(a540))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[159, 158])).
% 1.88/1.45 tff(161,plain,
% 1.88/1.45 ($false),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[160, 112, 11, 154, 143, 77, 132, 66, 60, 53])).
% 1.88/1.45 tff(162,plain,((~hskp11) | hskp10 | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.88/1.45 tff(163,plain,
% 1.88/1.45 (~hskp11),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[162, 43, 11])).
% 1.88/1.45 tff(164,plain,
% 1.88/1.45 ((hskp26 | hskp17 | hskp11) <=> (hskp26 | hskp17 | hskp11)),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(165,plain,
% 1.88/1.45 (((hskp11 | hskp17) | hskp26) <=> (hskp26 | hskp17 | hskp11)),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(166,axiom,((hskp11 | hskp17) | hskp26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 1.88/1.45 tff(167,plain,
% 1.88/1.45 (hskp26 | hskp17 | hskp11),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[166, 165])).
% 1.88/1.45 tff(168,plain,
% 1.88/1.45 (hskp26 | hskp17 | hskp11),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[167, 164])).
% 1.88/1.45 tff(169,plain,
% 1.88/1.45 (hskp26 | hskp17 | hskp11),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[168, 164])).
% 1.88/1.45 tff(170,plain,
% 1.88/1.45 (hskp26 | hskp17 | hskp11),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[169, 164])).
% 1.88/1.45 tff(171,plain,
% 1.88/1.45 (hskp26 | hskp17 | hskp11),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[170, 164])).
% 1.88/1.45 tff(172,plain,
% 1.88/1.45 (hskp26 | hskp17 | hskp11),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[171, 164])).
% 1.88/1.45 tff(173,plain,
% 1.88/1.45 (hskp26 | hskp17 | hskp11),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[172, 164])).
% 1.88/1.45 tff(174,plain,
% 1.88/1.45 (hskp26 | hskp17 | hskp11),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[173, 164])).
% 1.88/1.45 tff(175,plain,
% 1.88/1.45 (hskp17),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[174, 163, 32])).
% 1.88/1.45 tff(176,plain,
% 1.88/1.45 (((~hskp17) | (~c2_1(a532))) <=> ((~hskp17) | (~c2_1(a532)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(177,plain,
% 1.88/1.45 (((~c2_1(a532)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a532)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(178,axiom,((~c2_1(a532)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 1.88/1.45 tff(179,plain,
% 1.88/1.45 ((~hskp17) | (~c2_1(a532))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[178, 177])).
% 1.88/1.45 tff(180,plain,
% 1.88/1.45 ((~hskp17) | (~c2_1(a532))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[179, 176])).
% 1.88/1.45 tff(181,plain,
% 1.88/1.45 (~c2_1(a532)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[180, 175])).
% 1.88/1.45 tff(182,plain,
% 1.88/1.45 (((~hskp17) | c3_1(a532)) <=> ((~hskp17) | c3_1(a532))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(183,axiom,((~hskp17) | c3_1(a532)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 1.88/1.45 tff(184,plain,
% 1.88/1.45 ((~hskp17) | c3_1(a532)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[183, 182])).
% 1.88/1.45 tff(185,plain,
% 1.88/1.45 ((~hskp17) | c3_1(a532)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[184, 182])).
% 1.88/1.45 tff(186,plain,
% 1.88/1.45 ((~hskp17) | c3_1(a532)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[185, 182])).
% 1.88/1.45 tff(187,plain,
% 1.88/1.45 ((~hskp17) | c3_1(a532)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[186, 182])).
% 1.88/1.45 tff(188,plain,
% 1.88/1.45 ((~hskp17) | c3_1(a532)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[187, 182])).
% 1.88/1.45 tff(189,plain,
% 1.88/1.45 ((~hskp17) | c3_1(a532)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[188, 182])).
% 1.88/1.45 tff(190,plain,
% 1.88/1.45 ((~hskp17) | c3_1(a532)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[189, 182])).
% 1.88/1.45 tff(191,plain,
% 1.88/1.45 ((~hskp17) | c3_1(a532)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[190, 182])).
% 1.88/1.45 tff(192,plain,
% 1.88/1.45 (c3_1(a532)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[191, 175])).
% 1.88/1.45 tff(193,plain,
% 1.88/1.45 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | c2_1(a532) | (~ndr1_0) | (~c3_1(a532)) | (~c0_1(a532)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | c2_1(a532) | (~ndr1_0) | (~c3_1(a532)) | (~c0_1(a532)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(194,plain,
% 1.88/1.45 ((hskp15 | hskp10 | (~ndr1_0) | c2_1(a532) | (~c3_1(a532)) | (~c0_1(a532))) <=> (hskp15 | hskp10 | c2_1(a532) | (~ndr1_0) | (~c3_1(a532)) | (~c0_1(a532)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(195,plain,
% 1.88/1.45 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a532) | (~c3_1(a532)) | (~c0_1(a532)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | c2_1(a532) | (~ndr1_0) | (~c3_1(a532)) | (~c0_1(a532))))),
% 1.88/1.45 inference(monotonicity,[status(thm)],[194])).
% 1.88/1.45 tff(196,plain,
% 1.88/1.45 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a532) | (~c3_1(a532)) | (~c0_1(a532)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | c2_1(a532) | (~ndr1_0) | (~c3_1(a532)) | (~c0_1(a532)))),
% 1.88/1.45 inference(transitivity,[status(thm)],[195, 193])).
% 1.88/1.45 tff(197,plain,
% 1.88/1.45 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a532) | (~c3_1(a532)) | (~c0_1(a532)))),
% 1.88/1.45 inference(quant_inst,[status(thm)],[])).
% 1.88/1.45 tff(198,plain,
% 1.88/1.45 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | c2_1(a532) | (~ndr1_0) | (~c3_1(a532)) | (~c0_1(a532))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[197, 196])).
% 1.88/1.45 tff(199,plain,
% 1.88/1.45 (~c0_1(a532)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[198, 112, 43, 11, 192, 181, 42])).
% 1.88/1.45 tff(200,plain,
% 1.88/1.45 (hskp27),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[110, 11, 32])).
% 1.88/1.45 tff(201,plain,
% 1.88/1.45 (((~hskp27) | c3_1(a568)) <=> ((~hskp27) | c3_1(a568))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(202,axiom,((~hskp27) | c3_1(a568)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 1.88/1.45 tff(203,plain,
% 1.88/1.45 ((~hskp27) | c3_1(a568)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[202, 201])).
% 1.88/1.45 tff(204,plain,
% 1.88/1.45 ((~hskp27) | c3_1(a568)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[203, 201])).
% 1.88/1.45 tff(205,plain,
% 1.88/1.45 ((~hskp27) | c3_1(a568)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[204, 201])).
% 1.88/1.45 tff(206,plain,
% 1.88/1.45 ((~hskp27) | c3_1(a568)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[205, 201])).
% 1.88/1.45 tff(207,plain,
% 1.88/1.45 ((~hskp27) | c3_1(a568)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[206, 201])).
% 1.88/1.45 tff(208,plain,
% 1.88/1.45 ((~hskp27) | c3_1(a568)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[207, 201])).
% 1.88/1.45 tff(209,plain,
% 1.88/1.45 ((~hskp27) | c3_1(a568)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[208, 201])).
% 1.88/1.45 tff(210,plain,
% 1.88/1.45 ((~hskp27) | c3_1(a568)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[209, 201])).
% 1.88/1.45 tff(211,plain,
% 1.88/1.45 (c3_1(a568)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[210, 200])).
% 1.88/1.45 tff(212,plain,
% 1.88/1.45 (((~hskp27) | c0_1(a568)) <=> ((~hskp27) | c0_1(a568))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(213,axiom,((~hskp27) | c0_1(a568)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 1.88/1.45 tff(214,plain,
% 1.88/1.45 ((~hskp27) | c0_1(a568)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[213, 212])).
% 1.88/1.45 tff(215,plain,
% 1.88/1.45 ((~hskp27) | c0_1(a568)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[214, 212])).
% 1.88/1.45 tff(216,plain,
% 1.88/1.45 ((~hskp27) | c0_1(a568)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[215, 212])).
% 1.88/1.45 tff(217,plain,
% 1.88/1.45 ((~hskp27) | c0_1(a568)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[216, 212])).
% 1.88/1.45 tff(218,plain,
% 1.88/1.45 ((~hskp27) | c0_1(a568)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[217, 212])).
% 1.88/1.45 tff(219,plain,
% 1.88/1.45 ((~hskp27) | c0_1(a568)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[218, 212])).
% 1.88/1.45 tff(220,plain,
% 1.88/1.45 ((~hskp27) | c0_1(a568)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[219, 212])).
% 1.88/1.45 tff(221,plain,
% 1.88/1.45 ((~hskp27) | c0_1(a568)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[220, 212])).
% 1.88/1.45 tff(222,plain,
% 1.88/1.45 (c0_1(a568)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[221, 200])).
% 1.88/1.45 tff(223,plain,
% 1.88/1.45 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(224,plain,
% 1.88/1.45 ((hskp15 | hskp10 | (~ndr1_0) | c2_1(a568) | (~c3_1(a568)) | (~c0_1(a568))) <=> (hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(225,plain,
% 1.88/1.46 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a568) | (~c3_1(a568)) | (~c0_1(a568)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568)))),
% 1.88/1.46 inference(monotonicity,[status(thm)],[224])).
% 1.88/1.46 tff(226,plain,
% 1.88/1.46 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a568) | (~c3_1(a568)) | (~c0_1(a568)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568))),
% 1.88/1.46 inference(transitivity,[status(thm)],[225, 223])).
% 1.88/1.46 tff(227,plain,
% 1.88/1.46 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a568) | (~c3_1(a568)) | (~c0_1(a568)))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(228,plain,
% 1.88/1.46 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[227, 226])).
% 1.88/1.46 tff(229,plain,
% 1.88/1.46 (hskp15 | c2_1(a568)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[228, 112, 11, 222, 211, 42])).
% 1.88/1.46 tff(230,plain,
% 1.88/1.46 (c2_1(a568)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[229, 43])).
% 1.88/1.46 tff(231,plain,
% 1.88/1.46 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(232,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[231])).
% 1.88/1.46 tff(233,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(234,plain,
% 1.88/1.46 (^[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)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(235,plain,
% 1.88/1.46 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[234])).
% 1.88/1.46 tff(236,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 1.88/1.46 tff(237,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[236, 235])).
% 1.88/1.46 tff(238,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[237, 233])).
% 1.88/1.46 tff(239,plain,(
% 1.88/1.46 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.88/1.46 inference(skolemize,[status(sab)],[238])).
% 1.88/1.46 tff(240,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[239, 232])).
% 1.88/1.46 tff(241,plain,
% 1.88/1.46 (((~hskp17) | (~c1_1(a532))) <=> ((~hskp17) | (~c1_1(a532)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(242,plain,
% 1.88/1.46 (((~c1_1(a532)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a532)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(243,axiom,((~c1_1(a532)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 1.88/1.46 tff(244,plain,
% 1.88/1.46 ((~hskp17) | (~c1_1(a532))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[243, 242])).
% 1.88/1.46 tff(245,plain,
% 1.88/1.46 ((~hskp17) | (~c1_1(a532))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[244, 241])).
% 1.88/1.46 tff(246,plain,
% 1.88/1.46 (~c1_1(a532)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[245, 175])).
% 1.88/1.46 tff(247,plain,
% 1.88/1.46 (((~hskp27) | (~c1_1(a568))) <=> ((~hskp27) | (~c1_1(a568)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(248,plain,
% 1.88/1.46 (((~c1_1(a568)) | (~hskp27)) <=> ((~hskp27) | (~c1_1(a568)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(249,axiom,((~c1_1(a568)) | (~hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 1.88/1.46 tff(250,plain,
% 1.88/1.46 ((~hskp27) | (~c1_1(a568))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[249, 248])).
% 1.88/1.46 tff(251,plain,
% 1.88/1.46 ((~hskp27) | (~c1_1(a568))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[250, 247])).
% 1.88/1.46 tff(252,plain,
% 1.88/1.46 (~c1_1(a568)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[251, 200])).
% 1.88/1.46 tff(253,plain,
% 1.88/1.46 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(254,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[253])).
% 1.88/1.46 tff(255,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(256,plain,
% 1.88/1.46 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~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))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~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)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp28) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp28))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(257,plain,
% 1.88/1.46 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[256])).
% 1.88/1.46 tff(258,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 1.88/1.46 tff(259,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[258, 257])).
% 1.88/1.46 tff(260,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[259, 255])).
% 1.88/1.46 tff(261,plain,(
% 1.88/1.46 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.88/1.46 inference(skolemize,[status(sab)],[260])).
% 1.88/1.46 tff(262,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[261, 254])).
% 1.88/1.46 tff(263,assumption,(~c0_1(a502)), introduced(assumption)).
% 1.88/1.46 tff(264,plain,
% 1.88/1.46 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(265,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[264])).
% 1.88/1.46 tff(266,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(267,plain,
% 1.88/1.46 (^[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(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp29) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp29))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(268,plain,
% 1.88/1.46 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[267])).
% 1.88/1.46 tff(269,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 1.88/1.46 tff(270,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[269, 268])).
% 1.88/1.46 tff(271,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[270, 266])).
% 1.88/1.46 tff(272,plain,(
% 1.88/1.46 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.88/1.46 inference(skolemize,[status(sab)],[271])).
% 1.88/1.46 tff(273,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[272, 265])).
% 1.88/1.46 tff(274,plain,
% 1.88/1.46 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp29 | c1_1(a568) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | (~c2_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp29 | c1_1(a568) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(275,plain,
% 1.88/1.46 ((hskp29 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c3_1(a568)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568))) <=> (hskp29 | c1_1(a568) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(276,plain,
% 1.88/1.46 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c3_1(a568)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp29 | c1_1(a568) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | (~c2_1(a568))))),
% 1.88/1.46 inference(monotonicity,[status(thm)],[275])).
% 1.88/1.46 tff(277,plain,
% 1.88/1.46 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c3_1(a568)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp29 | c1_1(a568) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.88/1.46 inference(transitivity,[status(thm)],[276, 274])).
% 1.88/1.46 tff(278,plain,
% 1.88/1.46 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c3_1(a568)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(279,plain,
% 1.88/1.46 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp29 | c1_1(a568) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)) | (~c2_1(a568))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[278, 277])).
% 1.88/1.46 tff(280,plain,
% 1.88/1.46 (hskp29 | (~c2_1(a568))),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[279, 112, 222, 211, 252, 273])).
% 1.88/1.46 tff(281,plain,
% 1.88/1.46 (hskp29),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[280, 230])).
% 1.88/1.46 tff(282,plain,
% 1.88/1.46 (((~hskp29) | c3_1(a504)) <=> ((~hskp29) | c3_1(a504))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(283,axiom,((~hskp29) | c3_1(a504)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 1.88/1.46 tff(284,plain,
% 1.88/1.46 ((~hskp29) | c3_1(a504)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[283, 282])).
% 1.88/1.46 tff(285,plain,
% 1.88/1.46 ((~hskp29) | c3_1(a504)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[284, 282])).
% 1.88/1.46 tff(286,plain,
% 1.88/1.46 ((~hskp29) | c3_1(a504)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[285, 282])).
% 1.88/1.46 tff(287,plain,
% 1.88/1.46 ((~hskp29) | c3_1(a504)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[286, 282])).
% 1.88/1.46 tff(288,plain,
% 1.88/1.46 ((~hskp29) | c3_1(a504)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[287, 282])).
% 1.88/1.46 tff(289,plain,
% 1.88/1.46 ((~hskp29) | c3_1(a504)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[288, 282])).
% 1.88/1.46 tff(290,plain,
% 1.88/1.46 ((~hskp29) | c3_1(a504)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[289, 282])).
% 1.88/1.46 tff(291,plain,
% 1.88/1.46 ((~hskp29) | c3_1(a504)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[290, 282])).
% 1.88/1.46 tff(292,plain,
% 1.88/1.46 (c3_1(a504)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[291, 281])).
% 1.88/1.46 tff(293,plain,
% 1.88/1.46 (((~hskp29) | c0_1(a504)) <=> ((~hskp29) | c0_1(a504))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(294,axiom,((~hskp29) | c0_1(a504)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 1.88/1.46 tff(295,plain,
% 1.88/1.46 ((~hskp29) | c0_1(a504)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[294, 293])).
% 1.88/1.46 tff(296,plain,
% 1.88/1.46 ((~hskp29) | c0_1(a504)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[295, 293])).
% 1.88/1.46 tff(297,plain,
% 1.88/1.46 ((~hskp29) | c0_1(a504)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[296, 293])).
% 1.88/1.46 tff(298,plain,
% 1.88/1.46 ((~hskp29) | c0_1(a504)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[297, 293])).
% 1.88/1.46 tff(299,plain,
% 1.88/1.46 ((~hskp29) | c0_1(a504)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[298, 293])).
% 1.88/1.46 tff(300,plain,
% 1.88/1.46 ((~hskp29) | c0_1(a504)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[299, 293])).
% 1.88/1.46 tff(301,plain,
% 1.88/1.46 ((~hskp29) | c0_1(a504)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[300, 293])).
% 1.88/1.46 tff(302,plain,
% 1.88/1.46 ((~hskp29) | c0_1(a504)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[301, 293])).
% 1.88/1.46 tff(303,plain,
% 1.88/1.46 (c0_1(a504)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[302, 281])).
% 1.88/1.46 tff(304,plain,
% 1.88/1.46 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c0_1(a504)) | (~c3_1(a504)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c0_1(a504)) | (~c3_1(a504)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(305,plain,
% 1.88/1.46 ((hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c3_1(a504)) | (~c0_1(a504))) <=> (hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c0_1(a504)) | (~c3_1(a504)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(306,plain,
% 1.88/1.46 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c3_1(a504)) | (~c0_1(a504)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c0_1(a504)) | (~c3_1(a504))))),
% 1.88/1.46 inference(monotonicity,[status(thm)],[305])).
% 1.88/1.46 tff(307,plain,
% 1.88/1.46 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c3_1(a504)) | (~c0_1(a504)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c0_1(a504)) | (~c3_1(a504)))),
% 1.88/1.46 inference(transitivity,[status(thm)],[306, 304])).
% 1.88/1.46 tff(308,plain,
% 1.88/1.46 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c3_1(a504)) | (~c0_1(a504)))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(309,plain,
% 1.88/1.46 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | c2_1(a504) | (~c0_1(a504)) | (~c3_1(a504))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[308, 307])).
% 1.88/1.46 tff(310,plain,
% 1.88/1.46 (c2_1(a504)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[309, 112, 43, 11, 303, 292, 42])).
% 1.88/1.46 tff(311,plain,
% 1.88/1.46 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(312,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[311])).
% 1.88/1.46 tff(313,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(314,plain,
% 1.88/1.46 (^[V: $i, U: $i] : 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)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp2))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(315,plain,
% 1.88/1.46 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[314])).
% 1.88/1.46 tff(316,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 1.88/1.46 tff(317,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[316, 315])).
% 1.88/1.46 tff(318,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[317, 313])).
% 1.88/1.46 tff(319,plain,(
% 1.88/1.46 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.88/1.46 inference(skolemize,[status(sab)],[318])).
% 1.88/1.46 tff(320,plain,
% 1.88/1.46 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[319, 312])).
% 1.88/1.46 tff(321,plain,
% 1.88/1.46 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a568) | c1_1(a532) | (~ndr1_0) | (~c3_1(a532)) | c0_1(a532) | (~c0_1(a568)) | (~c2_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a568) | c1_1(a532) | (~ndr1_0) | (~c3_1(a532)) | c0_1(a532) | (~c0_1(a568)) | (~c2_1(a568)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(322,plain,
% 1.88/1.47 ((hskp7 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c1_1(a532) | c0_1(a532) | (~c3_1(a532))) <=> (hskp7 | c1_1(a568) | c1_1(a532) | (~ndr1_0) | (~c3_1(a532)) | c0_1(a532) | (~c0_1(a568)) | (~c2_1(a568)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(323,plain,
% 1.88/1.47 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c1_1(a532) | c0_1(a532) | (~c3_1(a532)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a568) | c1_1(a532) | (~ndr1_0) | (~c3_1(a532)) | c0_1(a532) | (~c0_1(a568)) | (~c2_1(a568))))),
% 1.88/1.47 inference(monotonicity,[status(thm)],[322])).
% 1.88/1.47 tff(324,plain,
% 1.88/1.47 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c1_1(a532) | c0_1(a532) | (~c3_1(a532)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a568) | c1_1(a532) | (~ndr1_0) | (~c3_1(a532)) | c0_1(a532) | (~c0_1(a568)) | (~c2_1(a568)))),
% 1.88/1.47 inference(transitivity,[status(thm)],[323, 321])).
% 1.88/1.47 tff(325,plain,
% 1.88/1.47 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c1_1(a532) | c0_1(a532) | (~c3_1(a532)))),
% 1.88/1.47 inference(quant_inst,[status(thm)],[])).
% 1.88/1.47 tff(326,plain,
% 1.88/1.47 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a568) | c1_1(a532) | (~ndr1_0) | (~c3_1(a532)) | c0_1(a532) | (~c0_1(a568)) | (~c2_1(a568))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[325, 324])).
% 1.88/1.47 tff(327,plain,
% 1.88/1.47 (hskp7),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[326, 112, 222, 192, 252, 246, 240, 230, 199])).
% 1.88/1.47 tff(328,plain,
% 1.88/1.47 (((~hskp7) | (~c3_1(a502))) <=> ((~hskp7) | (~c3_1(a502)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(329,plain,
% 1.88/1.47 (((~c3_1(a502)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a502)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(330,axiom,((~c3_1(a502)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 1.88/1.47 tff(331,plain,
% 1.88/1.47 ((~hskp7) | (~c3_1(a502))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[330, 329])).
% 1.88/1.47 tff(332,plain,
% 1.88/1.47 ((~hskp7) | (~c3_1(a502))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[331, 328])).
% 1.88/1.47 tff(333,plain,
% 1.88/1.47 (~c3_1(a502)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[332, 327])).
% 1.88/1.47 tff(334,plain,
% 1.88/1.47 (((~hskp7) | (~c1_1(a502))) <=> ((~hskp7) | (~c1_1(a502)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(335,plain,
% 1.88/1.47 (((~c1_1(a502)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a502)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(336,axiom,((~c1_1(a502)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 1.88/1.47 tff(337,plain,
% 1.88/1.47 ((~hskp7) | (~c1_1(a502))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[336, 335])).
% 1.88/1.47 tff(338,plain,
% 1.88/1.47 ((~hskp7) | (~c1_1(a502))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[337, 334])).
% 1.88/1.47 tff(339,plain,
% 1.88/1.47 (~c1_1(a502)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[338, 327])).
% 1.88/1.47 tff(340,plain,
% 1.88/1.47 (((~hskp29) | c1_1(a504)) <=> ((~hskp29) | c1_1(a504))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(341,axiom,((~hskp29) | c1_1(a504)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 1.88/1.47 tff(342,plain,
% 1.88/1.47 ((~hskp29) | c1_1(a504)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[341, 340])).
% 1.88/1.47 tff(343,plain,
% 1.88/1.47 ((~hskp29) | c1_1(a504)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[342, 340])).
% 1.88/1.47 tff(344,plain,
% 1.88/1.47 ((~hskp29) | c1_1(a504)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[343, 340])).
% 1.88/1.47 tff(345,plain,
% 1.88/1.47 ((~hskp29) | c1_1(a504)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[344, 340])).
% 1.88/1.47 tff(346,plain,
% 1.88/1.47 ((~hskp29) | c1_1(a504)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[345, 340])).
% 1.88/1.47 tff(347,plain,
% 1.88/1.47 ((~hskp29) | c1_1(a504)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[346, 340])).
% 1.88/1.47 tff(348,plain,
% 1.88/1.47 ((~hskp29) | c1_1(a504)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[347, 340])).
% 1.88/1.47 tff(349,plain,
% 1.88/1.47 ((~hskp29) | c1_1(a504)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[348, 340])).
% 1.88/1.47 tff(350,plain,
% 1.88/1.47 (c1_1(a504)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[349, 281])).
% 1.88/1.47 tff(351,plain,
% 1.88/1.47 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(352,plain,
% 1.88/1.47 ((hskp2 | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c1_1(a502) | c0_1(a502) | c3_1(a502)) <=> (hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(353,plain,
% 1.88/1.47 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504))))),
% 1.88/1.47 inference(monotonicity,[status(thm)],[352])).
% 1.88/1.47 tff(354,plain,
% 1.88/1.47 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)))),
% 1.88/1.47 inference(transitivity,[status(thm)],[353, 351])).
% 1.88/1.47 tff(355,plain,
% 1.88/1.47 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c1_1(a502) | c0_1(a502) | c3_1(a502))),
% 1.88/1.47 inference(quant_inst,[status(thm)],[])).
% 1.88/1.47 tff(356,plain,
% 1.88/1.47 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[355, 354])).
% 1.88/1.47 tff(357,plain,
% 1.88/1.47 (hskp2),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[356, 112, 303, 350, 263, 339, 333, 320, 310])).
% 1.88/1.47 tff(358,plain,
% 1.88/1.47 (((~hskp2) | (~c3_1(a496))) <=> ((~hskp2) | (~c3_1(a496)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(359,plain,
% 1.88/1.47 (((~c3_1(a496)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a496)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(360,axiom,((~c3_1(a496)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 1.88/1.47 tff(361,plain,
% 1.88/1.47 ((~hskp2) | (~c3_1(a496))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[360, 359])).
% 1.88/1.47 tff(362,plain,
% 1.88/1.47 ((~hskp2) | (~c3_1(a496))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[361, 358])).
% 1.88/1.47 tff(363,plain,
% 1.88/1.47 (~c3_1(a496)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[362, 357])).
% 1.88/1.47 tff(364,plain,
% 1.88/1.47 (((~hskp2) | (~c2_1(a496))) <=> ((~hskp2) | (~c2_1(a496)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(365,plain,
% 1.88/1.47 (((~c2_1(a496)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a496)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(366,axiom,((~c2_1(a496)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 1.88/1.47 tff(367,plain,
% 1.88/1.47 ((~hskp2) | (~c2_1(a496))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[366, 365])).
% 1.88/1.47 tff(368,plain,
% 1.88/1.47 ((~hskp2) | (~c2_1(a496))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[367, 364])).
% 1.88/1.47 tff(369,plain,
% 1.88/1.47 (~c2_1(a496)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[368, 357])).
% 1.88/1.47 tff(370,plain,
% 1.88/1.47 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(371,plain,
% 1.88/1.47 ((hskp11 | hskp10 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | c0_1(a496)) <=> (hskp11 | hskp10 | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(372,plain,
% 1.88/1.47 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | c0_1(a496))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496)))),
% 1.88/1.47 inference(monotonicity,[status(thm)],[371])).
% 1.88/1.47 tff(373,plain,
% 1.88/1.47 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | c0_1(a496))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496))),
% 1.88/1.47 inference(transitivity,[status(thm)],[372, 370])).
% 1.88/1.47 tff(374,plain,
% 1.88/1.47 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | c0_1(a496))),
% 1.88/1.47 inference(quant_inst,[status(thm)],[])).
% 1.88/1.47 tff(375,plain,
% 1.88/1.47 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[374, 373])).
% 1.88/1.47 tff(376,plain,
% 1.88/1.47 (c0_1(a496)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[375, 112, 163, 11, 369, 363, 10])).
% 1.88/1.47 tff(377,plain,
% 1.88/1.47 (((~hskp2) | (~c1_1(a496))) <=> ((~hskp2) | (~c1_1(a496)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(378,plain,
% 1.88/1.47 (((~c1_1(a496)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a496)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(379,axiom,((~c1_1(a496)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 1.88/1.47 tff(380,plain,
% 1.88/1.47 ((~hskp2) | (~c1_1(a496))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[379, 378])).
% 1.88/1.47 tff(381,plain,
% 1.88/1.47 ((~hskp2) | (~c1_1(a496))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[380, 377])).
% 1.88/1.47 tff(382,plain,
% 1.88/1.47 (~c1_1(a496)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[381, 357])).
% 1.88/1.47 tff(383,plain,
% 1.88/1.47 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(384,plain,
% 1.88/1.47 ((hskp11 | hskp10 | (~ndr1_0) | c3_1(a502) | c2_1(a502) | c0_1(a502)) <=> (hskp11 | hskp10 | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(385,plain,
% 1.88/1.47 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a502) | c2_1(a502) | c0_1(a502))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502)))),
% 1.88/1.47 inference(monotonicity,[status(thm)],[384])).
% 1.88/1.47 tff(386,plain,
% 1.88/1.47 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a502) | c2_1(a502) | c0_1(a502))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502))),
% 1.88/1.47 inference(transitivity,[status(thm)],[385, 383])).
% 1.88/1.47 tff(387,plain,
% 1.88/1.47 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a502) | c2_1(a502) | c0_1(a502))),
% 1.88/1.47 inference(quant_inst,[status(thm)],[])).
% 1.88/1.47 tff(388,plain,
% 1.88/1.47 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[387, 386])).
% 1.88/1.47 tff(389,plain,
% 1.88/1.47 (hskp11 | c3_1(a502) | c2_1(a502)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[388, 112, 11, 263, 10])).
% 1.88/1.47 tff(390,plain,
% 1.88/1.47 (c2_1(a502)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[389, 333, 163])).
% 1.88/1.47 tff(391,plain,
% 1.88/1.47 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.88/1.47 inference(bind,[status(th)],[])).
% 1.88/1.47 tff(392,plain,
% 1.88/1.47 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.88/1.47 inference(quant_intro,[status(thm)],[391])).
% 1.88/1.47 tff(393,plain,
% 1.88/1.47 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(394,plain,
% 1.88/1.47 (^[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)) | (~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(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.88/1.47 inference(bind,[status(th)],[])).
% 1.88/1.47 tff(395,plain,
% 1.88/1.47 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.88/1.47 inference(quant_intro,[status(thm)],[394])).
% 1.88/1.47 tff(396,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 1.88/1.47 tff(397,plain,
% 1.88/1.47 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[396, 395])).
% 1.88/1.47 tff(398,plain,
% 1.88/1.47 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[397, 393])).
% 1.88/1.47 tff(399,plain,(
% 1.88/1.47 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.88/1.47 inference(skolemize,[status(sab)],[398])).
% 1.88/1.47 tff(400,plain,
% 1.88/1.47 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[399, 392])).
% 1.88/1.47 tff(401,assumption,(c0_1(a568)), introduced(assumption)).
% 1.88/1.47 tff(402,assumption,(~c1_1(a568)), introduced(assumption)).
% 1.88/1.47 tff(403,assumption,(c3_1(a568)), introduced(assumption)).
% 1.88/1.47 tff(404,assumption,(~hskp13), introduced(assumption)).
% 1.88/1.47 tff(405,plain,
% 1.88/1.47 ((hskp28 | hskp13 | hskp10) <=> (hskp28 | hskp13 | hskp10)),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(406,plain,
% 1.88/1.47 (((hskp28 | hskp13) | hskp10) <=> (hskp28 | hskp13 | hskp10)),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(407,plain,
% 1.88/1.47 ((hskp28 | hskp13) <=> (hskp28 | hskp13)),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(408,plain,
% 1.88/1.47 (((hskp28 | hskp13) | hskp10) <=> ((hskp28 | hskp13) | hskp10)),
% 1.88/1.47 inference(monotonicity,[status(thm)],[407])).
% 1.88/1.47 tff(409,plain,
% 1.88/1.47 (((hskp28 | hskp13) | hskp10) <=> (hskp28 | hskp13 | hskp10)),
% 1.88/1.47 inference(transitivity,[status(thm)],[408, 406])).
% 1.88/1.47 tff(410,axiom,((hskp28 | hskp13) | hskp10), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 1.88/1.47 tff(411,plain,
% 1.88/1.47 (hskp28 | hskp13 | hskp10),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[410, 409])).
% 1.88/1.47 tff(412,plain,
% 1.88/1.47 (hskp28 | hskp13 | hskp10),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[411, 405])).
% 1.88/1.47 tff(413,plain,
% 1.88/1.47 (hskp28 | hskp13 | hskp10),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[412, 405])).
% 1.88/1.47 tff(414,plain,
% 1.88/1.47 (hskp28 | hskp13 | hskp10),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[413, 405])).
% 1.88/1.47 tff(415,plain,
% 1.88/1.47 (hskp28 | hskp13 | hskp10),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[414, 405])).
% 1.88/1.47 tff(416,plain,
% 1.88/1.47 (hskp28 | hskp13 | hskp10),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[415, 405])).
% 1.88/1.47 tff(417,plain,
% 1.88/1.47 (hskp28 | hskp13 | hskp10),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[416, 405])).
% 1.88/1.47 tff(418,plain,
% 1.88/1.47 (hskp28 | hskp13 | hskp10),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[417, 405])).
% 1.88/1.47 tff(419,plain,
% 1.88/1.47 (hskp28),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[418, 404, 11])).
% 1.88/1.47 tff(420,plain,
% 1.88/1.47 (((~hskp28) | c3_1(a500)) <=> ((~hskp28) | c3_1(a500))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(421,axiom,((~hskp28) | c3_1(a500)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 1.88/1.47 tff(422,plain,
% 1.88/1.47 ((~hskp28) | c3_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[421, 420])).
% 1.88/1.47 tff(423,plain,
% 1.88/1.47 ((~hskp28) | c3_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[422, 420])).
% 1.88/1.47 tff(424,plain,
% 1.88/1.47 ((~hskp28) | c3_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[423, 420])).
% 1.88/1.47 tff(425,plain,
% 1.88/1.47 ((~hskp28) | c3_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[424, 420])).
% 1.88/1.47 tff(426,plain,
% 1.88/1.47 ((~hskp28) | c3_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[425, 420])).
% 1.88/1.47 tff(427,plain,
% 1.88/1.47 ((~hskp28) | c3_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[426, 420])).
% 1.88/1.47 tff(428,plain,
% 1.88/1.47 ((~hskp28) | c3_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[427, 420])).
% 1.88/1.47 tff(429,plain,
% 1.88/1.47 ((~hskp28) | c3_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[428, 420])).
% 1.88/1.47 tff(430,plain,
% 1.88/1.47 (c3_1(a500)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[429, 419])).
% 1.88/1.47 tff(431,plain,
% 1.88/1.47 (((~hskp28) | c2_1(a500)) <=> ((~hskp28) | c2_1(a500))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(432,axiom,((~hskp28) | c2_1(a500)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 1.88/1.47 tff(433,plain,
% 1.88/1.47 ((~hskp28) | c2_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[432, 431])).
% 1.88/1.47 tff(434,plain,
% 1.88/1.47 ((~hskp28) | c2_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[433, 431])).
% 1.88/1.47 tff(435,plain,
% 1.88/1.47 ((~hskp28) | c2_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[434, 431])).
% 1.88/1.47 tff(436,plain,
% 1.88/1.47 ((~hskp28) | c2_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[435, 431])).
% 1.88/1.47 tff(437,plain,
% 1.88/1.47 ((~hskp28) | c2_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[436, 431])).
% 1.88/1.47 tff(438,plain,
% 1.88/1.47 ((~hskp28) | c2_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[437, 431])).
% 1.88/1.47 tff(439,plain,
% 1.88/1.47 ((~hskp28) | c2_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[438, 431])).
% 1.88/1.47 tff(440,plain,
% 1.88/1.47 ((~hskp28) | c2_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[439, 431])).
% 1.88/1.47 tff(441,plain,
% 1.88/1.47 (c2_1(a500)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[440, 419])).
% 1.88/1.47 tff(442,plain,
% 1.88/1.47 (((~hskp28) | c0_1(a500)) <=> ((~hskp28) | c0_1(a500))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(443,axiom,((~hskp28) | c0_1(a500)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 1.88/1.47 tff(444,plain,
% 1.88/1.47 ((~hskp28) | c0_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[443, 442])).
% 1.88/1.47 tff(445,plain,
% 1.88/1.47 ((~hskp28) | c0_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[444, 442])).
% 1.88/1.47 tff(446,plain,
% 1.88/1.47 ((~hskp28) | c0_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[445, 442])).
% 1.88/1.47 tff(447,plain,
% 1.88/1.47 ((~hskp28) | c0_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[446, 442])).
% 1.88/1.47 tff(448,plain,
% 1.88/1.47 ((~hskp28) | c0_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[447, 442])).
% 1.88/1.47 tff(449,plain,
% 1.88/1.47 ((~hskp28) | c0_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[448, 442])).
% 1.88/1.47 tff(450,plain,
% 1.88/1.47 ((~hskp28) | c0_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[449, 442])).
% 1.88/1.47 tff(451,plain,
% 1.88/1.47 ((~hskp28) | c0_1(a500)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[450, 442])).
% 1.88/1.47 tff(452,plain,
% 1.88/1.47 (c0_1(a500)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[451, 419])).
% 1.88/1.47 tff(453,assumption,(~hskp2), introduced(assumption)).
% 1.88/1.47 tff(454,plain,
% 1.88/1.47 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.88/1.47 inference(bind,[status(th)],[])).
% 1.88/1.47 tff(455,plain,
% 1.88/1.47 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.88/1.47 inference(quant_intro,[status(thm)],[454])).
% 1.88/1.47 tff(456,plain,
% 1.88/1.47 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(457,plain,
% 1.88/1.47 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp2))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp2) <=> (hskp2 | (~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)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.88/1.48 inference(bind,[status(th)],[])).
% 1.88/1.48 tff(458,plain,
% 1.88/1.48 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.88/1.48 inference(quant_intro,[status(thm)],[457])).
% 1.88/1.48 tff(459,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 1.88/1.48 tff(460,plain,
% 1.88/1.48 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[459, 458])).
% 1.88/1.48 tff(461,plain,
% 1.88/1.48 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[460, 456])).
% 1.88/1.48 tff(462,plain,(
% 1.88/1.48 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.88/1.48 inference(skolemize,[status(sab)],[461])).
% 1.88/1.48 tff(463,plain,
% 1.88/1.48 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[462, 455])).
% 1.88/1.48 tff(464,assumption,(hskp15), introduced(assumption)).
% 1.88/1.48 tff(465,plain,
% 1.88/1.48 (((~hskp15) | (~c3_1(a528))) <=> ((~hskp15) | (~c3_1(a528)))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(466,plain,
% 1.88/1.48 (((~c3_1(a528)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a528)))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(467,axiom,((~c3_1(a528)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 1.88/1.48 tff(468,plain,
% 1.88/1.48 ((~hskp15) | (~c3_1(a528))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[467, 466])).
% 1.88/1.48 tff(469,plain,
% 1.88/1.48 ((~hskp15) | (~c3_1(a528))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[468, 465])).
% 1.88/1.48 tff(470,plain,
% 1.88/1.48 (~c3_1(a528)),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[469, 464])).
% 1.88/1.48 tff(471,plain,
% 1.88/1.48 (((~hskp15) | c1_1(a528)) <=> ((~hskp15) | c1_1(a528))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(472,axiom,((~hskp15) | c1_1(a528)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 1.88/1.48 tff(473,plain,
% 1.88/1.48 ((~hskp15) | c1_1(a528)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[472, 471])).
% 1.88/1.48 tff(474,plain,
% 1.88/1.48 ((~hskp15) | c1_1(a528)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[473, 471])).
% 1.88/1.48 tff(475,plain,
% 1.88/1.48 ((~hskp15) | c1_1(a528)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[474, 471])).
% 1.88/1.48 tff(476,plain,
% 1.88/1.48 ((~hskp15) | c1_1(a528)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[475, 471])).
% 1.88/1.48 tff(477,plain,
% 1.88/1.48 ((~hskp15) | c1_1(a528)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[476, 471])).
% 1.88/1.48 tff(478,plain,
% 1.88/1.48 ((~hskp15) | c1_1(a528)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[477, 471])).
% 1.88/1.48 tff(479,plain,
% 1.88/1.48 ((~hskp15) | c1_1(a528)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[478, 471])).
% 1.88/1.48 tff(480,plain,
% 1.88/1.48 ((~hskp15) | c1_1(a528)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[479, 471])).
% 1.88/1.48 tff(481,plain,
% 1.88/1.48 (c1_1(a528)),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[480, 464])).
% 1.88/1.48 tff(482,plain,
% 1.88/1.48 (((~hskp15) | c0_1(a528)) <=> ((~hskp15) | c0_1(a528))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(483,axiom,((~hskp15) | c0_1(a528)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 1.88/1.48 tff(484,plain,
% 1.88/1.48 ((~hskp15) | c0_1(a528)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[483, 482])).
% 1.88/1.48 tff(485,plain,
% 1.88/1.48 ((~hskp15) | c0_1(a528)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[484, 482])).
% 1.88/1.48 tff(486,plain,
% 1.88/1.48 ((~hskp15) | c0_1(a528)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[485, 482])).
% 1.88/1.48 tff(487,plain,
% 1.88/1.48 ((~hskp15) | c0_1(a528)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[486, 482])).
% 1.88/1.48 tff(488,plain,
% 1.88/1.48 ((~hskp15) | c0_1(a528)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[487, 482])).
% 1.88/1.48 tff(489,plain,
% 1.88/1.48 ((~hskp15) | c0_1(a528)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[488, 482])).
% 1.88/1.48 tff(490,plain,
% 1.88/1.48 ((~hskp15) | c0_1(a528)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[489, 482])).
% 1.88/1.48 tff(491,plain,
% 1.88/1.48 ((~hskp15) | c0_1(a528)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[490, 482])).
% 1.88/1.48 tff(492,plain,
% 1.88/1.48 (c0_1(a528)),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[491, 464])).
% 1.88/1.48 tff(493,assumption,(c3_1(a500)), introduced(assumption)).
% 1.88/1.48 tff(494,assumption,(c2_1(a500)), introduced(assumption)).
% 1.88/1.48 tff(495,assumption,(c0_1(a500)), introduced(assumption)).
% 1.88/1.48 tff(496,plain,
% 1.88/1.48 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c3_1(a528) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c3_1(a528) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(497,plain,
% 1.88/1.48 ((hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528))) <=> (hskp2 | c3_1(a528) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(498,plain,
% 1.88/1.48 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c3_1(a528) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a528)) | (~c0_1(a528))))),
% 1.88/1.48 inference(monotonicity,[status(thm)],[497])).
% 1.88/1.48 tff(499,plain,
% 1.88/1.48 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c3_1(a528) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.88/1.48 inference(transitivity,[status(thm)],[498, 496])).
% 1.88/1.48 tff(500,plain,
% 1.88/1.48 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.88/1.48 inference(quant_inst,[status(thm)],[])).
% 1.88/1.48 tff(501,plain,
% 1.88/1.48 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c3_1(a528) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a528)) | (~c0_1(a528))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[500, 499])).
% 1.88/1.48 tff(502,plain,
% 1.88/1.48 ($false),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[501, 112, 453, 495, 494, 493, 492, 481, 470, 463])).
% 1.88/1.48 tff(503,plain,((~hskp15) | hskp2 | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500))), inference(lemma,lemma(discharge,[]))).
% 1.88/1.48 tff(504,plain,
% 1.88/1.48 (~hskp15),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[503, 453, 452, 441, 430])).
% 1.88/1.48 tff(505,plain,
% 1.88/1.48 (hskp15 | c2_1(a568)),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[228, 112, 11, 401, 403, 42])).
% 1.88/1.48 tff(506,plain,
% 1.88/1.48 (c2_1(a568)),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[505, 504])).
% 1.88/1.48 tff(507,plain,
% 1.88/1.48 (hskp29 | (~c2_1(a568))),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[279, 112, 401, 403, 402, 273])).
% 1.88/1.48 tff(508,plain,
% 1.88/1.48 (hskp29),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[507, 506])).
% 1.88/1.48 tff(509,plain,
% 1.88/1.48 (c3_1(a504)),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[291, 508])).
% 1.88/1.48 tff(510,plain,
% 1.88/1.48 (c0_1(a504)),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[302, 508])).
% 1.88/1.48 tff(511,plain,
% 1.88/1.48 (c2_1(a504)),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[309, 112, 504, 11, 510, 509, 42])).
% 1.88/1.48 tff(512,plain,
% 1.88/1.48 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 1.88/1.48 inference(bind,[status(th)],[])).
% 1.88/1.48 tff(513,plain,
% 1.88/1.48 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.88/1.48 inference(quant_intro,[status(thm)],[512])).
% 1.88/1.48 tff(514,plain,
% 1.88/1.48 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(515,plain,
% 1.88/1.48 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 1.88/1.48 inference(bind,[status(th)],[])).
% 1.88/1.48 tff(516,plain,
% 1.88/1.48 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.88/1.48 inference(quant_intro,[status(thm)],[515])).
% 1.88/1.48 tff(517,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 1.88/1.48 tff(518,plain,
% 1.88/1.48 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[517, 516])).
% 1.88/1.48 tff(519,plain,
% 1.88/1.48 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[518, 514])).
% 1.88/1.48 tff(520,plain,(
% 1.88/1.48 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.88/1.48 inference(skolemize,[status(sab)],[519])).
% 1.88/1.48 tff(521,plain,
% 1.88/1.48 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[520, 513])).
% 1.88/1.48 tff(522,plain,
% 1.88/1.48 ((hskp15 | hskp13 | hskp12) <=> (hskp15 | hskp13 | hskp12)),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(523,plain,
% 1.88/1.48 (((hskp15 | hskp13) | hskp12) <=> (hskp15 | hskp13 | hskp12)),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(524,plain,
% 1.88/1.48 ((hskp15 | hskp13) <=> (hskp15 | hskp13)),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(525,plain,
% 1.88/1.48 (((hskp15 | hskp13) | hskp12) <=> ((hskp15 | hskp13) | hskp12)),
% 1.88/1.48 inference(monotonicity,[status(thm)],[524])).
% 1.88/1.48 tff(526,plain,
% 1.88/1.48 (((hskp15 | hskp13) | hskp12) <=> (hskp15 | hskp13 | hskp12)),
% 1.88/1.48 inference(transitivity,[status(thm)],[525, 523])).
% 1.88/1.48 tff(527,axiom,((hskp15 | hskp13) | hskp12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 1.88/1.48 tff(528,plain,
% 1.88/1.48 (hskp15 | hskp13 | hskp12),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[527, 526])).
% 1.88/1.48 tff(529,plain,
% 1.88/1.48 (hskp15 | hskp13 | hskp12),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[528, 522])).
% 1.88/1.48 tff(530,plain,
% 1.88/1.48 (hskp15 | hskp13 | hskp12),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[529, 522])).
% 1.88/1.48 tff(531,plain,
% 1.88/1.48 (hskp15 | hskp13 | hskp12),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[530, 522])).
% 1.88/1.48 tff(532,plain,
% 1.88/1.48 (hskp15 | hskp13 | hskp12),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[531, 522])).
% 1.88/1.48 tff(533,plain,
% 1.88/1.48 (hskp15 | hskp13 | hskp12),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[532, 522])).
% 1.88/1.48 tff(534,plain,
% 1.88/1.48 (hskp15 | hskp13 | hskp12),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[533, 522])).
% 1.88/1.48 tff(535,plain,
% 1.88/1.48 (hskp15 | hskp13 | hskp12),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[534, 522])).
% 1.88/1.48 tff(536,plain,
% 1.88/1.48 (hskp12),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[535, 504, 404])).
% 1.88/1.48 tff(537,plain,
% 1.88/1.48 (((~hskp12) | (~c2_1(a514))) <=> ((~hskp12) | (~c2_1(a514)))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(538,plain,
% 1.88/1.48 (((~c2_1(a514)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a514)))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(539,axiom,((~c2_1(a514)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 1.88/1.48 tff(540,plain,
% 1.88/1.48 ((~hskp12) | (~c2_1(a514))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[539, 538])).
% 1.88/1.48 tff(541,plain,
% 1.88/1.48 ((~hskp12) | (~c2_1(a514))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[540, 537])).
% 1.88/1.48 tff(542,plain,
% 1.88/1.48 (~c2_1(a514)),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[541, 536])).
% 1.88/1.48 tff(543,plain,
% 1.88/1.48 (((~hskp12) | c3_1(a514)) <=> ((~hskp12) | c3_1(a514))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(544,axiom,((~hskp12) | c3_1(a514)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.88/1.48 tff(545,plain,
% 1.88/1.48 ((~hskp12) | c3_1(a514)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[544, 543])).
% 1.88/1.48 tff(546,plain,
% 1.88/1.48 ((~hskp12) | c3_1(a514)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[545, 543])).
% 1.88/1.48 tff(547,plain,
% 1.88/1.48 ((~hskp12) | c3_1(a514)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[546, 543])).
% 1.88/1.48 tff(548,plain,
% 1.88/1.48 ((~hskp12) | c3_1(a514)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[547, 543])).
% 1.88/1.48 tff(549,plain,
% 1.88/1.48 ((~hskp12) | c3_1(a514)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[548, 543])).
% 1.88/1.48 tff(550,plain,
% 1.88/1.48 ((~hskp12) | c3_1(a514)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[549, 543])).
% 1.88/1.48 tff(551,plain,
% 1.88/1.48 ((~hskp12) | c3_1(a514)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[550, 543])).
% 1.88/1.48 tff(552,plain,
% 1.88/1.48 ((~hskp12) | c3_1(a514)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[551, 543])).
% 1.88/1.48 tff(553,plain,
% 1.88/1.48 (c3_1(a514)),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[552, 536])).
% 1.88/1.48 tff(554,plain,
% 1.88/1.48 (((~hskp12) | c1_1(a514)) <=> ((~hskp12) | c1_1(a514))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(555,axiom,((~hskp12) | c1_1(a514)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.88/1.48 tff(556,plain,
% 1.88/1.48 ((~hskp12) | c1_1(a514)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[555, 554])).
% 1.88/1.48 tff(557,plain,
% 1.88/1.48 ((~hskp12) | c1_1(a514)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[556, 554])).
% 1.88/1.48 tff(558,plain,
% 1.88/1.48 ((~hskp12) | c1_1(a514)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[557, 554])).
% 1.88/1.48 tff(559,plain,
% 1.88/1.48 ((~hskp12) | c1_1(a514)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[558, 554])).
% 1.88/1.48 tff(560,plain,
% 1.88/1.48 ((~hskp12) | c1_1(a514)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[559, 554])).
% 1.88/1.48 tff(561,plain,
% 1.88/1.48 ((~hskp12) | c1_1(a514)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[560, 554])).
% 1.88/1.48 tff(562,plain,
% 1.88/1.48 ((~hskp12) | c1_1(a514)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[561, 554])).
% 1.88/1.48 tff(563,plain,
% 1.88/1.48 ((~hskp12) | c1_1(a514)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[562, 554])).
% 1.88/1.48 tff(564,plain,
% 1.88/1.48 (c1_1(a514)),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[563, 536])).
% 1.88/1.48 tff(565,plain,
% 1.88/1.48 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a568) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c3_1(a568)) | (~c2_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a568) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(566,plain,
% 1.88/1.48 ((hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a568) | (~c2_1(a568)) | (~c3_1(a568))) <=> (hskp20 | c1_1(a568) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(567,plain,
% 1.88/1.48 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a568) | (~c2_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a568) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c3_1(a568)) | (~c2_1(a568))))),
% 1.88/1.48 inference(monotonicity,[status(thm)],[566])).
% 1.88/1.48 tff(568,plain,
% 1.88/1.48 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a568) | (~c2_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a568) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c3_1(a568)) | (~c2_1(a568)))),
% 1.88/1.48 inference(transitivity,[status(thm)],[567, 565])).
% 1.88/1.48 tff(569,plain,
% 1.88/1.48 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a568) | (~c2_1(a568)) | (~c3_1(a568)))),
% 1.88/1.48 inference(quant_inst,[status(thm)],[])).
% 1.88/1.48 tff(570,plain,
% 1.88/1.48 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a568) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c3_1(a568)) | (~c2_1(a568))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[569, 568])).
% 1.88/1.48 tff(571,plain,
% 1.88/1.48 (hskp20),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[570, 112, 403, 564, 553, 402, 542, 521, 506])).
% 1.88/1.48 tff(572,plain,
% 1.88/1.48 (((~hskp20) | (~c1_1(a536))) <=> ((~hskp20) | (~c1_1(a536)))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(573,plain,
% 1.88/1.48 (((~c1_1(a536)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a536)))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(574,axiom,((~c1_1(a536)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 1.88/1.48 tff(575,plain,
% 1.88/1.48 ((~hskp20) | (~c1_1(a536))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[574, 573])).
% 1.88/1.48 tff(576,plain,
% 1.88/1.48 ((~hskp20) | (~c1_1(a536))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[575, 572])).
% 1.88/1.48 tff(577,plain,
% 1.88/1.48 (~c1_1(a536)),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[576, 571])).
% 1.88/1.48 tff(578,plain,
% 1.88/1.48 (((~hskp20) | (~c0_1(a536))) <=> ((~hskp20) | (~c0_1(a536)))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(579,plain,
% 1.88/1.48 (((~c0_1(a536)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a536)))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(580,axiom,((~c0_1(a536)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 1.88/1.48 tff(581,plain,
% 1.88/1.48 ((~hskp20) | (~c0_1(a536))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[580, 579])).
% 1.88/1.48 tff(582,plain,
% 1.88/1.48 ((~hskp20) | (~c0_1(a536))),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[581, 578])).
% 1.88/1.48 tff(583,plain,
% 1.88/1.48 (~c0_1(a536)),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[582, 571])).
% 1.88/1.48 tff(584,plain,
% 1.88/1.48 (c1_1(a504)),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[349, 508])).
% 1.88/1.48 tff(585,plain,
% 1.88/1.48 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c3_1(a536))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c3_1(a536))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(586,plain,
% 1.88/1.48 ((hskp2 | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c1_1(a536) | c0_1(a536) | c3_1(a536)) <=> (hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c3_1(a536))),
% 1.88/1.48 inference(rewrite,[status(thm)],[])).
% 1.88/1.48 tff(587,plain,
% 1.88/1.48 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c1_1(a536) | c0_1(a536) | c3_1(a536))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c3_1(a536)))),
% 1.88/1.48 inference(monotonicity,[status(thm)],[586])).
% 1.88/1.48 tff(588,plain,
% 1.88/1.48 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c1_1(a536) | c0_1(a536) | c3_1(a536))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c3_1(a536))),
% 1.88/1.48 inference(transitivity,[status(thm)],[587, 585])).
% 1.88/1.48 tff(589,plain,
% 1.88/1.48 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c1_1(a536) | c0_1(a536) | c3_1(a536))),
% 1.88/1.48 inference(quant_inst,[status(thm)],[])).
% 1.88/1.48 tff(590,plain,
% 1.88/1.48 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c2_1(a504)) | (~c1_1(a504)) | (~c0_1(a504)) | c3_1(a536)),
% 1.88/1.48 inference(modus_ponens,[status(thm)],[589, 588])).
% 1.88/1.48 tff(591,plain,
% 1.88/1.48 (c3_1(a536)),
% 1.88/1.48 inference(unit_resolution,[status(thm)],[590, 112, 453, 510, 584, 583, 577, 320, 511])).
% 1.88/1.48 tff(592,plain,
% 1.88/1.48 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.88/1.48 inference(bind,[status(th)],[])).
% 1.88/1.48 tff(593,plain,
% 1.88/1.48 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.88/1.49 inference(quant_intro,[status(thm)],[592])).
% 1.88/1.49 tff(594,plain,
% 1.88/1.49 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(595,plain,
% 1.88/1.49 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.88/1.49 inference(bind,[status(th)],[])).
% 1.88/1.49 tff(596,plain,
% 1.88/1.49 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.88/1.49 inference(quant_intro,[status(thm)],[595])).
% 1.88/1.49 tff(597,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 1.88/1.49 tff(598,plain,
% 1.88/1.49 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[597, 596])).
% 1.88/1.49 tff(599,plain,
% 1.88/1.49 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[598, 594])).
% 1.88/1.49 tff(600,plain,(
% 1.88/1.49 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.88/1.49 inference(skolemize,[status(sab)],[599])).
% 1.88/1.49 tff(601,plain,
% 1.88/1.49 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[600, 593])).
% 1.88/1.49 tff(602,plain,
% 1.88/1.49 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c0_1(a514)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c0_1(a514)))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(603,plain,
% 1.88/1.49 ((hskp2 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514))) <=> (hskp2 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c0_1(a514)))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(604,plain,
% 1.88/1.49 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c0_1(a514))))),
% 1.88/1.49 inference(monotonicity,[status(thm)],[603])).
% 1.88/1.49 tff(605,plain,
% 1.88/1.49 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c0_1(a514)))),
% 1.88/1.49 inference(transitivity,[status(thm)],[604, 602])).
% 1.88/1.49 tff(606,plain,
% 1.88/1.49 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)))),
% 1.88/1.49 inference(quant_inst,[status(thm)],[])).
% 1.88/1.49 tff(607,plain,
% 1.88/1.49 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | (~c0_1(a514))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[606, 605])).
% 1.88/1.49 tff(608,plain,
% 1.88/1.49 (~c0_1(a514)),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[607, 112, 453, 564, 553, 542, 601])).
% 1.88/1.49 tff(609,plain,
% 1.88/1.49 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.88/1.49 inference(bind,[status(th)],[])).
% 1.88/1.49 tff(610,plain,
% 1.88/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.88/1.49 inference(quant_intro,[status(thm)],[609])).
% 1.88/1.49 tff(611,plain,
% 1.88/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(612,plain,
% 1.88/1.49 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.88/1.49 inference(bind,[status(th)],[])).
% 1.88/1.49 tff(613,plain,
% 1.88/1.49 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.88/1.49 inference(quant_intro,[status(thm)],[612])).
% 1.88/1.49 tff(614,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 1.88/1.49 tff(615,plain,
% 1.88/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[614, 613])).
% 1.88/1.49 tff(616,plain,
% 1.88/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[615, 611])).
% 1.88/1.49 tff(617,plain,(
% 1.88/1.49 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.88/1.49 inference(skolemize,[status(sab)],[616])).
% 1.88/1.49 tff(618,plain,
% 1.88/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[617, 610])).
% 1.88/1.49 tff(619,plain,
% 1.88/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a536) | c1_1(a536) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | (~c3_1(a536)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a536) | c1_1(a536) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | (~c3_1(a536)))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(620,plain,
% 1.88/1.49 (((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a514) | c0_1(a514) | (~c1_1(a514)) | c1_1(a536) | c0_1(a536) | (~c3_1(a536))) <=> (c0_1(a536) | c1_1(a536) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | (~c3_1(a536)))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(621,plain,
% 1.88/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a514) | c0_1(a514) | (~c1_1(a514)) | c1_1(a536) | c0_1(a536) | (~c3_1(a536)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a536) | c1_1(a536) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | (~c3_1(a536))))),
% 1.88/1.49 inference(monotonicity,[status(thm)],[620])).
% 1.88/1.49 tff(622,plain,
% 1.88/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a514) | c0_1(a514) | (~c1_1(a514)) | c1_1(a536) | c0_1(a536) | (~c3_1(a536)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a536) | c1_1(a536) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | (~c3_1(a536)))),
% 1.88/1.49 inference(transitivity,[status(thm)],[621, 619])).
% 1.88/1.49 tff(623,plain,
% 1.88/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a514) | c0_1(a514) | (~c1_1(a514)) | c1_1(a536) | c0_1(a536) | (~c3_1(a536)))),
% 1.88/1.49 inference(quant_inst,[status(thm)],[])).
% 1.88/1.49 tff(624,plain,
% 1.88/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a536) | c1_1(a536) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | (~c3_1(a536))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[623, 622])).
% 1.88/1.49 tff(625,plain,
% 1.88/1.49 ($false),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[624, 112, 564, 553, 583, 577, 542, 618, 608, 591])).
% 1.88/1.49 tff(626,plain,(hskp2 | hskp10 | (~c3_1(a568)) | c1_1(a568) | (~c0_1(a568)) | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.88/1.49 tff(627,plain,
% 1.88/1.49 (hskp2),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[626, 404, 403, 402, 401, 11])).
% 1.88/1.49 tff(628,plain,
% 1.88/1.49 (~c2_1(a496)),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[368, 627])).
% 1.88/1.49 tff(629,plain,
% 1.88/1.49 (~c1_1(a496)),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[381, 627])).
% 1.88/1.49 tff(630,plain,
% 1.88/1.49 (~c3_1(a496)),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[362, 627])).
% 1.88/1.49 tff(631,assumption,(~hskp1), introduced(assumption)).
% 1.88/1.49 tff(632,assumption,(~c1_1(a496)), introduced(assumption)).
% 1.88/1.49 tff(633,assumption,(~c3_1(a496)), introduced(assumption)).
% 1.88/1.49 tff(634,assumption,(~c2_1(a496)), introduced(assumption)).
% 1.88/1.49 tff(635,assumption,(~c0_1(a496)), introduced(assumption)).
% 1.88/1.49 tff(636,plain,
% 1.88/1.49 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 1.88/1.49 inference(bind,[status(th)],[])).
% 1.88/1.49 tff(637,plain,
% 1.88/1.49 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.88/1.49 inference(quant_intro,[status(thm)],[636])).
% 1.88/1.49 tff(638,plain,
% 1.88/1.49 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(639,plain,
% 1.88/1.49 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 1.88/1.49 inference(bind,[status(th)],[])).
% 1.88/1.49 tff(640,plain,
% 1.88/1.49 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.88/1.49 inference(quant_intro,[status(thm)],[639])).
% 1.88/1.49 tff(641,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 1.88/1.49 tff(642,plain,
% 1.88/1.49 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[641, 640])).
% 1.88/1.49 tff(643,plain,
% 1.88/1.49 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[642, 638])).
% 1.88/1.49 tff(644,plain,(
% 1.88/1.49 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.88/1.49 inference(skolemize,[status(sab)],[643])).
% 1.88/1.49 tff(645,plain,
% 1.88/1.49 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[644, 637])).
% 1.88/1.49 tff(646,assumption,(hskp6), introduced(assumption)).
% 1.88/1.49 tff(647,plain,
% 1.88/1.49 (((~hskp6) | (~c3_1(a501))) <=> ((~hskp6) | (~c3_1(a501)))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(648,plain,
% 1.88/1.49 (((~c3_1(a501)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a501)))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(649,axiom,((~c3_1(a501)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.88/1.49 tff(650,plain,
% 1.88/1.49 ((~hskp6) | (~c3_1(a501))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[649, 648])).
% 1.88/1.49 tff(651,plain,
% 1.88/1.49 ((~hskp6) | (~c3_1(a501))),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[650, 647])).
% 1.88/1.49 tff(652,plain,
% 1.88/1.49 (~c3_1(a501)),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[651, 646])).
% 1.88/1.49 tff(653,plain,
% 1.88/1.49 (((~hskp6) | c2_1(a501)) <=> ((~hskp6) | c2_1(a501))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(654,axiom,((~hskp6) | c2_1(a501)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 1.88/1.49 tff(655,plain,
% 1.88/1.49 ((~hskp6) | c2_1(a501)),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[654, 653])).
% 1.88/1.49 tff(656,plain,
% 1.88/1.49 ((~hskp6) | c2_1(a501)),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[655, 653])).
% 1.88/1.49 tff(657,plain,
% 1.88/1.49 ((~hskp6) | c2_1(a501)),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[656, 653])).
% 1.88/1.49 tff(658,plain,
% 1.88/1.49 ((~hskp6) | c2_1(a501)),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[657, 653])).
% 1.88/1.49 tff(659,plain,
% 1.88/1.49 ((~hskp6) | c2_1(a501)),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[658, 653])).
% 1.88/1.49 tff(660,plain,
% 1.88/1.49 ((~hskp6) | c2_1(a501)),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[659, 653])).
% 1.88/1.49 tff(661,plain,
% 1.88/1.49 ((~hskp6) | c2_1(a501)),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[660, 653])).
% 1.88/1.49 tff(662,plain,
% 1.88/1.49 ((~hskp6) | c2_1(a501)),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[661, 653])).
% 1.88/1.49 tff(663,plain,
% 1.88/1.49 (c2_1(a501)),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[662, 646])).
% 1.88/1.49 tff(664,plain,
% 1.88/1.49 (((~hskp6) | c1_1(a501)) <=> ((~hskp6) | c1_1(a501))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(665,axiom,((~hskp6) | c1_1(a501)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 1.88/1.49 tff(666,plain,
% 1.88/1.49 ((~hskp6) | c1_1(a501)),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[665, 664])).
% 1.88/1.49 tff(667,plain,
% 1.88/1.49 ((~hskp6) | c1_1(a501)),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[666, 664])).
% 1.88/1.49 tff(668,plain,
% 1.88/1.49 ((~hskp6) | c1_1(a501)),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[667, 664])).
% 1.88/1.49 tff(669,plain,
% 1.88/1.49 ((~hskp6) | c1_1(a501)),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[668, 664])).
% 1.88/1.49 tff(670,plain,
% 1.88/1.49 ((~hskp6) | c1_1(a501)),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[669, 664])).
% 1.88/1.49 tff(671,plain,
% 1.88/1.49 ((~hskp6) | c1_1(a501)),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[670, 664])).
% 1.88/1.49 tff(672,plain,
% 1.88/1.49 ((~hskp6) | c1_1(a501)),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[671, 664])).
% 1.88/1.49 tff(673,plain,
% 1.88/1.49 ((~hskp6) | c1_1(a501)),
% 1.88/1.49 inference(modus_ponens,[status(thm)],[672, 664])).
% 1.88/1.49 tff(674,plain,
% 1.88/1.49 (c1_1(a501)),
% 1.88/1.49 inference(unit_resolution,[status(thm)],[673, 646])).
% 1.88/1.49 tff(675,assumption,(~c3_1(a501)), introduced(assumption)).
% 1.88/1.49 tff(676,assumption,(c1_1(a501)), introduced(assumption)).
% 1.88/1.49 tff(677,plain,
% 1.88/1.49 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c3_1(a501) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a501)) | (~c0_1(a501)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c3_1(a501) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a501)) | (~c0_1(a501)))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(678,plain,
% 1.88/1.49 ((hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a501) | (~c1_1(a501)) | (~c0_1(a501))) <=> (hskp2 | c3_1(a501) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a501)) | (~c0_1(a501)))),
% 1.88/1.49 inference(rewrite,[status(thm)],[])).
% 1.88/1.49 tff(679,plain,
% 1.88/1.49 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a501) | (~c1_1(a501)) | (~c0_1(a501)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c3_1(a501) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a501)) | (~c0_1(a501))))),
% 1.88/1.49 inference(monotonicity,[status(thm)],[678])).
% 1.88/1.49 tff(680,plain,
% 1.88/1.49 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a501) | (~c1_1(a501)) | (~c0_1(a501)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c3_1(a501) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a501)) | (~c0_1(a501)))),
% 1.88/1.50 inference(transitivity,[status(thm)],[679, 677])).
% 1.88/1.50 tff(681,plain,
% 1.88/1.50 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a501) | (~c1_1(a501)) | (~c0_1(a501)))),
% 1.88/1.50 inference(quant_inst,[status(thm)],[])).
% 1.88/1.50 tff(682,plain,
% 1.88/1.50 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c3_1(a501) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a501)) | (~c0_1(a501))),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[681, 680])).
% 1.88/1.50 tff(683,plain,
% 1.88/1.50 (hskp2 | (~c0_1(a501))),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[682, 112, 495, 494, 493, 676, 675, 463])).
% 1.88/1.50 tff(684,plain,
% 1.88/1.50 (~c0_1(a501)),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[683, 453])).
% 1.88/1.50 tff(685,plain,
% 1.88/1.50 (^[U: $i] : refl((hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))),
% 1.88/1.50 inference(bind,[status(th)],[])).
% 1.88/1.50 tff(686,plain,
% 1.88/1.50 (![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.88/1.50 inference(quant_intro,[status(thm)],[685])).
% 1.88/1.50 tff(687,plain,
% 1.88/1.50 (![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.88/1.50 inference(rewrite,[status(thm)],[])).
% 1.88/1.50 tff(688,plain,
% 1.88/1.50 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) | hskp7) <=> ((hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp7))), rewrite(((hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp7) <=> (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) | hskp7) <=> (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))))),
% 1.88/1.50 inference(bind,[status(th)],[])).
% 1.88/1.50 tff(689,plain,
% 1.88/1.50 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) | hskp7) <=> ![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.88/1.50 inference(quant_intro,[status(thm)],[688])).
% 1.88/1.50 tff(690,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp1) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 1.88/1.50 tff(691,plain,
% 1.88/1.50 (![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[690, 689])).
% 1.88/1.50 tff(692,plain,
% 1.88/1.50 (![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[691, 687])).
% 1.88/1.50 tff(693,plain,(
% 1.88/1.50 ![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.88/1.50 inference(skolemize,[status(sab)],[692])).
% 1.88/1.50 tff(694,plain,
% 1.88/1.50 (![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[693, 686])).
% 1.88/1.50 tff(695,plain,
% 1.88/1.50 (((~![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp7 | hskp1 | c3_1(a501) | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501))) <=> ((~![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp7 | hskp1 | c3_1(a501) | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501))),
% 1.88/1.50 inference(rewrite,[status(thm)],[])).
% 1.88/1.50 tff(696,plain,
% 1.88/1.50 ((hskp7 | hskp1 | (~ndr1_0) | c3_1(a501) | c0_1(a501) | (~c1_1(a501))) <=> (hskp7 | hskp1 | c3_1(a501) | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501))),
% 1.88/1.50 inference(rewrite,[status(thm)],[])).
% 1.88/1.50 tff(697,plain,
% 1.88/1.50 (((~![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp7 | hskp1 | (~ndr1_0) | c3_1(a501) | c0_1(a501) | (~c1_1(a501)))) <=> ((~![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp7 | hskp1 | c3_1(a501) | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501)))),
% 1.88/1.50 inference(monotonicity,[status(thm)],[696])).
% 1.88/1.50 tff(698,plain,
% 1.88/1.50 (((~![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp7 | hskp1 | (~ndr1_0) | c3_1(a501) | c0_1(a501) | (~c1_1(a501)))) <=> ((~![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp7 | hskp1 | c3_1(a501) | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501))),
% 1.88/1.50 inference(transitivity,[status(thm)],[697, 695])).
% 1.88/1.50 tff(699,plain,
% 1.88/1.50 ((~![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp7 | hskp1 | (~ndr1_0) | c3_1(a501) | c0_1(a501) | (~c1_1(a501)))),
% 1.88/1.50 inference(quant_inst,[status(thm)],[])).
% 1.88/1.50 tff(700,plain,
% 1.88/1.50 ((~![U: $i] : (hskp7 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp7 | hskp1 | c3_1(a501) | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[699, 698])).
% 1.88/1.50 tff(701,plain,
% 1.88/1.50 (hskp7 | c0_1(a501)),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[700, 112, 631, 676, 675, 694])).
% 1.88/1.50 tff(702,plain,
% 1.88/1.50 (hskp7),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[701, 684])).
% 1.88/1.50 tff(703,plain,
% 1.88/1.50 (~c3_1(a502)),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[332, 702])).
% 1.88/1.50 tff(704,plain,
% 1.88/1.50 (~c1_1(a502)),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[338, 702])).
% 1.88/1.50 tff(705,plain,
% 1.88/1.50 (((~hskp7) | (~c0_1(a502))) <=> ((~hskp7) | (~c0_1(a502)))),
% 1.88/1.50 inference(rewrite,[status(thm)],[])).
% 1.88/1.50 tff(706,plain,
% 1.88/1.50 (((~c0_1(a502)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a502)))),
% 1.88/1.50 inference(rewrite,[status(thm)],[])).
% 1.88/1.50 tff(707,axiom,((~c0_1(a502)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 1.88/1.50 tff(708,plain,
% 1.88/1.50 ((~hskp7) | (~c0_1(a502))),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[707, 706])).
% 1.88/1.50 tff(709,plain,
% 1.88/1.50 ((~hskp7) | (~c0_1(a502))),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[708, 705])).
% 1.88/1.50 tff(710,plain,
% 1.88/1.50 (~c0_1(a502)),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[709, 702])).
% 1.88/1.50 tff(711,plain,
% 1.88/1.50 (^[U: $i] : refl((hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.88/1.50 inference(bind,[status(th)],[])).
% 1.88/1.50 tff(712,plain,
% 1.88/1.50 (![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.88/1.50 inference(quant_intro,[status(thm)],[711])).
% 1.88/1.50 tff(713,plain,
% 1.88/1.50 (![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.88/1.50 inference(rewrite,[status(thm)],[])).
% 1.88/1.50 tff(714,plain,
% 1.88/1.50 (^[U: $i] : 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)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp31) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp31))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp31) <=> (hskp31 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp31) <=> (hskp31 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp31) | hskp1) <=> ((hskp31 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp1))), rewrite(((hskp31 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp1) <=> (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp31) | hskp1) <=> (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.88/1.50 inference(bind,[status(th)],[])).
% 1.88/1.50 tff(715,plain,
% 1.88/1.50 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp31) | hskp1) <=> ![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.88/1.50 inference(quant_intro,[status(thm)],[714])).
% 1.88/1.50 tff(716,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp31) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 1.88/1.50 tff(717,plain,
% 1.88/1.50 (![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[716, 715])).
% 1.88/1.50 tff(718,plain,
% 1.88/1.50 (![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[717, 713])).
% 1.88/1.50 tff(719,plain,(
% 1.88/1.50 ![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.88/1.50 inference(skolemize,[status(sab)],[718])).
% 1.88/1.50 tff(720,plain,
% 1.88/1.50 (![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[719, 712])).
% 1.88/1.50 tff(721,assumption,(c2_1(a501)), introduced(assumption)).
% 1.88/1.50 tff(722,plain,
% 1.88/1.50 (((~![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp31 | hskp1 | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501) | (~c2_1(a501)))) <=> ((~![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp31 | hskp1 | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501) | (~c2_1(a501)))),
% 1.88/1.50 inference(rewrite,[status(thm)],[])).
% 1.88/1.50 tff(723,plain,
% 1.88/1.50 ((hskp31 | hskp1 | (~ndr1_0) | c0_1(a501) | (~c2_1(a501)) | (~c1_1(a501))) <=> (hskp31 | hskp1 | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501) | (~c2_1(a501)))),
% 1.88/1.50 inference(rewrite,[status(thm)],[])).
% 1.88/1.50 tff(724,plain,
% 1.88/1.50 (((~![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp31 | hskp1 | (~ndr1_0) | c0_1(a501) | (~c2_1(a501)) | (~c1_1(a501)))) <=> ((~![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp31 | hskp1 | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501) | (~c2_1(a501))))),
% 1.88/1.50 inference(monotonicity,[status(thm)],[723])).
% 1.88/1.50 tff(725,plain,
% 1.88/1.50 (((~![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp31 | hskp1 | (~ndr1_0) | c0_1(a501) | (~c2_1(a501)) | (~c1_1(a501)))) <=> ((~![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp31 | hskp1 | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501) | (~c2_1(a501)))),
% 1.88/1.50 inference(transitivity,[status(thm)],[724, 722])).
% 1.88/1.50 tff(726,plain,
% 1.88/1.50 ((~![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp31 | hskp1 | (~ndr1_0) | c0_1(a501) | (~c2_1(a501)) | (~c1_1(a501)))),
% 1.88/1.50 inference(quant_inst,[status(thm)],[])).
% 1.88/1.50 tff(727,plain,
% 1.88/1.50 ((~![U: $i] : (hskp31 | hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp31 | hskp1 | (~ndr1_0) | (~c1_1(a501)) | c0_1(a501) | (~c2_1(a501))),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[726, 725])).
% 1.88/1.50 tff(728,plain,
% 1.88/1.50 (hskp31 | c0_1(a501)),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[727, 112, 631, 676, 721, 720])).
% 1.88/1.50 tff(729,plain,
% 1.88/1.50 (hskp31),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[728, 684])).
% 1.88/1.50 tff(730,plain,
% 1.88/1.50 (((~hskp31) | c2_1(a522)) <=> ((~hskp31) | c2_1(a522))),
% 1.88/1.50 inference(rewrite,[status(thm)],[])).
% 1.88/1.50 tff(731,axiom,((~hskp31) | c2_1(a522)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 1.88/1.50 tff(732,plain,
% 1.88/1.50 ((~hskp31) | c2_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[731, 730])).
% 1.88/1.50 tff(733,plain,
% 1.88/1.50 ((~hskp31) | c2_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[732, 730])).
% 1.88/1.50 tff(734,plain,
% 1.88/1.50 ((~hskp31) | c2_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[733, 730])).
% 1.88/1.50 tff(735,plain,
% 1.88/1.50 ((~hskp31) | c2_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[734, 730])).
% 1.88/1.50 tff(736,plain,
% 1.88/1.50 ((~hskp31) | c2_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[735, 730])).
% 1.88/1.50 tff(737,plain,
% 1.88/1.50 ((~hskp31) | c2_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[736, 730])).
% 1.88/1.50 tff(738,plain,
% 1.88/1.50 ((~hskp31) | c2_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[737, 730])).
% 1.88/1.50 tff(739,plain,
% 1.88/1.50 ((~hskp31) | c2_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[738, 730])).
% 1.88/1.50 tff(740,plain,
% 1.88/1.50 (c2_1(a522)),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[739, 729])).
% 1.88/1.50 tff(741,plain,
% 1.88/1.50 (((~hskp31) | c1_1(a522)) <=> ((~hskp31) | c1_1(a522))),
% 1.88/1.50 inference(rewrite,[status(thm)],[])).
% 1.88/1.50 tff(742,axiom,((~hskp31) | c1_1(a522)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 1.88/1.50 tff(743,plain,
% 1.88/1.50 ((~hskp31) | c1_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[742, 741])).
% 1.88/1.50 tff(744,plain,
% 1.88/1.50 ((~hskp31) | c1_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[743, 741])).
% 1.88/1.50 tff(745,plain,
% 1.88/1.50 ((~hskp31) | c1_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[744, 741])).
% 1.88/1.50 tff(746,plain,
% 1.88/1.50 ((~hskp31) | c1_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[745, 741])).
% 1.88/1.50 tff(747,plain,
% 1.88/1.50 ((~hskp31) | c1_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[746, 741])).
% 1.88/1.50 tff(748,plain,
% 1.88/1.50 ((~hskp31) | c1_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[747, 741])).
% 1.88/1.50 tff(749,plain,
% 1.88/1.50 ((~hskp31) | c1_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[748, 741])).
% 1.88/1.50 tff(750,plain,
% 1.88/1.50 ((~hskp31) | c1_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[749, 741])).
% 1.88/1.50 tff(751,plain,
% 1.88/1.50 (c1_1(a522)),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[750, 729])).
% 1.88/1.50 tff(752,plain,
% 1.88/1.50 (((~hskp31) | c0_1(a522)) <=> ((~hskp31) | c0_1(a522))),
% 1.88/1.50 inference(rewrite,[status(thm)],[])).
% 1.88/1.50 tff(753,axiom,((~hskp31) | c0_1(a522)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 1.88/1.50 tff(754,plain,
% 1.88/1.50 ((~hskp31) | c0_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[753, 752])).
% 1.88/1.50 tff(755,plain,
% 1.88/1.50 ((~hskp31) | c0_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[754, 752])).
% 1.88/1.50 tff(756,plain,
% 1.88/1.50 ((~hskp31) | c0_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[755, 752])).
% 1.88/1.50 tff(757,plain,
% 1.88/1.50 ((~hskp31) | c0_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[756, 752])).
% 1.88/1.50 tff(758,plain,
% 1.88/1.50 ((~hskp31) | c0_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[757, 752])).
% 1.88/1.50 tff(759,plain,
% 1.88/1.50 ((~hskp31) | c0_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[758, 752])).
% 1.88/1.50 tff(760,plain,
% 1.88/1.50 ((~hskp31) | c0_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[759, 752])).
% 1.88/1.50 tff(761,plain,
% 1.88/1.50 ((~hskp31) | c0_1(a522)),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[760, 752])).
% 1.88/1.50 tff(762,plain,
% 1.88/1.50 (c0_1(a522)),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[761, 729])).
% 1.88/1.50 tff(763,plain,
% 1.88/1.50 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)))),
% 1.88/1.50 inference(rewrite,[status(thm)],[])).
% 1.88/1.50 tff(764,plain,
% 1.88/1.50 ((hskp2 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c1_1(a502) | c0_1(a502) | c3_1(a502)) <=> (hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)))),
% 1.88/1.50 inference(rewrite,[status(thm)],[])).
% 1.88/1.50 tff(765,plain,
% 1.88/1.50 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522))))),
% 1.88/1.50 inference(monotonicity,[status(thm)],[764])).
% 1.88/1.50 tff(766,plain,
% 1.88/1.50 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)))),
% 1.88/1.50 inference(transitivity,[status(thm)],[765, 763])).
% 1.88/1.50 tff(767,plain,
% 1.88/1.50 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c1_1(a502) | c0_1(a502) | c3_1(a502))),
% 1.88/1.50 inference(quant_inst,[status(thm)],[])).
% 1.88/1.50 tff(768,plain,
% 1.88/1.50 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522))),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[767, 766])).
% 1.88/1.50 tff(769,plain,
% 1.88/1.50 ($false),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[768, 112, 453, 762, 751, 740, 710, 704, 703, 320])).
% 1.88/1.50 tff(770,plain,(hskp2 | hskp1 | (~c1_1(a501)) | c3_1(a501) | (~c2_1(a501)) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500))), inference(lemma,lemma(discharge,[]))).
% 1.88/1.50 tff(771,plain,
% 1.88/1.50 (hskp2),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[770, 674, 631, 652, 663, 495, 494, 493])).
% 1.88/1.50 tff(772,plain,
% 1.88/1.50 (~c1_1(a496)),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[381, 771])).
% 1.88/1.50 tff(773,plain,
% 1.88/1.50 (~c2_1(a496)),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[368, 771])).
% 1.88/1.50 tff(774,plain,
% 1.88/1.50 (~c3_1(a496)),
% 1.88/1.50 inference(unit_resolution,[status(thm)],[362, 771])).
% 1.88/1.50 tff(775,plain,
% 1.88/1.50 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.88/1.50 inference(bind,[status(th)],[])).
% 1.88/1.50 tff(776,plain,
% 1.88/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_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) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.88/1.50 inference(quant_intro,[status(thm)],[775])).
% 1.88/1.50 tff(777,plain,
% 1.88/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_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) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.88/1.50 inference(rewrite,[status(thm)],[])).
% 1.88/1.50 tff(778,plain,
% 1.88/1.50 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | 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)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.88/1.50 inference(bind,[status(th)],[])).
% 1.88/1.50 tff(779,plain,
% 1.88/1.50 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.88/1.50 inference(quant_intro,[status(thm)],[778])).
% 1.88/1.50 tff(780,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 1.88/1.50 tff(781,plain,
% 1.88/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[780, 779])).
% 1.88/1.50 tff(782,plain,
% 1.88/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.88/1.50 inference(modus_ponens,[status(thm)],[781, 777])).
% 1.93/1.51 tff(783,plain,(
% 1.93/1.51 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.93/1.51 inference(skolemize,[status(sab)],[782])).
% 1.93/1.51 tff(784,plain,
% 1.93/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[783, 776])).
% 1.93/1.51 tff(785,plain,
% 1.93/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a501) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a501) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(786,plain,
% 1.93/1.51 (((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496)) <=> (c3_1(a501) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(787,plain,
% 1.93/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a501) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501))))),
% 1.93/1.51 inference(monotonicity,[status(thm)],[786])).
% 1.93/1.51 tff(788,plain,
% 1.93/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a501) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))),
% 1.93/1.51 inference(transitivity,[status(thm)],[787, 785])).
% 1.93/1.51 tff(789,plain,
% 1.93/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496))),
% 1.93/1.51 inference(quant_inst,[status(thm)],[])).
% 1.93/1.51 tff(790,plain,
% 1.93/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a501) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501))),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[789, 788])).
% 1.93/1.51 tff(791,plain,
% 1.93/1.51 (c0_1(a496)),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[790, 112, 676, 721, 675, 632, 634, 633, 784])).
% 1.93/1.51 tff(792,plain,
% 1.93/1.51 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(793,plain,
% 1.93/1.51 ((hskp22 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | (~c0_1(a496)) | c1_1(a496) | c3_1(a496) | (~c0_1(a496))) <=> (hskp22 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(794,plain,
% 1.93/1.51 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | (~c0_1(a496)) | c1_1(a496) | c3_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496))))),
% 1.93/1.51 inference(monotonicity,[status(thm)],[793])).
% 1.93/1.51 tff(795,plain,
% 1.93/1.51 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | (~c0_1(a496)) | c1_1(a496) | c3_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))),
% 1.93/1.51 inference(transitivity,[status(thm)],[794, 792])).
% 1.93/1.51 tff(796,plain,
% 1.93/1.51 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | (~c0_1(a496)) | c1_1(a496) | c3_1(a496) | (~c0_1(a496)))),
% 1.93/1.51 inference(quant_inst,[status(thm)],[])).
% 1.93/1.51 tff(797,plain,
% 1.93/1.51 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496))),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[796, 795])).
% 1.93/1.51 tff(798,plain,
% 1.93/1.51 (hskp22),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[797, 112, 632, 634, 633, 31, 791])).
% 1.93/1.51 tff(799,plain,
% 1.93/1.51 (~c0_1(a540)),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[131, 798])).
% 1.93/1.51 tff(800,plain,
% 1.93/1.51 (c3_1(a540)),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[142, 798])).
% 1.93/1.51 tff(801,plain,
% 1.93/1.51 (c1_1(a540)),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[153, 798])).
% 1.93/1.51 tff(802,plain,
% 1.93/1.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(803,plain,
% 1.93/1.51 ((hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a540))) <=> (hskp10 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(804,plain,
% 1.93/1.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540))))),
% 1.93/1.51 inference(monotonicity,[status(thm)],[803])).
% 1.93/1.51 tff(805,plain,
% 1.93/1.51 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.93/1.51 inference(transitivity,[status(thm)],[804, 802])).
% 1.93/1.51 tff(806,plain,
% 1.93/1.51 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a540)))),
% 1.93/1.51 inference(quant_inst,[status(thm)],[])).
% 1.93/1.51 tff(807,plain,
% 1.93/1.51 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540))),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[806, 805])).
% 1.93/1.51 tff(808,plain,
% 1.93/1.51 ($false),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[807, 112, 11, 801, 800, 799, 632, 634, 53, 791])).
% 1.93/1.51 tff(809,plain,(c3_1(a496) | hskp10 | c1_1(a496) | c2_1(a496) | (~c1_1(a501)) | (~c2_1(a501)) | c3_1(a501)), inference(lemma,lemma(discharge,[]))).
% 1.93/1.51 tff(810,plain,
% 1.93/1.51 ($false),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[809, 774, 773, 772, 11, 674, 663, 652])).
% 1.93/1.51 tff(811,plain,((~hskp6) | hskp10 | hskp1 | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500))), inference(lemma,lemma(discharge,[]))).
% 1.93/1.51 tff(812,plain,
% 1.93/1.51 (~hskp6),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[811, 631, 11, 452, 441, 430])).
% 1.93/1.51 tff(813,plain,
% 1.93/1.51 ((hskp14 | hskp13 | hskp6) <=> (hskp14 | hskp13 | hskp6)),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(814,plain,
% 1.93/1.51 (((hskp13 | hskp6) | hskp14) <=> (hskp14 | hskp13 | hskp6)),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(815,axiom,((hskp13 | hskp6) | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 1.93/1.51 tff(816,plain,
% 1.93/1.51 (hskp14 | hskp13 | hskp6),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[815, 814])).
% 1.93/1.51 tff(817,plain,
% 1.93/1.51 (hskp14 | hskp13 | hskp6),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[816, 813])).
% 1.93/1.51 tff(818,plain,
% 1.93/1.51 (hskp14 | hskp13 | hskp6),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[817, 813])).
% 1.93/1.51 tff(819,plain,
% 1.93/1.51 (hskp14 | hskp13 | hskp6),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[818, 813])).
% 1.93/1.51 tff(820,plain,
% 1.93/1.51 (hskp14 | hskp13 | hskp6),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[819, 813])).
% 1.93/1.51 tff(821,plain,
% 1.93/1.51 (hskp14 | hskp13 | hskp6),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[820, 813])).
% 1.93/1.51 tff(822,plain,
% 1.93/1.51 (hskp14 | hskp13 | hskp6),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[821, 813])).
% 1.93/1.51 tff(823,plain,
% 1.93/1.51 (hskp14 | hskp13 | hskp6),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[822, 813])).
% 1.93/1.51 tff(824,plain,
% 1.93/1.51 (hskp14),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[823, 812, 404])).
% 1.93/1.51 tff(825,plain,
% 1.93/1.51 (((~hskp14) | (~c3_1(a527))) <=> ((~hskp14) | (~c3_1(a527)))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(826,plain,
% 1.93/1.51 (((~c3_1(a527)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a527)))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(827,axiom,((~c3_1(a527)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 1.93/1.51 tff(828,plain,
% 1.93/1.51 ((~hskp14) | (~c3_1(a527))),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[827, 826])).
% 1.93/1.51 tff(829,plain,
% 1.93/1.51 ((~hskp14) | (~c3_1(a527))),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[828, 825])).
% 1.93/1.51 tff(830,plain,
% 1.93/1.51 (~c3_1(a527)),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[829, 824])).
% 1.93/1.51 tff(831,plain,
% 1.93/1.51 (((~hskp14) | (~c1_1(a527))) <=> ((~hskp14) | (~c1_1(a527)))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(832,plain,
% 1.93/1.51 (((~c1_1(a527)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a527)))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(833,axiom,((~c1_1(a527)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 1.93/1.51 tff(834,plain,
% 1.93/1.51 ((~hskp14) | (~c1_1(a527))),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[833, 832])).
% 1.93/1.51 tff(835,plain,
% 1.93/1.51 ((~hskp14) | (~c1_1(a527))),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[834, 831])).
% 1.93/1.51 tff(836,plain,
% 1.93/1.51 (~c1_1(a527)),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[835, 824])).
% 1.93/1.51 tff(837,plain,
% 1.93/1.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c0_1(a527)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c0_1(a527)))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(838,plain,
% 1.93/1.51 ((hskp1 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c0_1(a527)) | c1_1(a496) | c0_1(a496) | c3_1(a496)) <=> (hskp1 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c0_1(a527)))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(839,plain,
% 1.93/1.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c0_1(a527)) | c1_1(a496) | c0_1(a496) | c3_1(a496))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c0_1(a527))))),
% 1.93/1.51 inference(monotonicity,[status(thm)],[838])).
% 1.93/1.51 tff(840,plain,
% 1.93/1.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c0_1(a527)) | c1_1(a496) | c0_1(a496) | c3_1(a496))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c0_1(a527)))),
% 1.93/1.51 inference(transitivity,[status(thm)],[839, 837])).
% 1.93/1.51 tff(841,plain,
% 1.93/1.51 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c0_1(a527)) | c1_1(a496) | c0_1(a496) | c3_1(a496))),
% 1.93/1.51 inference(quant_inst,[status(thm)],[])).
% 1.93/1.51 tff(842,plain,
% 1.93/1.51 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c0_1(a527))),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[841, 840])).
% 1.93/1.51 tff(843,plain,
% 1.93/1.51 (c3_1(a496) | c0_1(a496) | (~c0_1(a527))),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[842, 112, 631, 836, 830, 632, 645])).
% 1.93/1.51 tff(844,plain,
% 1.93/1.51 (~c0_1(a527)),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[843, 635, 633])).
% 1.93/1.51 tff(845,plain,
% 1.93/1.51 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.93/1.51 inference(bind,[status(th)],[])).
% 1.93/1.51 tff(846,plain,
% 1.93/1.51 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.93/1.51 inference(quant_intro,[status(thm)],[845])).
% 1.93/1.51 tff(847,plain,
% 1.93/1.51 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(848,plain,
% 1.93/1.51 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.93/1.51 inference(bind,[status(th)],[])).
% 1.93/1.51 tff(849,plain,
% 1.93/1.51 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.93/1.51 inference(quant_intro,[status(thm)],[848])).
% 1.93/1.51 tff(850,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 1.93/1.51 tff(851,plain,
% 1.93/1.51 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[850, 849])).
% 1.93/1.51 tff(852,plain,
% 1.93/1.51 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[851, 847])).
% 1.93/1.51 tff(853,plain,(
% 1.93/1.51 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.93/1.51 inference(skolemize,[status(sab)],[852])).
% 1.93/1.51 tff(854,plain,
% 1.93/1.51 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[853, 846])).
% 1.93/1.51 tff(855,plain,
% 1.93/1.51 (((~hskp14) | c2_1(a527)) <=> ((~hskp14) | c2_1(a527))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(856,axiom,((~hskp14) | c2_1(a527)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 1.93/1.51 tff(857,plain,
% 1.93/1.51 ((~hskp14) | c2_1(a527)),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[856, 855])).
% 1.93/1.51 tff(858,plain,
% 1.93/1.51 ((~hskp14) | c2_1(a527)),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[857, 855])).
% 1.93/1.51 tff(859,plain,
% 1.93/1.51 ((~hskp14) | c2_1(a527)),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[858, 855])).
% 1.93/1.51 tff(860,plain,
% 1.93/1.51 ((~hskp14) | c2_1(a527)),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[859, 855])).
% 1.93/1.51 tff(861,plain,
% 1.93/1.51 ((~hskp14) | c2_1(a527)),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[860, 855])).
% 1.93/1.51 tff(862,plain,
% 1.93/1.51 ((~hskp14) | c2_1(a527)),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[861, 855])).
% 1.93/1.51 tff(863,plain,
% 1.93/1.51 ((~hskp14) | c2_1(a527)),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[862, 855])).
% 1.93/1.51 tff(864,plain,
% 1.93/1.51 ((~hskp14) | c2_1(a527)),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[863, 855])).
% 1.93/1.51 tff(865,plain,
% 1.93/1.51 (c2_1(a527)),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[864, 824])).
% 1.93/1.51 tff(866,plain,
% 1.93/1.51 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c2_1(a527)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c2_1(a527)))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(867,plain,
% 1.93/1.51 ((hskp0 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c2_1(a527)) | c2_1(a496) | c1_1(a496) | c0_1(a496)) <=> (hskp0 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c2_1(a527)))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(868,plain,
% 1.93/1.51 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c2_1(a527)) | c2_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c2_1(a527))))),
% 1.93/1.51 inference(monotonicity,[status(thm)],[867])).
% 1.93/1.51 tff(869,plain,
% 1.93/1.51 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c2_1(a527)) | c2_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c2_1(a527)))),
% 1.93/1.51 inference(transitivity,[status(thm)],[868, 866])).
% 1.93/1.51 tff(870,plain,
% 1.93/1.51 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c2_1(a527)) | c2_1(a496) | c1_1(a496) | c0_1(a496))),
% 1.93/1.51 inference(quant_inst,[status(thm)],[])).
% 1.93/1.51 tff(871,plain,
% 1.93/1.51 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a527) | c3_1(a527) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c2_1(a527))),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[870, 869])).
% 1.93/1.51 tff(872,plain,
% 1.93/1.51 (hskp0 | c0_1(a496)),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[871, 112, 865, 836, 830, 632, 634, 854])).
% 1.93/1.51 tff(873,plain,
% 1.93/1.51 (hskp0),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[872, 635])).
% 1.93/1.51 tff(874,plain,
% 1.93/1.51 (((~hskp0) | (~c0_1(a494))) <=> ((~hskp0) | (~c0_1(a494)))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(875,plain,
% 1.93/1.51 (((~c0_1(a494)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a494)))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(876,axiom,((~c0_1(a494)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 1.93/1.51 tff(877,plain,
% 1.93/1.51 ((~hskp0) | (~c0_1(a494))),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[876, 875])).
% 1.93/1.51 tff(878,plain,
% 1.93/1.51 ((~hskp0) | (~c0_1(a494))),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[877, 874])).
% 1.93/1.51 tff(879,plain,
% 1.93/1.51 (~c0_1(a494)),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[878, 873])).
% 1.93/1.51 tff(880,plain,
% 1.93/1.51 (hskp11 | c2_1(a496) | c0_1(a496)),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[375, 112, 11, 633, 10])).
% 1.93/1.51 tff(881,plain,
% 1.93/1.51 (hskp11),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[880, 635, 634])).
% 1.93/1.51 tff(882,plain,
% 1.93/1.51 (~c2_1(a510)),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[59, 881])).
% 1.93/1.51 tff(883,plain,
% 1.93/1.51 (~c1_1(a510)),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[65, 881])).
% 1.93/1.51 tff(884,plain,
% 1.93/1.51 (((~hskp0) | c3_1(a494)) <=> ((~hskp0) | c3_1(a494))),
% 1.93/1.51 inference(rewrite,[status(thm)],[])).
% 1.93/1.51 tff(885,axiom,((~hskp0) | c3_1(a494)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 1.93/1.51 tff(886,plain,
% 1.93/1.51 ((~hskp0) | c3_1(a494)),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[885, 884])).
% 1.93/1.51 tff(887,plain,
% 1.93/1.51 ((~hskp0) | c3_1(a494)),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[886, 884])).
% 1.93/1.51 tff(888,plain,
% 1.93/1.51 ((~hskp0) | c3_1(a494)),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[887, 884])).
% 1.93/1.51 tff(889,plain,
% 1.93/1.51 ((~hskp0) | c3_1(a494)),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[888, 884])).
% 1.93/1.51 tff(890,plain,
% 1.93/1.51 ((~hskp0) | c3_1(a494)),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[889, 884])).
% 1.93/1.51 tff(891,plain,
% 1.93/1.51 ((~hskp0) | c3_1(a494)),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[890, 884])).
% 1.93/1.51 tff(892,plain,
% 1.93/1.51 ((~hskp0) | c3_1(a494)),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[891, 884])).
% 1.93/1.51 tff(893,plain,
% 1.93/1.51 ((~hskp0) | c3_1(a494)),
% 1.93/1.51 inference(modus_ponens,[status(thm)],[892, 884])).
% 1.93/1.51 tff(894,plain,
% 1.93/1.51 (c3_1(a494)),
% 1.93/1.51 inference(unit_resolution,[status(thm)],[893, 873])).
% 1.93/1.51 tff(895,plain,
% 1.93/1.52 (c0_1(a510)),
% 1.93/1.52 inference(unit_resolution,[status(thm)],[76, 881])).
% 1.93/1.52 tff(896,plain,
% 1.93/1.52 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c1_1(a510) | c2_1(a510) | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a494)) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a510) | c2_1(a510) | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a494)) | (~c0_1(a510)))),
% 1.93/1.52 inference(rewrite,[status(thm)],[])).
% 1.93/1.52 tff(897,plain,
% 1.93/1.52 ((hskp10 | (~ndr1_0) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)) | c0_1(a494) | (~c1_1(a494)) | (~c3_1(a494))) <=> (hskp10 | c1_1(a510) | c2_1(a510) | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a494)) | (~c0_1(a510)))),
% 1.93/1.52 inference(rewrite,[status(thm)],[])).
% 1.93/1.52 tff(898,plain,
% 1.93/1.52 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)) | c0_1(a494) | (~c1_1(a494)) | (~c3_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c1_1(a510) | c2_1(a510) | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a494)) | (~c0_1(a510))))),
% 1.93/1.52 inference(monotonicity,[status(thm)],[897])).
% 1.93/1.52 tff(899,plain,
% 1.93/1.52 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)) | c0_1(a494) | (~c1_1(a494)) | (~c3_1(a494)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a510) | c2_1(a510) | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a494)) | (~c0_1(a510)))),
% 1.93/1.52 inference(transitivity,[status(thm)],[898, 896])).
% 1.93/1.52 tff(900,plain,
% 1.93/1.52 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)) | c0_1(a494) | (~c1_1(a494)) | (~c3_1(a494)))),
% 1.93/1.52 inference(quant_inst,[status(thm)],[])).
% 1.93/1.52 tff(901,plain,
% 1.93/1.52 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a510) | c2_1(a510) | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a494)) | (~c0_1(a510))),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[900, 899])).
% 1.93/1.52 tff(902,plain,
% 1.93/1.52 (~c1_1(a494)),
% 1.93/1.52 inference(unit_resolution,[status(thm)],[901, 112, 11, 895, 894, 883, 882, 879, 53])).
% 1.93/1.52 tff(903,plain,
% 1.93/1.52 (^[U: $i] : refl((hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))))),
% 1.93/1.52 inference(bind,[status(th)],[])).
% 1.93/1.52 tff(904,plain,
% 1.93/1.52 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.93/1.52 inference(quant_intro,[status(thm)],[903])).
% 1.93/1.52 tff(905,plain,
% 1.93/1.52 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.93/1.52 inference(rewrite,[status(thm)],[])).
% 1.93/1.52 tff(906,plain,
% 1.93/1.52 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) | hskp6))), rewrite((((~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp9) <=> ((hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) | hskp9))), rewrite(((hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U))) | hskp9) <=> (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp9) <=> (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))))),
% 1.93/1.52 inference(bind,[status(th)],[])).
% 1.93/1.52 tff(907,plain,
% 1.93/1.52 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp9) <=> ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.93/1.52 inference(quant_intro,[status(thm)],[906])).
% 1.93/1.52 tff(908,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 1.93/1.52 tff(909,plain,
% 1.93/1.52 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[908, 907])).
% 1.93/1.52 tff(910,plain,
% 1.93/1.52 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[909, 905])).
% 1.93/1.52 tff(911,plain,(
% 1.93/1.52 ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.93/1.52 inference(skolemize,[status(sab)],[910])).
% 1.93/1.52 tff(912,plain,
% 1.93/1.52 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[911, 904])).
% 1.93/1.52 tff(913,plain,
% 1.93/1.52 (((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | c1_1(a494))) <=> ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | hskp9 | hskp6 | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | c1_1(a494))),
% 1.93/1.52 inference(rewrite,[status(thm)],[])).
% 1.93/1.52 tff(914,plain,
% 1.93/1.52 ((hskp9 | hskp6 | (~ndr1_0) | c0_1(a494) | c1_1(a494) | (~c3_1(a494))) <=> (hskp9 | hskp6 | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | c1_1(a494))),
% 1.93/1.52 inference(rewrite,[status(thm)],[])).
% 1.93/1.52 tff(915,plain,
% 1.93/1.52 (((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | c0_1(a494) | c1_1(a494) | (~c3_1(a494)))) <=> ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | c1_1(a494)))),
% 1.93/1.52 inference(monotonicity,[status(thm)],[914])).
% 1.93/1.52 tff(916,plain,
% 1.93/1.52 (((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | c0_1(a494) | c1_1(a494) | (~c3_1(a494)))) <=> ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | hskp9 | hskp6 | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | c1_1(a494))),
% 1.93/1.52 inference(transitivity,[status(thm)],[915, 913])).
% 1.93/1.52 tff(917,plain,
% 1.93/1.52 ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | c0_1(a494) | c1_1(a494) | (~c3_1(a494)))),
% 1.93/1.52 inference(quant_inst,[status(thm)],[])).
% 1.93/1.52 tff(918,plain,
% 1.93/1.52 ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c0_1(U) | c1_1(U) | (~c3_1(U)))) | hskp9 | hskp6 | c0_1(a494) | (~ndr1_0) | (~c3_1(a494)) | c1_1(a494)),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[917, 916])).
% 1.93/1.52 tff(919,plain,
% 1.93/1.52 (hskp9),
% 1.93/1.52 inference(unit_resolution,[status(thm)],[918, 112, 812, 894, 879, 912, 902])).
% 1.93/1.52 tff(920,plain,
% 1.93/1.52 (((~hskp9) | (~c1_1(a507))) <=> ((~hskp9) | (~c1_1(a507)))),
% 1.93/1.52 inference(rewrite,[status(thm)],[])).
% 1.93/1.52 tff(921,plain,
% 1.93/1.52 (((~c1_1(a507)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a507)))),
% 1.93/1.52 inference(rewrite,[status(thm)],[])).
% 1.93/1.52 tff(922,axiom,((~c1_1(a507)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 1.93/1.52 tff(923,plain,
% 1.93/1.52 ((~hskp9) | (~c1_1(a507))),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[922, 921])).
% 1.93/1.52 tff(924,plain,
% 1.93/1.52 ((~hskp9) | (~c1_1(a507))),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[923, 920])).
% 1.93/1.52 tff(925,plain,
% 1.93/1.52 (~c1_1(a507)),
% 1.93/1.52 inference(unit_resolution,[status(thm)],[924, 919])).
% 1.93/1.52 tff(926,plain,
% 1.93/1.52 (((~hskp9) | (~c0_1(a507))) <=> ((~hskp9) | (~c0_1(a507)))),
% 1.93/1.52 inference(rewrite,[status(thm)],[])).
% 1.93/1.52 tff(927,plain,
% 1.93/1.52 (((~c0_1(a507)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a507)))),
% 1.93/1.52 inference(rewrite,[status(thm)],[])).
% 1.93/1.52 tff(928,axiom,((~c0_1(a507)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.93/1.52 tff(929,plain,
% 1.93/1.52 ((~hskp9) | (~c0_1(a507))),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[928, 927])).
% 1.93/1.52 tff(930,plain,
% 1.93/1.52 ((~hskp9) | (~c0_1(a507))),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[929, 926])).
% 1.93/1.52 tff(931,plain,
% 1.93/1.52 (~c0_1(a507)),
% 1.93/1.52 inference(unit_resolution,[status(thm)],[930, 919])).
% 1.93/1.52 tff(932,plain,
% 1.93/1.52 (((~hskp9) | c3_1(a507)) <=> ((~hskp9) | c3_1(a507))),
% 1.93/1.52 inference(rewrite,[status(thm)],[])).
% 1.93/1.52 tff(933,axiom,((~hskp9) | c3_1(a507)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 1.93/1.52 tff(934,plain,
% 1.93/1.52 ((~hskp9) | c3_1(a507)),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[933, 932])).
% 1.93/1.52 tff(935,plain,
% 1.93/1.52 ((~hskp9) | c3_1(a507)),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[934, 932])).
% 1.93/1.52 tff(936,plain,
% 1.93/1.52 ((~hskp9) | c3_1(a507)),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[935, 932])).
% 1.93/1.52 tff(937,plain,
% 1.93/1.52 ((~hskp9) | c3_1(a507)),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[936, 932])).
% 1.93/1.52 tff(938,plain,
% 1.93/1.52 ((~hskp9) | c3_1(a507)),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[937, 932])).
% 1.93/1.52 tff(939,plain,
% 1.93/1.52 ((~hskp9) | c3_1(a507)),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[938, 932])).
% 1.93/1.52 tff(940,plain,
% 1.93/1.52 ((~hskp9) | c3_1(a507)),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[939, 932])).
% 1.93/1.52 tff(941,plain,
% 1.93/1.52 ((~hskp9) | c3_1(a507)),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[940, 932])).
% 1.93/1.52 tff(942,plain,
% 1.93/1.52 (c3_1(a507)),
% 1.93/1.52 inference(unit_resolution,[status(thm)],[941, 919])).
% 1.93/1.52 tff(943,assumption,(~c1_1(a507)), introduced(assumption)).
% 1.93/1.52 tff(944,assumption,(~c0_1(a507)), introduced(assumption)).
% 1.93/1.52 tff(945,assumption,(hskp12), introduced(assumption)).
% 1.93/1.52 tff(946,plain,
% 1.93/1.52 (~c2_1(a514)),
% 1.93/1.52 inference(unit_resolution,[status(thm)],[541, 945])).
% 1.93/1.52 tff(947,assumption,(c3_1(a507)), introduced(assumption)).
% 1.93/1.52 tff(948,plain,
% 1.93/1.52 (c3_1(a514)),
% 1.93/1.52 inference(unit_resolution,[status(thm)],[552, 945])).
% 1.93/1.52 tff(949,plain,
% 1.93/1.52 (c1_1(a514)),
% 1.93/1.52 inference(unit_resolution,[status(thm)],[563, 945])).
% 1.93/1.52 tff(950,plain,
% 1.93/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a514) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a514) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))),
% 1.93/1.52 inference(rewrite,[status(thm)],[])).
% 1.93/1.52 tff(951,plain,
% 1.93/1.52 (((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a514) | c0_1(a514) | (~c1_1(a514)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507))) <=> (c2_1(a514) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))),
% 1.93/1.52 inference(rewrite,[status(thm)],[])).
% 1.93/1.52 tff(952,plain,
% 1.93/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a514) | c0_1(a514) | (~c1_1(a514)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a514) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514)))),
% 1.93/1.52 inference(monotonicity,[status(thm)],[951])).
% 1.93/1.52 tff(953,plain,
% 1.93/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a514) | c0_1(a514) | (~c1_1(a514)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a514) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))),
% 1.93/1.52 inference(transitivity,[status(thm)],[952, 950])).
% 1.93/1.52 tff(954,plain,
% 1.93/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a514) | c0_1(a514) | (~c1_1(a514)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))),
% 1.93/1.52 inference(quant_inst,[status(thm)],[])).
% 1.93/1.52 tff(955,plain,
% 1.93/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a514) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514)),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[954, 953])).
% 1.93/1.52 tff(956,plain,
% 1.93/1.52 (c0_1(a514)),
% 1.93/1.52 inference(unit_resolution,[status(thm)],[955, 112, 949, 948, 947, 946, 944, 943, 618])).
% 1.93/1.52 tff(957,plain,
% 1.93/1.52 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 1.93/1.52 inference(bind,[status(th)],[])).
% 1.93/1.52 tff(958,plain,
% 1.93/1.52 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.93/1.52 inference(quant_intro,[status(thm)],[957])).
% 1.93/1.52 tff(959,plain,
% 1.93/1.52 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.93/1.52 inference(rewrite,[status(thm)],[])).
% 1.93/1.52 tff(960,plain,
% 1.93/1.52 (^[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(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)) | 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))) | (~ndr1_0)) | c2_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))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 1.93/1.52 inference(bind,[status(th)],[])).
% 1.93/1.52 tff(961,plain,
% 1.93/1.52 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.93/1.52 inference(quant_intro,[status(thm)],[960])).
% 1.93/1.52 tff(962,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 1.93/1.52 tff(963,plain,
% 1.93/1.52 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[962, 961])).
% 1.93/1.52 tff(964,plain,
% 1.93/1.52 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[963, 959])).
% 1.93/1.52 tff(965,plain,(
% 1.93/1.52 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.93/1.52 inference(skolemize,[status(sab)],[964])).
% 1.93/1.52 tff(966,plain,
% 1.93/1.52 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[965, 958])).
% 1.93/1.52 tff(967,assumption,(~hskp6), introduced(assumption)).
% 1.93/1.52 tff(968,plain,
% 1.93/1.52 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)))),
% 1.93/1.52 inference(rewrite,[status(thm)],[])).
% 1.93/1.52 tff(969,plain,
% 1.93/1.52 ((hskp6 | (~ndr1_0) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c2_1(a496) | c0_1(a496) | c3_1(a496)) <=> (hskp6 | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)))),
% 1.93/1.52 inference(rewrite,[status(thm)],[])).
% 1.93/1.52 tff(970,plain,
% 1.93/1.52 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c2_1(a496) | c0_1(a496) | c3_1(a496))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514))))),
% 1.93/1.52 inference(monotonicity,[status(thm)],[969])).
% 1.93/1.52 tff(971,plain,
% 1.93/1.52 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c2_1(a496) | c0_1(a496) | c3_1(a496))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)))),
% 1.93/1.52 inference(transitivity,[status(thm)],[970, 968])).
% 1.93/1.52 tff(972,plain,
% 1.93/1.52 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c2_1(a496) | c0_1(a496) | c3_1(a496))),
% 1.93/1.52 inference(quant_inst,[status(thm)],[])).
% 1.93/1.52 tff(973,plain,
% 1.93/1.52 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514))),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[972, 971])).
% 1.93/1.52 tff(974,plain,
% 1.93/1.52 ($false),
% 1.93/1.52 inference(unit_resolution,[status(thm)],[973, 112, 967, 949, 946, 634, 633, 966, 635, 956])).
% 1.93/1.52 tff(975,plain,((~hskp12) | hskp6 | c2_1(a496) | c3_1(a496) | c0_1(a496) | (~c3_1(a507)) | c0_1(a507) | c1_1(a507)), inference(lemma,lemma(discharge,[]))).
% 1.93/1.52 tff(976,plain,
% 1.93/1.52 (~hskp12),
% 1.93/1.52 inference(unit_resolution,[status(thm)],[975, 942, 634, 633, 812, 635, 931, 925])).
% 1.93/1.52 tff(977,plain,
% 1.93/1.52 (hskp15),
% 1.93/1.52 inference(unit_resolution,[status(thm)],[535, 976, 404])).
% 1.93/1.52 tff(978,plain,
% 1.93/1.52 (~c3_1(a528)),
% 1.93/1.52 inference(unit_resolution,[status(thm)],[469, 977])).
% 1.93/1.52 tff(979,plain,
% 1.93/1.52 (c1_1(a528)),
% 1.93/1.52 inference(unit_resolution,[status(thm)],[480, 977])).
% 1.93/1.52 tff(980,plain,
% 1.93/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a528) | c1_1(a527) | c3_1(a527) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a528) | c1_1(a527) | c3_1(a527) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.93/1.52 inference(rewrite,[status(thm)],[])).
% 1.93/1.52 tff(981,plain,
% 1.93/1.52 (((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a527) | c1_1(a527) | c0_1(a527)) <=> (c3_1(a528) | c1_1(a527) | c3_1(a527) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.93/1.52 inference(rewrite,[status(thm)],[])).
% 1.93/1.52 tff(982,plain,
% 1.93/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a527) | c1_1(a527) | c0_1(a527))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a528) | c1_1(a527) | c3_1(a527) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528))))),
% 1.93/1.52 inference(monotonicity,[status(thm)],[981])).
% 1.93/1.52 tff(983,plain,
% 1.93/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a527) | c1_1(a527) | c0_1(a527))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a528) | c1_1(a527) | c3_1(a527) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.93/1.52 inference(transitivity,[status(thm)],[982, 980])).
% 1.93/1.52 tff(984,plain,
% 1.93/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a527) | c1_1(a527) | c0_1(a527))),
% 1.93/1.52 inference(quant_inst,[status(thm)],[])).
% 1.93/1.52 tff(985,plain,
% 1.93/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a528) | c1_1(a527) | c3_1(a527) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528))),
% 1.93/1.52 inference(modus_ponens,[status(thm)],[984, 983])).
% 1.93/1.52 tff(986,plain,
% 1.93/1.52 (~c2_1(a528)),
% 1.93/1.52 inference(unit_resolution,[status(thm)],[985, 112, 979, 978, 836, 830, 634, 633, 784, 844, 635])).
% 1.93/1.52 tff(987,plain,
% 1.93/1.52 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)))),
% 1.93/1.52 inference(bind,[status(th)],[])).
% 1.93/1.52 tff(988,plain,
% 1.93/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.93/1.52 inference(quant_intro,[status(thm)],[987])).
% 1.93/1.52 tff(989,plain,
% 1.93/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.93/1.52 inference(rewrite,[status(thm)],[])).
% 1.93/1.52 tff(990,plain,
% 1.93/1.52 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_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))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_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))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))))),
% 1.93/1.53 inference(bind,[status(th)],[])).
% 1.93/1.53 tff(991,plain,
% 1.93/1.53 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.93/1.53 inference(quant_intro,[status(thm)],[990])).
% 1.93/1.53 tff(992,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 1.93/1.53 tff(993,plain,
% 1.93/1.53 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[992, 991])).
% 1.93/1.53 tff(994,plain,
% 1.93/1.53 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[993, 989])).
% 1.93/1.53 tff(995,plain,(
% 1.93/1.53 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.93/1.53 inference(skolemize,[status(sab)],[994])).
% 1.93/1.53 tff(996,plain,
% 1.93/1.53 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[995, 988])).
% 1.93/1.53 tff(997,plain,
% 1.93/1.53 (c0_1(a528)),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[491, 977])).
% 1.93/1.53 tff(998,plain,
% 1.93/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(999,plain,
% 1.93/1.53 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a496) | c0_1(a496) | c2_1(a496)) <=> (c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1000,plain,
% 1.93/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528)))),
% 1.93/1.53 inference(monotonicity,[status(thm)],[999])).
% 1.93/1.53 tff(1001,plain,
% 1.93/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))),
% 1.93/1.53 inference(transitivity,[status(thm)],[1000, 998])).
% 1.93/1.53 tff(1002,plain,
% 1.93/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a496) | c0_1(a496) | c2_1(a496))),
% 1.93/1.53 inference(quant_inst,[status(thm)],[])).
% 1.93/1.53 tff(1003,plain,
% 1.93/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 1.93/1.53 tff(1004,plain,
% 1.93/1.53 ($false),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[1003, 112, 997, 979, 978, 634, 633, 996, 635, 986])).
% 1.93/1.53 tff(1005,plain,(c0_1(a496) | c2_1(a496) | c3_1(a496) | hskp13 | hskp10 | c1_1(a496) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.93/1.53 tff(1006,plain,
% 1.93/1.53 (c0_1(a496)),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[1005, 634, 633, 404, 11, 632, 631])).
% 1.93/1.53 tff(1007,plain,
% 1.93/1.53 (hskp22 | c2_1(a496) | (~c0_1(a496))),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[797, 112, 632, 633, 31])).
% 1.93/1.53 tff(1008,plain,
% 1.93/1.53 (hskp22),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[1007, 1006, 634])).
% 1.93/1.53 tff(1009,plain,
% 1.93/1.53 (~c0_1(a540)),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[131, 1008])).
% 1.93/1.53 tff(1010,plain,
% 1.93/1.53 (c3_1(a540)),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[142, 1008])).
% 1.93/1.53 tff(1011,plain,
% 1.93/1.53 (c1_1(a540)),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[153, 1008])).
% 1.93/1.53 tff(1012,plain,
% 1.93/1.53 ($false),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[807, 112, 11, 1011, 1010, 1009, 632, 634, 53, 1006])).
% 1.93/1.53 tff(1013,plain,(c2_1(a496) | hskp10 | c1_1(a496) | c3_1(a496) | hskp13 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.93/1.53 tff(1014,plain,
% 1.93/1.53 (hskp1),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[1013, 630, 629, 11, 404, 628])).
% 1.93/1.53 tff(1015,plain,
% 1.93/1.53 (((~hskp1) | (~c3_1(a495))) <=> ((~hskp1) | (~c3_1(a495)))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1016,plain,
% 1.93/1.53 (((~c3_1(a495)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a495)))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1017,axiom,((~c3_1(a495)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.93/1.53 tff(1018,plain,
% 1.93/1.53 ((~hskp1) | (~c3_1(a495))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1017, 1016])).
% 1.93/1.53 tff(1019,plain,
% 1.93/1.53 ((~hskp1) | (~c3_1(a495))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1018, 1015])).
% 1.93/1.53 tff(1020,plain,
% 1.93/1.53 (~c3_1(a495)),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[1019, 1014])).
% 1.93/1.53 tff(1021,plain,
% 1.93/1.53 (((~hskp1) | (~c0_1(a495))) <=> ((~hskp1) | (~c0_1(a495)))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1022,plain,
% 1.93/1.53 (((~c0_1(a495)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a495)))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1023,axiom,((~c0_1(a495)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 1.93/1.53 tff(1024,plain,
% 1.93/1.53 ((~hskp1) | (~c0_1(a495))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 1.93/1.53 tff(1025,plain,
% 1.93/1.53 ((~hskp1) | (~c0_1(a495))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1024, 1021])).
% 1.93/1.53 tff(1026,plain,
% 1.93/1.53 (~c0_1(a495)),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[1025, 1014])).
% 1.93/1.53 tff(1027,assumption,(~c3_1(a502)), introduced(assumption)).
% 1.93/1.53 tff(1028,plain,
% 1.93/1.53 (((~hskp1) | c1_1(a495)) <=> ((~hskp1) | c1_1(a495))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1029,axiom,((~hskp1) | c1_1(a495)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 1.93/1.53 tff(1030,plain,
% 1.93/1.53 ((~hskp1) | c1_1(a495)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 1.93/1.53 tff(1031,plain,
% 1.93/1.53 ((~hskp1) | c1_1(a495)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1030, 1028])).
% 1.93/1.53 tff(1032,plain,
% 1.93/1.53 ((~hskp1) | c1_1(a495)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1031, 1028])).
% 1.93/1.53 tff(1033,plain,
% 1.93/1.53 ((~hskp1) | c1_1(a495)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1032, 1028])).
% 1.93/1.53 tff(1034,plain,
% 1.93/1.53 ((~hskp1) | c1_1(a495)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1033, 1028])).
% 1.93/1.53 tff(1035,plain,
% 1.93/1.53 ((~hskp1) | c1_1(a495)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1034, 1028])).
% 1.93/1.53 tff(1036,plain,
% 1.93/1.53 ((~hskp1) | c1_1(a495)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1035, 1028])).
% 1.93/1.53 tff(1037,plain,
% 1.93/1.53 ((~hskp1) | c1_1(a495)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1036, 1028])).
% 1.93/1.53 tff(1038,plain,
% 1.93/1.53 (c1_1(a495)),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[1037, 1014])).
% 1.93/1.53 tff(1039,assumption,(~c1_1(a502)), introduced(assumption)).
% 1.93/1.53 tff(1040,plain,
% 1.93/1.53 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.93/1.53 inference(bind,[status(th)],[])).
% 1.93/1.53 tff(1041,plain,
% 1.93/1.53 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.93/1.53 inference(quant_intro,[status(thm)],[1040])).
% 1.93/1.53 tff(1042,plain,
% 1.93/1.53 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1043,plain,
% 1.93/1.53 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp8) <=> (hskp8 | (~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))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.93/1.53 inference(bind,[status(th)],[])).
% 1.93/1.53 tff(1044,plain,
% 1.93/1.53 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.93/1.53 inference(quant_intro,[status(thm)],[1043])).
% 1.93/1.53 tff(1045,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 1.93/1.53 tff(1046,plain,
% 1.93/1.53 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1045, 1044])).
% 1.93/1.53 tff(1047,plain,
% 1.93/1.53 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1046, 1042])).
% 1.93/1.53 tff(1048,plain,(
% 1.93/1.53 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.93/1.53 inference(skolemize,[status(sab)],[1047])).
% 1.93/1.53 tff(1049,plain,
% 1.93/1.53 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1048, 1041])).
% 1.93/1.53 tff(1050,plain,
% 1.93/1.53 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a568) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a568) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1051,plain,
% 1.93/1.53 ((hskp8 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495))) <=> (hskp8 | c1_1(a568) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1052,plain,
% 1.93/1.53 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a568) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.93/1.53 inference(monotonicity,[status(thm)],[1051])).
% 1.93/1.53 tff(1053,plain,
% 1.93/1.53 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a568) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.93/1.53 inference(transitivity,[status(thm)],[1052, 1050])).
% 1.93/1.53 tff(1054,plain,
% 1.93/1.53 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)))),
% 1.93/1.53 inference(quant_inst,[status(thm)],[])).
% 1.93/1.53 tff(1055,plain,
% 1.93/1.53 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a568) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1054, 1053])).
% 1.93/1.53 tff(1056,plain,
% 1.93/1.53 (hskp8),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[1055, 112, 401, 403, 1038, 402, 1026, 1020, 1049])).
% 1.93/1.53 tff(1057,plain,
% 1.93/1.53 (((~hskp8) | c2_1(a505)) <=> ((~hskp8) | c2_1(a505))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1058,axiom,((~hskp8) | c2_1(a505)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 1.93/1.53 tff(1059,plain,
% 1.93/1.53 ((~hskp8) | c2_1(a505)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 1.93/1.53 tff(1060,plain,
% 1.93/1.53 ((~hskp8) | c2_1(a505)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1059, 1057])).
% 1.93/1.53 tff(1061,plain,
% 1.93/1.53 ((~hskp8) | c2_1(a505)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1060, 1057])).
% 1.93/1.53 tff(1062,plain,
% 1.93/1.53 ((~hskp8) | c2_1(a505)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1061, 1057])).
% 1.93/1.53 tff(1063,plain,
% 1.93/1.53 ((~hskp8) | c2_1(a505)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1062, 1057])).
% 1.93/1.53 tff(1064,plain,
% 1.93/1.53 ((~hskp8) | c2_1(a505)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1063, 1057])).
% 1.93/1.53 tff(1065,plain,
% 1.93/1.53 ((~hskp8) | c2_1(a505)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1064, 1057])).
% 1.93/1.53 tff(1066,plain,
% 1.93/1.53 ((~hskp8) | c2_1(a505)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1065, 1057])).
% 1.93/1.53 tff(1067,plain,
% 1.93/1.53 (c2_1(a505)),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[1066, 1056])).
% 1.93/1.53 tff(1068,plain,
% 1.93/1.53 (((~hskp8) | (~c0_1(a505))) <=> ((~hskp8) | (~c0_1(a505)))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1069,plain,
% 1.93/1.53 (((~c0_1(a505)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a505)))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1070,axiom,((~c0_1(a505)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 1.93/1.53 tff(1071,plain,
% 1.93/1.53 ((~hskp8) | (~c0_1(a505))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1070, 1069])).
% 1.93/1.53 tff(1072,plain,
% 1.93/1.53 ((~hskp8) | (~c0_1(a505))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1071, 1068])).
% 1.93/1.53 tff(1073,plain,
% 1.93/1.53 (~c0_1(a505)),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[1072, 1056])).
% 1.93/1.53 tff(1074,assumption,(~hskp12), introduced(assumption)).
% 1.93/1.53 tff(1075,assumption,(~c3_1(a495)), introduced(assumption)).
% 1.93/1.53 tff(1076,assumption,(~c0_1(a495)), introduced(assumption)).
% 1.93/1.53 tff(1077,assumption,(c1_1(a495)), introduced(assumption)).
% 1.93/1.53 tff(1078,plain,
% 1.93/1.53 (hskp15),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[535, 1074, 404])).
% 1.93/1.53 tff(1079,plain,
% 1.93/1.53 (~c3_1(a528)),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[469, 1078])).
% 1.93/1.53 tff(1080,plain,
% 1.93/1.53 (c1_1(a528)),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[480, 1078])).
% 1.93/1.53 tff(1081,plain,
% 1.93/1.53 (c0_1(a528)),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[491, 1078])).
% 1.93/1.53 tff(1082,assumption,(~c3_1(a528)), introduced(assumption)).
% 1.93/1.53 tff(1083,assumption,(hskp20), introduced(assumption)).
% 1.93/1.53 tff(1084,plain,
% 1.93/1.53 (((~hskp20) | (~c2_1(a536))) <=> ((~hskp20) | (~c2_1(a536)))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1085,plain,
% 1.93/1.53 (((~c2_1(a536)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a536)))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1086,axiom,((~c2_1(a536)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 1.93/1.53 tff(1087,plain,
% 1.93/1.53 ((~hskp20) | (~c2_1(a536))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 1.93/1.53 tff(1088,plain,
% 1.93/1.53 ((~hskp20) | (~c2_1(a536))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1087, 1084])).
% 1.93/1.53 tff(1089,plain,
% 1.93/1.53 (~c2_1(a536)),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[1088, 1083])).
% 1.93/1.53 tff(1090,plain,
% 1.93/1.53 (~c0_1(a536)),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[582, 1083])).
% 1.93/1.53 tff(1091,assumption,(c1_1(a528)), introduced(assumption)).
% 1.93/1.53 tff(1092,assumption,(c0_1(a528)), introduced(assumption)).
% 1.93/1.53 tff(1093,plain,
% 1.93/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536)))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1094,plain,
% 1.93/1.53 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a536) | (~c3_1(a536)) | c2_1(a536)) <=> (c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536)))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1095,plain,
% 1.93/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a536) | (~c3_1(a536)) | c2_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536))))),
% 1.93/1.53 inference(monotonicity,[status(thm)],[1094])).
% 1.93/1.53 tff(1096,plain,
% 1.93/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a536) | (~c3_1(a536)) | c2_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536)))),
% 1.93/1.53 inference(transitivity,[status(thm)],[1095, 1093])).
% 1.93/1.53 tff(1097,plain,
% 1.93/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a536) | (~c3_1(a536)) | c2_1(a536))),
% 1.93/1.53 inference(quant_inst,[status(thm)],[])).
% 1.93/1.53 tff(1098,plain,
% 1.93/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 1.93/1.53 tff(1099,plain,
% 1.93/1.53 (~c3_1(a536)),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[1098, 112, 1092, 1091, 1077, 1090, 1089, 1082, 1076, 1075, 21])).
% 1.93/1.53 tff(1100,plain,
% 1.93/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1101,plain,
% 1.93/1.53 (((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a502) | c1_1(a502) | c0_1(a502)) <=> (c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1102,plain,
% 1.93/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a502) | c1_1(a502) | c0_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536)))),
% 1.93/1.53 inference(monotonicity,[status(thm)],[1101])).
% 1.93/1.53 tff(1103,plain,
% 1.93/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a502) | c1_1(a502) | c0_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))),
% 1.93/1.53 inference(transitivity,[status(thm)],[1102, 1100])).
% 1.93/1.53 tff(1104,plain,
% 1.93/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a502) | c1_1(a502) | c0_1(a502))),
% 1.93/1.53 inference(quant_inst,[status(thm)],[])).
% 1.93/1.53 tff(1105,plain,
% 1.93/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1104, 1103])).
% 1.93/1.53 tff(1106,plain,
% 1.93/1.53 ((~c2_1(a528)) | c3_1(a536)),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[1105, 112, 1091, 1090, 1089, 1082, 263, 1039, 1027, 784])).
% 1.93/1.53 tff(1107,plain,
% 1.93/1.53 (~c2_1(a528)),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[1106, 1099])).
% 1.93/1.53 tff(1108,plain,
% 1.93/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c3_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c3_1(a536))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1109,plain,
% 1.93/1.53 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a536) | c0_1(a536) | c2_1(a536)) <=> (c0_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c3_1(a536))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1110,plain,
% 1.93/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a536) | c0_1(a536) | c2_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c3_1(a536)))),
% 1.93/1.53 inference(monotonicity,[status(thm)],[1109])).
% 1.93/1.53 tff(1111,plain,
% 1.93/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a536) | c0_1(a536) | c2_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c3_1(a536))),
% 1.93/1.53 inference(transitivity,[status(thm)],[1110, 1108])).
% 1.93/1.53 tff(1112,plain,
% 1.93/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a536) | c0_1(a536) | c2_1(a536))),
% 1.93/1.53 inference(quant_inst,[status(thm)],[])).
% 1.93/1.53 tff(1113,plain,
% 1.93/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c3_1(a536)),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1112, 1111])).
% 1.93/1.53 tff(1114,plain,
% 1.93/1.53 ($false),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[1113, 112, 1092, 1091, 1090, 1089, 1082, 996, 1107, 1099])).
% 1.93/1.53 tff(1115,plain,((~hskp20) | (~c0_1(a528)) | (~c1_1(a528)) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~c1_1(a495)) | c0_1(a495) | c3_1(a495)), inference(lemma,lemma(discharge,[]))).
% 1.93/1.53 tff(1116,plain,
% 1.93/1.53 (~hskp20),
% 1.93/1.53 inference(unit_resolution,[status(thm)],[1115, 1081, 1080, 1079, 263, 1039, 1027, 1077, 1076, 1075])).
% 1.93/1.53 tff(1117,plain,
% 1.93/1.53 (^[U: $i] : refl((hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 1.93/1.53 inference(bind,[status(th)],[])).
% 1.93/1.53 tff(1118,plain,
% 1.93/1.53 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.93/1.53 inference(quant_intro,[status(thm)],[1117])).
% 1.93/1.53 tff(1119,plain,
% 1.93/1.53 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.93/1.53 inference(rewrite,[status(thm)],[])).
% 1.93/1.53 tff(1120,plain,
% 1.93/1.53 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp20) <=> ((hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp20))), rewrite(((hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp20) <=> (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp20) <=> (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 1.93/1.53 inference(bind,[status(th)],[])).
% 1.93/1.53 tff(1121,plain,
% 1.93/1.53 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp20) <=> ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.93/1.53 inference(quant_intro,[status(thm)],[1120])).
% 1.93/1.53 tff(1122,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp12) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 1.93/1.53 tff(1123,plain,
% 1.93/1.53 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 1.93/1.53 tff(1124,plain,
% 1.93/1.53 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1123, 1119])).
% 1.93/1.53 tff(1125,plain,(
% 1.93/1.53 ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.93/1.53 inference(skolemize,[status(sab)],[1124])).
% 1.93/1.53 tff(1126,plain,
% 1.93/1.53 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.93/1.53 inference(modus_ponens,[status(thm)],[1125, 1118])).
% 1.93/1.53 tff(1127,plain,
% 1.93/1.53 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a502)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a502)))),
% 1.93/1.54 inference(rewrite,[status(thm)],[])).
% 1.93/1.54 tff(1128,plain,
% 1.93/1.54 ((hskp20 | hskp12 | (~ndr1_0) | c3_1(a502) | c1_1(a502) | (~c2_1(a502))) <=> (hskp20 | hskp12 | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a502)))),
% 1.93/1.54 inference(rewrite,[status(thm)],[])).
% 1.93/1.54 tff(1129,plain,
% 1.93/1.54 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a502) | c1_1(a502) | (~c2_1(a502)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a502))))),
% 1.93/1.54 inference(monotonicity,[status(thm)],[1128])).
% 1.93/1.54 tff(1130,plain,
% 1.93/1.54 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a502) | c1_1(a502) | (~c2_1(a502)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a502)))),
% 1.93/1.54 inference(transitivity,[status(thm)],[1129, 1127])).
% 1.93/1.54 tff(1131,plain,
% 1.93/1.54 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a502) | c1_1(a502) | (~c2_1(a502)))),
% 1.93/1.54 inference(quant_inst,[status(thm)],[])).
% 1.93/1.54 tff(1132,plain,
% 1.93/1.54 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c2_1(a502))),
% 1.93/1.54 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 1.93/1.54 tff(1133,plain,
% 1.93/1.54 (hskp20 | hskp12 | c3_1(a502) | (~c2_1(a502))),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[1132, 112, 1039, 1126])).
% 1.93/1.54 tff(1134,plain,
% 1.93/1.54 (~c2_1(a502)),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[1133, 1116, 1027, 1074])).
% 1.93/1.54 tff(1135,plain,
% 1.93/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c2_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.93/1.54 inference(rewrite,[status(thm)],[])).
% 1.93/1.54 tff(1136,plain,
% 1.93/1.54 (((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a502) | c0_1(a502) | c3_1(a502) | c3_1(a502) | c1_1(a502) | c0_1(a502)) <=> (c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.93/1.54 inference(rewrite,[status(thm)],[])).
% 1.93/1.54 tff(1137,plain,
% 1.93/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a502) | c0_1(a502) | c3_1(a502) | c3_1(a502) | c1_1(a502) | c0_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c2_1(a528))))),
% 1.93/1.54 inference(monotonicity,[status(thm)],[1136])).
% 1.93/1.54 tff(1138,plain,
% 1.93/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a502) | c0_1(a502) | c3_1(a502) | c3_1(a502) | c1_1(a502) | c0_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.93/1.54 inference(transitivity,[status(thm)],[1137, 1135])).
% 1.93/1.54 tff(1139,plain,
% 1.93/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a502) | c0_1(a502) | c3_1(a502) | c3_1(a502) | c1_1(a502) | c0_1(a502))),
% 1.93/1.54 inference(quant_inst,[status(thm)],[])).
% 1.93/1.54 tff(1140,plain,
% 1.93/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a528) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c2_1(a528))),
% 1.93/1.54 inference(modus_ponens,[status(thm)],[1139, 1138])).
% 1.93/1.54 tff(1141,plain,
% 1.93/1.54 (~c2_1(a528)),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[1140, 112, 1080, 1079, 263, 1039, 1027, 784, 1134])).
% 1.93/1.54 tff(1142,plain,
% 1.93/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))),
% 1.93/1.54 inference(rewrite,[status(thm)],[])).
% 1.93/1.54 tff(1143,plain,
% 1.93/1.54 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a502) | c0_1(a502) | c2_1(a502)) <=> (c3_1(a528) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))),
% 1.93/1.54 inference(rewrite,[status(thm)],[])).
% 1.93/1.54 tff(1144,plain,
% 1.93/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a502) | c0_1(a502) | c2_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528)))),
% 1.93/1.54 inference(monotonicity,[status(thm)],[1143])).
% 1.93/1.54 tff(1145,plain,
% 1.93/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a502) | c0_1(a502) | c2_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))),
% 1.93/1.54 inference(transitivity,[status(thm)],[1144, 1142])).
% 1.93/1.54 tff(1146,plain,
% 1.93/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a502) | c0_1(a502) | c2_1(a502))),
% 1.93/1.54 inference(quant_inst,[status(thm)],[])).
% 1.93/1.54 tff(1147,plain,
% 1.93/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528)),
% 1.93/1.54 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 1.93/1.54 tff(1148,plain,
% 1.93/1.54 ($false),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[1147, 112, 1081, 1080, 1079, 263, 1027, 996, 1134, 1141])).
% 1.93/1.54 tff(1149,plain,(hskp12 | c0_1(a502) | c3_1(a502) | c1_1(a502) | (~c1_1(a495)) | c0_1(a495) | c3_1(a495) | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.93/1.54 tff(1150,plain,
% 1.93/1.54 (hskp12),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[1149, 263, 1027, 1039, 1038, 1026, 1020, 404])).
% 1.93/1.54 tff(1151,plain,
% 1.93/1.54 (~c2_1(a514)),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[541, 1150])).
% 1.93/1.54 tff(1152,plain,
% 1.93/1.54 (((~hskp8) | c3_1(a505)) <=> ((~hskp8) | c3_1(a505))),
% 1.93/1.54 inference(rewrite,[status(thm)],[])).
% 1.93/1.54 tff(1153,axiom,((~hskp8) | c3_1(a505)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.93/1.54 tff(1154,plain,
% 1.93/1.54 ((~hskp8) | c3_1(a505)),
% 1.93/1.54 inference(modus_ponens,[status(thm)],[1153, 1152])).
% 1.93/1.54 tff(1155,plain,
% 1.93/1.54 ((~hskp8) | c3_1(a505)),
% 1.93/1.54 inference(modus_ponens,[status(thm)],[1154, 1152])).
% 1.93/1.54 tff(1156,plain,
% 1.93/1.54 ((~hskp8) | c3_1(a505)),
% 1.93/1.54 inference(modus_ponens,[status(thm)],[1155, 1152])).
% 1.93/1.54 tff(1157,plain,
% 1.93/1.54 ((~hskp8) | c3_1(a505)),
% 1.93/1.54 inference(modus_ponens,[status(thm)],[1156, 1152])).
% 1.93/1.54 tff(1158,plain,
% 1.93/1.54 ((~hskp8) | c3_1(a505)),
% 1.93/1.54 inference(modus_ponens,[status(thm)],[1157, 1152])).
% 1.93/1.54 tff(1159,plain,
% 1.93/1.54 ((~hskp8) | c3_1(a505)),
% 1.93/1.54 inference(modus_ponens,[status(thm)],[1158, 1152])).
% 1.93/1.54 tff(1160,plain,
% 1.93/1.54 ((~hskp8) | c3_1(a505)),
% 1.93/1.54 inference(modus_ponens,[status(thm)],[1159, 1152])).
% 1.93/1.54 tff(1161,plain,
% 1.93/1.54 ((~hskp8) | c3_1(a505)),
% 1.93/1.54 inference(modus_ponens,[status(thm)],[1160, 1152])).
% 1.93/1.54 tff(1162,plain,
% 1.93/1.54 (c3_1(a505)),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[1161, 1056])).
% 1.93/1.54 tff(1163,plain,
% 1.93/1.54 (c3_1(a514)),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[552, 1150])).
% 1.93/1.54 tff(1164,plain,
% 1.93/1.54 (c1_1(a514)),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[563, 1150])).
% 1.93/1.54 tff(1165,assumption,(~c0_1(a514)), introduced(assumption)).
% 1.93/1.54 tff(1166,plain,
% 1.93/1.54 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))))),
% 1.93/1.54 inference(bind,[status(th)],[])).
% 1.93/1.54 tff(1167,plain,
% 1.93/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.93/1.54 inference(quant_intro,[status(thm)],[1166])).
% 1.93/1.54 tff(1168,plain,
% 1.93/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.93/1.54 inference(rewrite,[status(thm)],[])).
% 1.93/1.54 tff(1169,plain,
% 1.93/1.54 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))))),
% 1.93/1.54 inference(bind,[status(th)],[])).
% 1.93/1.54 tff(1170,plain,
% 1.93/1.54 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.93/1.54 inference(quant_intro,[status(thm)],[1169])).
% 1.93/1.54 tff(1171,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 1.93/1.54 tff(1172,plain,
% 1.93/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.93/1.54 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 1.93/1.54 tff(1173,plain,
% 1.93/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.93/1.54 inference(modus_ponens,[status(thm)],[1172, 1168])).
% 1.93/1.54 tff(1174,plain,(
% 1.93/1.54 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.93/1.54 inference(skolemize,[status(sab)],[1173])).
% 1.93/1.54 tff(1175,plain,
% 1.93/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.93/1.54 inference(modus_ponens,[status(thm)],[1174, 1167])).
% 1.93/1.54 tff(1176,assumption,(~c0_1(a505)), introduced(assumption)).
% 1.93/1.54 tff(1177,assumption,(~c2_1(a514)), introduced(assumption)).
% 1.93/1.54 tff(1178,assumption,(c2_1(a505)), introduced(assumption)).
% 1.93/1.54 tff(1179,assumption,(c3_1(a514)), introduced(assumption)).
% 1.93/1.54 tff(1180,assumption,(c1_1(a514)), introduced(assumption)).
% 1.93/1.54 tff(1181,plain,
% 1.93/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a514) | c0_1(a505) | (~ndr1_0) | (~c1_1(a505)) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a514) | c0_1(a505) | (~ndr1_0) | (~c1_1(a505)) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))),
% 1.93/1.54 inference(rewrite,[status(thm)],[])).
% 1.93/1.54 tff(1182,plain,
% 1.93/1.54 (((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a505) | (~c1_1(a505)) | (~c2_1(a505)) | c0_1(a514) | c2_1(a514) | (~c1_1(a514))) <=> (c2_1(a514) | c0_1(a505) | (~ndr1_0) | (~c1_1(a505)) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))),
% 1.93/1.54 inference(rewrite,[status(thm)],[])).
% 1.93/1.54 tff(1183,plain,
% 1.93/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a505) | (~c1_1(a505)) | (~c2_1(a505)) | c0_1(a514) | c2_1(a514) | (~c1_1(a514)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a514) | c0_1(a505) | (~ndr1_0) | (~c1_1(a505)) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514)))),
% 1.93/1.54 inference(monotonicity,[status(thm)],[1182])).
% 1.93/1.54 tff(1184,plain,
% 1.93/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a505) | (~c1_1(a505)) | (~c2_1(a505)) | c0_1(a514) | c2_1(a514) | (~c1_1(a514)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a514) | c0_1(a505) | (~ndr1_0) | (~c1_1(a505)) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))),
% 1.93/1.54 inference(transitivity,[status(thm)],[1183, 1181])).
% 1.93/1.54 tff(1185,plain,
% 1.93/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a505) | (~c1_1(a505)) | (~c2_1(a505)) | c0_1(a514) | c2_1(a514) | (~c1_1(a514)))),
% 1.93/1.54 inference(quant_inst,[status(thm)],[])).
% 1.93/1.54 tff(1186,plain,
% 1.93/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a514) | c0_1(a505) | (~ndr1_0) | (~c1_1(a505)) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514)),
% 1.93/1.54 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 1.93/1.54 tff(1187,plain,
% 1.93/1.54 (~c1_1(a505)),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[1186, 112, 1180, 1179, 1178, 1177, 1176, 1175, 1165])).
% 1.93/1.54 tff(1188,plain,
% 1.93/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a514) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a514) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))),
% 1.93/1.54 inference(rewrite,[status(thm)],[])).
% 1.93/1.54 tff(1189,plain,
% 1.93/1.54 (((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a495) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a514) | c2_1(a514) | (~c1_1(a514))) <=> (c2_1(a514) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))),
% 1.93/1.54 inference(rewrite,[status(thm)],[])).
% 1.93/1.54 tff(1190,plain,
% 1.93/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a495) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a514) | c2_1(a514) | (~c1_1(a514)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a514) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514)))),
% 1.93/1.54 inference(monotonicity,[status(thm)],[1189])).
% 1.93/1.54 tff(1191,plain,
% 1.93/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a495) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a514) | c2_1(a514) | (~c1_1(a514)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a514) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514))),
% 1.93/1.54 inference(transitivity,[status(thm)],[1190, 1188])).
% 1.93/1.54 tff(1192,plain,
% 1.93/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a495) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a514) | c2_1(a514) | (~c1_1(a514)))),
% 1.93/1.54 inference(quant_inst,[status(thm)],[])).
% 1.93/1.54 tff(1193,plain,
% 1.93/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a514) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514)),
% 1.93/1.54 inference(modus_ponens,[status(thm)],[1192, 1191])).
% 1.93/1.54 tff(1194,plain,
% 1.93/1.54 (~c2_1(a495)),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[1193, 112, 1180, 1179, 1077, 1177, 1076, 1175, 1165])).
% 1.93/1.54 tff(1195,assumption,(c3_1(a505)), introduced(assumption)).
% 1.93/1.54 tff(1196,plain,
% 1.93/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a514) | c0_1(a505) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | c2_1(a495) | (~c3_1(a505)) | c1_1(a505) | (~c3_1(a514)) | (~c1_1(a514)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a514) | c0_1(a505) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | c2_1(a495) | (~c3_1(a505)) | c1_1(a505) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.93/1.54 inference(rewrite,[status(thm)],[])).
% 1.93/1.54 tff(1197,plain,
% 1.93/1.54 (((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a495) | c0_1(a495) | (~c1_1(a495)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505))) <=> (c2_1(a514) | c0_1(a505) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | c2_1(a495) | (~c3_1(a505)) | c1_1(a505) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.93/1.54 inference(rewrite,[status(thm)],[])).
% 1.93/1.54 tff(1198,plain,
% 1.93/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a495) | c0_1(a495) | (~c1_1(a495)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a514) | c0_1(a505) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | c2_1(a495) | (~c3_1(a505)) | c1_1(a505) | (~c3_1(a514)) | (~c1_1(a514))))),
% 1.93/1.54 inference(monotonicity,[status(thm)],[1197])).
% 1.93/1.54 tff(1199,plain,
% 1.93/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a495) | c0_1(a495) | (~c1_1(a495)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a514) | c0_1(a505) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | c2_1(a495) | (~c3_1(a505)) | c1_1(a505) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.93/1.54 inference(transitivity,[status(thm)],[1198, 1196])).
% 1.93/1.54 tff(1200,plain,
% 1.93/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c2_1(a495) | c0_1(a495) | (~c1_1(a495)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))),
% 1.93/1.54 inference(quant_inst,[status(thm)],[])).
% 1.93/1.54 tff(1201,plain,
% 1.93/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a514) | c0_1(a505) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | c2_1(a495) | (~c3_1(a505)) | c1_1(a505) | (~c3_1(a514)) | (~c1_1(a514))),
% 1.93/1.54 inference(modus_ponens,[status(thm)],[1200, 1199])).
% 1.93/1.54 tff(1202,plain,
% 1.93/1.54 ($false),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[1201, 112, 1180, 1179, 1195, 1077, 1177, 1176, 1076, 618, 1194, 1187])).
% 1.93/1.54 tff(1203,plain,(c0_1(a514) | (~c1_1(a514)) | (~c3_1(a514)) | (~c3_1(a505)) | (~c1_1(a495)) | c2_1(a514) | c0_1(a505) | c0_1(a495) | (~c2_1(a505))), inference(lemma,lemma(discharge,[]))).
% 1.93/1.54 tff(1204,plain,
% 1.93/1.54 (c0_1(a514)),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[1203, 1164, 1163, 1162, 1038, 1151, 1073, 1026, 1067])).
% 1.93/1.54 tff(1205,plain,
% 1.93/1.54 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)))),
% 1.93/1.54 inference(rewrite,[status(thm)],[])).
% 1.93/1.54 tff(1206,plain,
% 1.93/1.54 ((hskp15 | hskp10 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514))) <=> (hskp15 | hskp10 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)))),
% 1.93/1.54 inference(rewrite,[status(thm)],[])).
% 1.93/1.54 tff(1207,plain,
% 1.93/1.54 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514))))),
% 1.93/1.54 inference(monotonicity,[status(thm)],[1206])).
% 1.93/1.54 tff(1208,plain,
% 1.93/1.54 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)))),
% 1.93/1.54 inference(transitivity,[status(thm)],[1207, 1205])).
% 1.93/1.54 tff(1209,plain,
% 1.93/1.54 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)))),
% 1.93/1.54 inference(quant_inst,[status(thm)],[])).
% 1.93/1.54 tff(1210,plain,
% 1.93/1.54 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514))),
% 1.93/1.54 inference(modus_ponens,[status(thm)],[1209, 1208])).
% 1.93/1.54 tff(1211,plain,
% 1.93/1.54 (hskp15 | (~c0_1(a514))),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[1210, 112, 11, 1163, 1151, 42])).
% 1.93/1.54 tff(1212,plain,
% 1.93/1.54 (hskp15),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[1211, 1204])).
% 1.93/1.54 tff(1213,plain,
% 1.93/1.54 (~c3_1(a528)),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[469, 1212])).
% 1.93/1.54 tff(1214,plain,
% 1.93/1.54 (c0_1(a528)),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[491, 1212])).
% 1.93/1.54 tff(1215,plain,
% 1.93/1.54 (c1_1(a528)),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[480, 1212])).
% 1.93/1.54 tff(1216,plain,
% 1.93/1.54 (~hskp20),
% 1.93/1.54 inference(unit_resolution,[status(thm)],[1115, 1215, 1214, 1213, 263, 1039, 1027, 1038, 1026, 1020])).
% 1.93/1.54 tff(1217,plain,
% 1.93/1.55 (hskp20 | (~c2_1(a568))),
% 1.93/1.55 inference(unit_resolution,[status(thm)],[570, 112, 403, 1164, 1163, 402, 1151, 521])).
% 1.93/1.55 tff(1218,plain,
% 1.93/1.55 (~c2_1(a568)),
% 1.93/1.55 inference(unit_resolution,[status(thm)],[1217, 1216])).
% 1.93/1.55 tff(1219,plain,
% 1.93/1.55 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c0_1(a568)) | c2_1(a568))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c0_1(a568)) | c2_1(a568))),
% 1.93/1.55 inference(rewrite,[status(thm)],[])).
% 1.93/1.55 tff(1220,plain,
% 1.93/1.55 ((hskp10 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a505) | (~c1_1(a505)) | (~c3_1(a505))) <=> (hskp10 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c0_1(a568)) | c2_1(a568))),
% 1.93/1.55 inference(rewrite,[status(thm)],[])).
% 1.93/1.55 tff(1221,plain,
% 1.93/1.55 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a505) | (~c1_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c0_1(a568)) | c2_1(a568)))),
% 1.93/1.55 inference(monotonicity,[status(thm)],[1220])).
% 1.93/1.55 tff(1222,plain,
% 1.93/1.55 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a505) | (~c1_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c0_1(a568)) | c2_1(a568))),
% 1.93/1.55 inference(transitivity,[status(thm)],[1221, 1219])).
% 1.93/1.55 tff(1223,plain,
% 1.93/1.55 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a505) | (~c1_1(a505)) | (~c3_1(a505)))),
% 1.93/1.55 inference(quant_inst,[status(thm)],[])).
% 1.93/1.55 tff(1224,plain,
% 1.93/1.55 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c0_1(a568)) | c2_1(a568)),
% 1.93/1.55 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 1.93/1.55 tff(1225,plain,
% 1.93/1.55 (~c1_1(a505)),
% 1.93/1.55 inference(unit_resolution,[status(thm)],[1224, 112, 11, 401, 1162, 402, 1073, 53, 1218])).
% 1.93/1.55 tff(1226,plain,
% 1.93/1.55 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c2_1(a514) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c2_1(a514) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.93/1.55 inference(rewrite,[status(thm)],[])).
% 1.93/1.55 tff(1227,plain,
% 1.93/1.55 ((hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a505))) <=> (hskp20 | c2_1(a514) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.93/1.55 inference(rewrite,[status(thm)],[])).
% 1.93/1.55 tff(1228,plain,
% 1.93/1.55 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c2_1(a514) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514))))),
% 1.93/1.55 inference(monotonicity,[status(thm)],[1227])).
% 1.93/1.55 tff(1229,plain,
% 1.93/1.55 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c2_1(a514) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.93/1.55 inference(transitivity,[status(thm)],[1228, 1226])).
% 1.93/1.55 tff(1230,plain,
% 1.93/1.55 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))),
% 1.93/1.55 inference(quant_inst,[status(thm)],[])).
% 1.93/1.55 tff(1231,plain,
% 1.93/1.55 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c2_1(a514) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c2_1(a505)) | (~c3_1(a514)) | (~c1_1(a514))),
% 1.93/1.55 inference(modus_ponens,[status(thm)],[1230, 1229])).
% 1.93/1.55 tff(1232,plain,
% 1.93/1.55 ($false),
% 1.93/1.55 inference(unit_resolution,[status(thm)],[1231, 112, 1216, 1164, 1163, 1067, 1162, 1151, 521, 1225])).
% 1.93/1.55 tff(1233,plain,(c0_1(a502) | hskp10 | (~c0_1(a568)) | c1_1(a568) | (~c3_1(a568)) | c1_1(a502) | c3_1(a502) | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.93/1.55 tff(1234,plain,
% 1.93/1.55 (c1_1(a502)),
% 1.93/1.55 inference(unit_resolution,[status(thm)],[1233, 1027, 401, 402, 403, 263, 11, 404])).
% 1.93/1.55 tff(1235,plain,
% 1.93/1.55 (~hskp7),
% 1.93/1.55 inference(unit_resolution,[status(thm)],[338, 1234])).
% 1.93/1.55 tff(1236,assumption,(c1_1(a505)), introduced(assumption)).
% 1.93/1.55 tff(1237,plain,
% 1.93/1.55 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_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)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)))),
% 1.93/1.55 inference(bind,[status(th)],[])).
% 1.93/1.55 tff(1238,plain,
% 1.93/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_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)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.93/1.55 inference(quant_intro,[status(thm)],[1237])).
% 1.93/1.55 tff(1239,plain,
% 1.93/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_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)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.93/1.55 inference(rewrite,[status(thm)],[])).
% 1.93/1.55 tff(1240,plain,
% 1.93/1.55 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))))),
% 1.93/1.55 inference(bind,[status(th)],[])).
% 1.93/1.55 tff(1241,plain,
% 1.93/1.55 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.93/1.55 inference(quant_intro,[status(thm)],[1240])).
% 1.93/1.55 tff(1242,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 1.93/1.55 tff(1243,plain,
% 1.93/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.93/1.55 inference(modus_ponens,[status(thm)],[1242, 1241])).
% 1.93/1.55 tff(1244,plain,
% 1.93/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.93/1.55 inference(modus_ponens,[status(thm)],[1243, 1239])).
% 1.93/1.55 tff(1245,plain,(
% 1.93/1.55 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.98/1.55 inference(skolemize,[status(sab)],[1244])).
% 1.98/1.55 tff(1246,plain,
% 1.98/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[1245, 1238])).
% 1.98/1.55 tff(1247,plain,
% 1.98/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a505) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a505)) | (~c1_1(a505)) | (~c2_1(a505)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a505) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a505)) | (~c1_1(a505)) | (~c2_1(a505)))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(1248,plain,
% 1.98/1.55 (((~ndr1_0) | (~c2_1(a505)) | (~c3_1(a505)) | (~c1_1(a505)) | c0_1(a505) | (~c1_1(a505)) | (~c2_1(a505)) | c3_1(a496) | c0_1(a496) | c2_1(a496)) <=> (c0_1(a505) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a505)) | (~c1_1(a505)) | (~c2_1(a505)))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(1249,plain,
% 1.98/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a505)) | (~c3_1(a505)) | (~c1_1(a505)) | c0_1(a505) | (~c1_1(a505)) | (~c2_1(a505)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a505) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a505)) | (~c1_1(a505)) | (~c2_1(a505))))),
% 1.98/1.55 inference(monotonicity,[status(thm)],[1248])).
% 1.98/1.55 tff(1250,plain,
% 1.98/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a505)) | (~c3_1(a505)) | (~c1_1(a505)) | c0_1(a505) | (~c1_1(a505)) | (~c2_1(a505)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a505) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a505)) | (~c1_1(a505)) | (~c2_1(a505)))),
% 1.98/1.55 inference(transitivity,[status(thm)],[1249, 1247])).
% 1.98/1.55 tff(1251,plain,
% 1.98/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a505)) | (~c3_1(a505)) | (~c1_1(a505)) | c0_1(a505) | (~c1_1(a505)) | (~c2_1(a505)) | c3_1(a496) | c0_1(a496) | c2_1(a496))),
% 1.98/1.55 inference(quant_inst,[status(thm)],[])).
% 1.98/1.55 tff(1252,plain,
% 1.98/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a505) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a505)) | (~c1_1(a505)) | (~c2_1(a505))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[1251, 1250])).
% 1.98/1.55 tff(1253,plain,
% 1.98/1.55 (c0_1(a496) | (~c1_1(a505))),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[1252, 112, 1178, 1195, 1176, 634, 633, 1246])).
% 1.98/1.55 tff(1254,plain,
% 1.98/1.55 (c0_1(a496)),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[1253, 1236])).
% 1.98/1.55 tff(1255,plain,
% 1.98/1.55 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c0_1(a505) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a505)) | (~c1_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a505) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a505)) | (~c1_1(a505)))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(1256,plain,
% 1.98/1.55 ((hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a505) | (~c1_1(a505)) | (~c3_1(a505))) <=> (hskp10 | c0_1(a505) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a505)) | (~c1_1(a505)))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(1257,plain,
% 1.98/1.55 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a505) | (~c1_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c0_1(a505) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a505)) | (~c1_1(a505))))),
% 1.98/1.55 inference(monotonicity,[status(thm)],[1256])).
% 1.98/1.55 tff(1258,plain,
% 1.98/1.55 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a505) | (~c1_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a505) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a505)) | (~c1_1(a505)))),
% 1.98/1.55 inference(transitivity,[status(thm)],[1257, 1255])).
% 1.98/1.55 tff(1259,plain,
% 1.98/1.55 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a505) | (~c1_1(a505)) | (~c3_1(a505)))),
% 1.98/1.55 inference(quant_inst,[status(thm)],[])).
% 1.98/1.55 tff(1260,plain,
% 1.98/1.55 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a505) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a505)) | (~c1_1(a505))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[1259, 1258])).
% 1.98/1.55 tff(1261,plain,
% 1.98/1.55 ((~c0_1(a496)) | (~c1_1(a505))),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[1260, 112, 11, 1195, 1176, 632, 634, 53])).
% 1.98/1.55 tff(1262,plain,
% 1.98/1.55 ($false),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[1261, 1254, 1236])).
% 1.98/1.55 tff(1263,plain,((~c1_1(a505)) | hskp10 | (~c3_1(a505)) | c0_1(a505) | c1_1(a496) | c2_1(a496) | (~c2_1(a505)) | c3_1(a496)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.55 tff(1264,plain,
% 1.98/1.55 (~c1_1(a505)),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[1263, 1162, 11, 1073, 629, 628, 1067, 630])).
% 1.98/1.55 tff(1265,plain,
% 1.98/1.55 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c2_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c2_1(a568)))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(1266,plain,
% 1.98/1.55 ((hskp7 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505))) <=> (hskp7 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c2_1(a568)))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(1267,plain,
% 1.98/1.55 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c2_1(a568))))),
% 1.98/1.55 inference(monotonicity,[status(thm)],[1266])).
% 1.98/1.55 tff(1268,plain,
% 1.98/1.55 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c2_1(a568)))),
% 1.98/1.55 inference(transitivity,[status(thm)],[1267, 1265])).
% 1.98/1.55 tff(1269,plain,
% 1.98/1.55 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))),
% 1.98/1.55 inference(quant_inst,[status(thm)],[])).
% 1.98/1.55 tff(1270,plain,
% 1.98/1.55 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c2_1(a568))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[1269, 1268])).
% 1.98/1.55 tff(1271,plain,
% 1.98/1.55 (hskp7 | (~c2_1(a568))),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[1270, 112, 401, 1162, 402, 1073, 240, 1264])).
% 1.98/1.55 tff(1272,plain,
% 1.98/1.55 (~c2_1(a568)),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[1271, 1235])).
% 1.98/1.55 tff(1273,plain,
% 1.98/1.55 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.98/1.55 inference(bind,[status(th)],[])).
% 1.98/1.55 tff(1274,plain,
% 1.98/1.55 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.55 inference(quant_intro,[status(thm)],[1273])).
% 1.98/1.55 tff(1275,plain,
% 1.98/1.55 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(1276,plain,
% 1.98/1.55 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.98/1.55 inference(bind,[status(th)],[])).
% 1.98/1.55 tff(1277,plain,
% 1.98/1.55 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.55 inference(quant_intro,[status(thm)],[1276])).
% 1.98/1.55 tff(1278,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 1.98/1.55 tff(1279,plain,
% 1.98/1.55 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[1278, 1277])).
% 1.98/1.55 tff(1280,plain,
% 1.98/1.55 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[1279, 1275])).
% 1.98/1.55 tff(1281,plain,(
% 1.98/1.55 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.55 inference(skolemize,[status(sab)],[1280])).
% 1.98/1.55 tff(1282,plain,
% 1.98/1.55 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.55 inference(modus_ponens,[status(thm)],[1281, 1274])).
% 1.98/1.55 tff(1283,plain,
% 1.98/1.55 (hskp15),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[505, 1272])).
% 1.98/1.55 tff(1284,plain,
% 1.98/1.55 (~c3_1(a528)),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[469, 1283])).
% 1.98/1.55 tff(1285,plain,
% 1.98/1.55 (c1_1(a528)),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[480, 1283])).
% 1.98/1.55 tff(1286,plain,
% 1.98/1.55 (c0_1(a528)),
% 1.98/1.55 inference(unit_resolution,[status(thm)],[491, 1283])).
% 1.98/1.55 tff(1287,plain,
% 1.98/1.55 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a568) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | c2_1(a568))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a568) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | c2_1(a568))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(1288,plain,
% 1.98/1.55 ((hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a568) | c1_1(a568) | (~c0_1(a568))) <=> (hskp9 | c1_1(a568) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | c2_1(a568))),
% 1.98/1.55 inference(rewrite,[status(thm)],[])).
% 1.98/1.55 tff(1289,plain,
% 1.98/1.55 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a568) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | c2_1(a568)))),
% 1.98/1.55 inference(monotonicity,[status(thm)],[1288])).
% 1.98/1.55 tff(1290,plain,
% 1.98/1.55 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a568) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | c2_1(a568))),
% 1.98/1.55 inference(transitivity,[status(thm)],[1289, 1287])).
% 1.98/1.55 tff(1291,plain,
% 1.98/1.55 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)))),
% 1.98/1.55 inference(quant_inst,[status(thm)],[])).
% 1.98/1.55 tff(1292,plain,
% 1.98/1.55 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a568) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | c2_1(a568)),
% 1.98/1.56 inference(modus_ponens,[status(thm)],[1291, 1290])).
% 1.98/1.56 tff(1293,plain,
% 1.98/1.56 (hskp9),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[1292, 112, 401, 1286, 1285, 402, 1284, 1282, 1272])).
% 1.98/1.56 tff(1294,plain,
% 1.98/1.56 (~c0_1(a507)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[930, 1293])).
% 1.98/1.56 tff(1295,plain,
% 1.98/1.56 (c3_1(a507)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[941, 1293])).
% 1.98/1.56 tff(1296,plain,
% 1.98/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c3_1(a528) | c0_1(a507) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c3_1(a528) | c0_1(a507) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(1297,plain,
% 1.98/1.56 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507)) <=> (c3_1(a528) | c0_1(a507) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(1298,plain,
% 1.98/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c3_1(a528) | c0_1(a507) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528))))),
% 1.98/1.56 inference(monotonicity,[status(thm)],[1297])).
% 1.98/1.56 tff(1299,plain,
% 1.98/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c3_1(a528) | c0_1(a507) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.98/1.56 inference(transitivity,[status(thm)],[1298, 1296])).
% 1.98/1.56 tff(1300,plain,
% 1.98/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507))),
% 1.98/1.56 inference(quant_inst,[status(thm)],[])).
% 1.98/1.56 tff(1301,plain,
% 1.98/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c3_1(a528) | c0_1(a507) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528))),
% 1.98/1.56 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 1.98/1.56 tff(1302,plain,
% 1.98/1.56 (c2_1(a507)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[1301, 112, 1286, 1285, 1295, 1284, 1294, 263, 1234, 1027, 21])).
% 1.98/1.56 tff(1303,plain,
% 1.98/1.56 (~c1_1(a507)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[924, 1293])).
% 1.98/1.56 tff(1304,plain,
% 1.98/1.56 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 1.98/1.56 inference(bind,[status(th)],[])).
% 1.98/1.56 tff(1305,plain,
% 1.98/1.56 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.98/1.56 inference(quant_intro,[status(thm)],[1304])).
% 1.98/1.56 tff(1306,plain,
% 1.98/1.56 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(1307,plain,
% 1.98/1.56 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 1.98/1.56 inference(bind,[status(th)],[])).
% 1.98/1.56 tff(1308,plain,
% 1.98/1.56 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.98/1.56 inference(quant_intro,[status(thm)],[1307])).
% 1.98/1.56 tff(1309,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 1.98/1.56 tff(1310,plain,
% 1.98/1.56 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.98/1.56 inference(modus_ponens,[status(thm)],[1309, 1308])).
% 1.98/1.56 tff(1311,plain,
% 1.98/1.56 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.98/1.56 inference(modus_ponens,[status(thm)],[1310, 1306])).
% 1.98/1.56 tff(1312,plain,(
% 1.98/1.56 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.98/1.56 inference(skolemize,[status(sab)],[1311])).
% 1.98/1.56 tff(1313,plain,
% 1.98/1.56 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 1.98/1.56 inference(modus_ponens,[status(thm)],[1312, 1305])).
% 1.98/1.56 tff(1314,plain,
% 1.98/1.56 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c0_1(a568)) | c2_1(a568))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp14 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c0_1(a568)) | c2_1(a568))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(1315,plain,
% 1.98/1.56 ((hskp14 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505))) <=> (hskp14 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c0_1(a568)) | c2_1(a568))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(1316,plain,
% 1.98/1.56 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c0_1(a568)) | c2_1(a568)))),
% 1.98/1.56 inference(monotonicity,[status(thm)],[1315])).
% 1.98/1.56 tff(1317,plain,
% 1.98/1.56 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp14 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c0_1(a568)) | c2_1(a568))),
% 1.98/1.56 inference(transitivity,[status(thm)],[1316, 1314])).
% 1.98/1.56 tff(1318,plain,
% 1.98/1.56 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))),
% 1.98/1.56 inference(quant_inst,[status(thm)],[])).
% 1.98/1.56 tff(1319,plain,
% 1.98/1.56 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp14 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c0_1(a568)) | c2_1(a568)),
% 1.98/1.56 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 1.98/1.56 tff(1320,plain,
% 1.98/1.56 (hskp14),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[1319, 112, 401, 1067, 1162, 402, 1073, 1313, 1272])).
% 1.98/1.56 tff(1321,plain,
% 1.98/1.56 (~c1_1(a527)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[835, 1320])).
% 1.98/1.56 tff(1322,plain,
% 1.98/1.56 (c2_1(a527)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[864, 1320])).
% 1.98/1.56 tff(1323,plain,
% 1.98/1.56 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a527) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a527)) | (~c2_1(a527)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a527) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a527)) | (~c2_1(a527)))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(1324,plain,
% 1.98/1.56 ((hskp7 | (~ndr1_0) | c1_1(a527) | (~c2_1(a527)) | (~c0_1(a527)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507))) <=> (hskp7 | c1_1(a527) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a527)) | (~c2_1(a527)))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(1325,plain,
% 1.98/1.56 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a527) | (~c2_1(a527)) | (~c0_1(a527)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a527) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a527)) | (~c2_1(a527))))),
% 1.98/1.56 inference(monotonicity,[status(thm)],[1324])).
% 1.98/1.56 tff(1326,plain,
% 1.98/1.56 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a527) | (~c2_1(a527)) | (~c0_1(a527)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a527) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a527)) | (~c2_1(a527)))),
% 1.98/1.56 inference(transitivity,[status(thm)],[1325, 1323])).
% 1.98/1.56 tff(1327,plain,
% 1.98/1.56 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a527) | (~c2_1(a527)) | (~c0_1(a527)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))),
% 1.98/1.56 inference(quant_inst,[status(thm)],[])).
% 1.98/1.56 tff(1328,plain,
% 1.98/1.56 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a527) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a527)) | (~c2_1(a527))),
% 1.98/1.56 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 1.98/1.56 tff(1329,plain,
% 1.98/1.56 (~c0_1(a527)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[1328, 112, 1235, 1322, 1295, 1321, 1294, 1303, 240])).
% 1.98/1.56 tff(1330,plain,
% 1.98/1.56 (~c3_1(a527)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[829, 1320])).
% 1.98/1.56 tff(1331,assumption,(c1_1(a502)), introduced(assumption)).
% 1.98/1.56 tff(1332,plain,
% 1.98/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536)))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(1333,plain,
% 1.98/1.56 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)) | c0_1(a536) | (~c3_1(a536)) | c2_1(a536)) <=> (c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536)))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(1334,plain,
% 1.98/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)) | c0_1(a536) | (~c3_1(a536)) | c2_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536))))),
% 1.98/1.56 inference(monotonicity,[status(thm)],[1333])).
% 1.98/1.56 tff(1335,plain,
% 1.98/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)) | c0_1(a536) | (~c3_1(a536)) | c2_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536)))),
% 1.98/1.56 inference(transitivity,[status(thm)],[1334, 1332])).
% 1.98/1.56 tff(1336,plain,
% 1.98/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)) | c0_1(a536) | (~c3_1(a536)) | c2_1(a536))),
% 1.98/1.56 inference(quant_inst,[status(thm)],[])).
% 1.98/1.56 tff(1337,plain,
% 1.98/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a536))),
% 1.98/1.56 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 1.98/1.56 tff(1338,plain,
% 1.98/1.56 (~c3_1(a536)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[1337, 112, 1092, 1091, 1090, 1089, 1082, 263, 1331, 1027, 21])).
% 1.98/1.56 tff(1339,assumption,(~c0_1(a527)), introduced(assumption)).
% 1.98/1.56 tff(1340,assumption,(~c3_1(a527)), introduced(assumption)).
% 1.98/1.56 tff(1341,assumption,(~c1_1(a527)), introduced(assumption)).
% 1.98/1.56 tff(1342,plain,
% 1.98/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | c1_1(a527) | c3_1(a527) | (~ndr1_0) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c1_1(a527) | c3_1(a527) | (~ndr1_0) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(1343,plain,
% 1.98/1.56 (((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a527) | c1_1(a527) | c0_1(a527)) <=> (c0_1(a536) | c2_1(a536) | c3_1(a528) | c1_1(a527) | c3_1(a527) | (~ndr1_0) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(1344,plain,
% 1.98/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a527) | c1_1(a527) | c0_1(a527))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a536) | c2_1(a536) | c3_1(a528) | c1_1(a527) | c3_1(a527) | (~ndr1_0) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536)))),
% 1.98/1.56 inference(monotonicity,[status(thm)],[1343])).
% 1.98/1.56 tff(1345,plain,
% 1.98/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a527) | c1_1(a527) | c0_1(a527))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c1_1(a527) | c3_1(a527) | (~ndr1_0) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))),
% 1.98/1.56 inference(transitivity,[status(thm)],[1344, 1342])).
% 1.98/1.56 tff(1346,plain,
% 1.98/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a527) | c1_1(a527) | c0_1(a527))),
% 1.98/1.56 inference(quant_inst,[status(thm)],[])).
% 1.98/1.56 tff(1347,plain,
% 1.98/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a536) | c2_1(a536) | c3_1(a528) | c1_1(a527) | c3_1(a527) | (~ndr1_0) | c0_1(a527) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536)),
% 1.98/1.56 inference(modus_ponens,[status(thm)],[1346, 1345])).
% 1.98/1.56 tff(1348,plain,
% 1.98/1.56 (~c2_1(a528)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[1347, 112, 1091, 1090, 1089, 1082, 1341, 1340, 784, 1339, 1338])).
% 1.98/1.56 tff(1349,plain,
% 1.98/1.56 ($false),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[1113, 112, 1092, 1091, 1090, 1089, 1082, 996, 1348, 1338])).
% 1.98/1.56 tff(1350,plain,((~hskp20) | (~c0_1(a528)) | (~c1_1(a528)) | c3_1(a528) | c1_1(a527) | c3_1(a527) | c0_1(a527) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.56 tff(1351,plain,
% 1.98/1.56 (~hskp20),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[1350, 1286, 1285, 1284, 1321, 1330, 1329, 263, 1234, 1027])).
% 1.98/1.56 tff(1352,plain,
% 1.98/1.56 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | c1_1(a527) | c3_1(a527) | (~ndr1_0) | (~c2_1(a527)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a527) | c3_1(a527) | (~ndr1_0) | (~c2_1(a527)))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(1353,plain,
% 1.98/1.56 ((hskp20 | hskp12 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c2_1(a527))) <=> (hskp20 | hskp12 | c1_1(a527) | c3_1(a527) | (~ndr1_0) | (~c2_1(a527)))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(1354,plain,
% 1.98/1.56 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c2_1(a527)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | c1_1(a527) | c3_1(a527) | (~ndr1_0) | (~c2_1(a527))))),
% 1.98/1.56 inference(monotonicity,[status(thm)],[1353])).
% 1.98/1.56 tff(1355,plain,
% 1.98/1.56 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c2_1(a527)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a527) | c3_1(a527) | (~ndr1_0) | (~c2_1(a527)))),
% 1.98/1.56 inference(transitivity,[status(thm)],[1354, 1352])).
% 1.98/1.56 tff(1356,plain,
% 1.98/1.56 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a527) | c1_1(a527) | (~c2_1(a527)))),
% 1.98/1.56 inference(quant_inst,[status(thm)],[])).
% 1.98/1.56 tff(1357,plain,
% 1.98/1.56 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a527) | c3_1(a527) | (~ndr1_0) | (~c2_1(a527))),
% 1.98/1.56 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 1.98/1.56 tff(1358,plain,
% 1.98/1.56 (hskp20 | hskp12),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[1357, 112, 1322, 1321, 1330, 1126])).
% 1.98/1.56 tff(1359,plain,
% 1.98/1.56 (hskp12),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[1358, 1351])).
% 1.98/1.56 tff(1360,plain,
% 1.98/1.56 (~c2_1(a514)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[541, 1359])).
% 1.98/1.56 tff(1361,plain,
% 1.98/1.56 (c3_1(a514)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[552, 1359])).
% 1.98/1.56 tff(1362,plain,
% 1.98/1.56 (c1_1(a514)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[563, 1359])).
% 1.98/1.56 tff(1363,plain,
% 1.98/1.56 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c2_1(a514) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c2_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c2_1(a514) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c2_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(1364,plain,
% 1.98/1.56 ((hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a507) | (~c2_1(a507)) | (~c3_1(a507))) <=> (hskp20 | c2_1(a514) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c2_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(1365,plain,
% 1.98/1.56 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a507) | (~c2_1(a507)) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c2_1(a514) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c2_1(a507)) | (~c3_1(a514)) | (~c1_1(a514))))),
% 1.98/1.56 inference(monotonicity,[status(thm)],[1364])).
% 1.98/1.56 tff(1366,plain,
% 1.98/1.56 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a507) | (~c2_1(a507)) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c2_1(a514) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c2_1(a507)) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.98/1.56 inference(transitivity,[status(thm)],[1365, 1363])).
% 1.98/1.56 tff(1367,plain,
% 1.98/1.56 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c1_1(a507) | (~c2_1(a507)) | (~c3_1(a507)))),
% 1.98/1.56 inference(quant_inst,[status(thm)],[])).
% 1.98/1.56 tff(1368,plain,
% 1.98/1.56 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c2_1(a514) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c2_1(a507)) | (~c3_1(a514)) | (~c1_1(a514))),
% 1.98/1.56 inference(modus_ponens,[status(thm)],[1367, 1366])).
% 1.98/1.56 tff(1369,plain,
% 1.98/1.56 ($false),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[1368, 112, 1351, 1362, 1361, 1295, 1360, 1303, 521, 1302])).
% 1.98/1.56 tff(1370,plain,(c3_1(a502) | c0_1(a502) | (~c0_1(a568)) | c1_1(a568) | hskp10 | (~c3_1(a568)) | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.98/1.56 tff(1371,plain,
% 1.98/1.56 (c3_1(a502)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[1370, 263, 401, 402, 11, 403, 404])).
% 1.98/1.56 tff(1372,plain,
% 1.98/1.56 (~hskp7),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[332, 1371])).
% 1.98/1.56 tff(1373,plain,
% 1.98/1.56 (~c2_1(a568)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[1271, 1372])).
% 1.98/1.56 tff(1374,plain,
% 1.98/1.56 (hskp15),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[505, 1373])).
% 1.98/1.56 tff(1375,plain,
% 1.98/1.56 (~c3_1(a528)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[469, 1374])).
% 1.98/1.56 tff(1376,plain,
% 1.98/1.56 (c1_1(a528)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[480, 1374])).
% 1.98/1.56 tff(1377,plain,
% 1.98/1.56 (c0_1(a528)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[491, 1374])).
% 1.98/1.56 tff(1378,plain,
% 1.98/1.56 (hskp9),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[1292, 112, 401, 1377, 1376, 402, 1375, 1282, 1373])).
% 1.98/1.56 tff(1379,plain,
% 1.98/1.56 (~c0_1(a507)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[930, 1378])).
% 1.98/1.56 tff(1380,plain,
% 1.98/1.56 (c3_1(a507)),
% 1.98/1.56 inference(unit_resolution,[status(thm)],[941, 1378])).
% 1.98/1.56 tff(1381,plain,
% 1.98/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c3_1(a528) | c0_1(a507) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c3_1(a528) | c0_1(a507) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(1382,plain,
% 1.98/1.56 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507)) <=> (c3_1(a528) | c0_1(a507) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.98/1.56 inference(rewrite,[status(thm)],[])).
% 1.98/1.56 tff(1383,plain,
% 1.98/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c3_1(a528) | c0_1(a507) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528))))),
% 1.98/1.57 inference(monotonicity,[status(thm)],[1382])).
% 1.98/1.57 tff(1384,plain,
% 1.98/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c3_1(a528) | c0_1(a507) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.98/1.57 inference(transitivity,[status(thm)],[1383, 1381])).
% 1.98/1.57 tff(1385,plain,
% 1.98/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507))),
% 1.98/1.57 inference(quant_inst,[status(thm)],[])).
% 1.98/1.57 tff(1386,plain,
% 1.98/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c3_1(a528) | c0_1(a507) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1385, 1384])).
% 1.98/1.57 tff(1387,plain,
% 1.98/1.57 (c2_1(a507)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1386, 112, 1377, 1376, 1380, 1038, 1375, 1379, 1026, 1020, 21])).
% 1.98/1.57 tff(1388,plain,
% 1.98/1.57 (~c1_1(a507)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[924, 1378])).
% 1.98/1.57 tff(1389,plain,
% 1.98/1.57 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))))),
% 1.98/1.57 inference(bind,[status(th)],[])).
% 1.98/1.57 tff(1390,plain,
% 1.98/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.98/1.57 inference(quant_intro,[status(thm)],[1389])).
% 1.98/1.57 tff(1391,plain,
% 1.98/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1392,plain,
% 1.98/1.57 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))))),
% 1.98/1.57 inference(bind,[status(th)],[])).
% 1.98/1.57 tff(1393,plain,
% 1.98/1.57 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.98/1.57 inference(quant_intro,[status(thm)],[1392])).
% 1.98/1.57 tff(1394,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 1.98/1.57 tff(1395,plain,
% 1.98/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1394, 1393])).
% 1.98/1.57 tff(1396,plain,
% 1.98/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1395, 1391])).
% 1.98/1.57 tff(1397,plain,(
% 1.98/1.57 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.98/1.57 inference(skolemize,[status(sab)],[1396])).
% 1.98/1.57 tff(1398,plain,
% 1.98/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1397, 1390])).
% 1.98/1.57 tff(1399,plain,
% 1.98/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | (~c3_1(a502)) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | (~c3_1(a502)) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1400,plain,
% 1.98/1.57 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a502) | (~c3_1(a502)) | (~c1_1(a502))) <=> (c1_1(a568) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | (~c3_1(a502)) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1401,plain,
% 1.98/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a502) | (~c3_1(a502)) | (~c1_1(a502)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | (~c3_1(a502)) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.98/1.57 inference(monotonicity,[status(thm)],[1400])).
% 1.98/1.57 tff(1402,plain,
% 1.98/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a502) | (~c3_1(a502)) | (~c1_1(a502)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | (~c3_1(a502)) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.57 inference(transitivity,[status(thm)],[1401, 1399])).
% 1.98/1.57 tff(1403,plain,
% 1.98/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a502) | (~c3_1(a502)) | (~c1_1(a502)))),
% 1.98/1.57 inference(quant_inst,[status(thm)],[])).
% 1.98/1.57 tff(1404,plain,
% 1.98/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c3_1(a528) | c0_1(a502) | (~c1_1(a502)) | (~c3_1(a502)) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 1.98/1.57 tff(1405,plain,
% 1.98/1.57 (~c1_1(a502)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1404, 112, 401, 403, 1377, 1376, 402, 1375, 263, 1371, 1398])).
% 1.98/1.57 tff(1406,plain,
% 1.98/1.57 (hskp14),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1319, 112, 401, 1067, 1162, 402, 1073, 1313, 1373])).
% 1.98/1.57 tff(1407,plain,
% 1.98/1.57 (~c1_1(a527)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[835, 1406])).
% 1.98/1.57 tff(1408,plain,
% 1.98/1.57 (c2_1(a527)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[864, 1406])).
% 1.98/1.57 tff(1409,plain,
% 1.98/1.57 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a527) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a527)) | (~c2_1(a527)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a527) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a527)) | (~c2_1(a527)))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1410,plain,
% 1.98/1.57 ((hskp7 | (~ndr1_0) | c1_1(a527) | (~c2_1(a527)) | (~c0_1(a527)) | c1_1(a502) | c0_1(a502) | (~c3_1(a502))) <=> (hskp7 | c1_1(a527) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a527)) | (~c2_1(a527)))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1411,plain,
% 1.98/1.57 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a527) | (~c2_1(a527)) | (~c0_1(a527)) | c1_1(a502) | c0_1(a502) | (~c3_1(a502)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a527) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a527)) | (~c2_1(a527))))),
% 1.98/1.57 inference(monotonicity,[status(thm)],[1410])).
% 1.98/1.57 tff(1412,plain,
% 1.98/1.57 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a527) | (~c2_1(a527)) | (~c0_1(a527)) | c1_1(a502) | c0_1(a502) | (~c3_1(a502)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a527) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a527)) | (~c2_1(a527)))),
% 1.98/1.57 inference(transitivity,[status(thm)],[1411, 1409])).
% 1.98/1.57 tff(1413,plain,
% 1.98/1.57 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a527) | (~c2_1(a527)) | (~c0_1(a527)) | c1_1(a502) | c0_1(a502) | (~c3_1(a502)))),
% 1.98/1.57 inference(quant_inst,[status(thm)],[])).
% 1.98/1.57 tff(1414,plain,
% 1.98/1.57 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a527) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a527)) | (~c2_1(a527))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 1.98/1.57 tff(1415,plain,
% 1.98/1.57 (~c0_1(a527)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1414, 112, 1372, 1408, 1407, 263, 1405, 1371, 240])).
% 1.98/1.57 tff(1416,plain,
% 1.98/1.57 (~c3_1(a527)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[829, 1406])).
% 1.98/1.57 tff(1417,plain,
% 1.98/1.57 (~c2_1(a528)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1347, 112, 1091, 1090, 1089, 1082, 1341, 1340, 784, 1339, 1099])).
% 1.98/1.57 tff(1418,plain,
% 1.98/1.57 ($false),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1113, 112, 1092, 1091, 1090, 1089, 1082, 996, 1417, 1099])).
% 1.98/1.57 tff(1419,plain,((~hskp20) | (~c0_1(a528)) | (~c1_1(a528)) | c3_1(a528) | c1_1(a527) | c3_1(a527) | c0_1(a527) | (~c1_1(a495)) | c0_1(a495) | c3_1(a495)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.57 tff(1420,plain,
% 1.98/1.57 (~hskp20),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1419, 1377, 1376, 1375, 1407, 1416, 1415, 1038, 1026, 1020])).
% 1.98/1.57 tff(1421,plain,
% 1.98/1.57 (hskp20 | hskp12),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1357, 112, 1408, 1407, 1416, 1126])).
% 1.98/1.57 tff(1422,plain,
% 1.98/1.57 (hskp12),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1421, 1420])).
% 1.98/1.57 tff(1423,plain,
% 1.98/1.57 (~c2_1(a514)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[541, 1422])).
% 1.98/1.57 tff(1424,plain,
% 1.98/1.57 (c3_1(a514)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[552, 1422])).
% 1.98/1.57 tff(1425,plain,
% 1.98/1.57 (c1_1(a514)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[563, 1422])).
% 1.98/1.57 tff(1426,plain,
% 1.98/1.57 ($false),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1368, 112, 1420, 1425, 1424, 1380, 1423, 1388, 521, 1387])).
% 1.98/1.57 tff(1427,plain,(c0_1(a502) | (~c0_1(a568)) | c1_1(a568) | (~c3_1(a568)) | hskp10 | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.98/1.57 tff(1428,plain,
% 1.98/1.57 (c0_1(a502)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1427, 404, 402, 403, 11, 401])).
% 1.98/1.57 tff(1429,plain,
% 1.98/1.57 (~hskp7),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[709, 1428])).
% 1.98/1.57 tff(1430,plain,
% 1.98/1.57 (~c2_1(a568)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1271, 1429])).
% 1.98/1.57 tff(1431,plain,
% 1.98/1.57 (hskp15),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[505, 1430])).
% 1.98/1.57 tff(1432,plain,
% 1.98/1.57 (~c3_1(a528)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[469, 1431])).
% 1.98/1.57 tff(1433,plain,
% 1.98/1.57 (c1_1(a528)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[480, 1431])).
% 1.98/1.57 tff(1434,plain,
% 1.98/1.57 (c0_1(a528)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[491, 1431])).
% 1.98/1.57 tff(1435,plain,
% 1.98/1.57 (hskp9),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1292, 112, 401, 1434, 1433, 402, 1432, 1282, 1430])).
% 1.98/1.57 tff(1436,plain,
% 1.98/1.57 (~c0_1(a507)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[930, 1435])).
% 1.98/1.57 tff(1437,plain,
% 1.98/1.57 (c3_1(a507)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[941, 1435])).
% 1.98/1.57 tff(1438,plain,
% 1.98/1.57 (c2_1(a507)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1386, 112, 1434, 1433, 1437, 1038, 1432, 1436, 1026, 1020, 21])).
% 1.98/1.57 tff(1439,plain,
% 1.98/1.57 (~c1_1(a507)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[924, 1435])).
% 1.98/1.57 tff(1440,plain,
% 1.98/1.57 (hskp14),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1319, 112, 401, 1067, 1162, 402, 1073, 1313, 1430])).
% 1.98/1.57 tff(1441,plain,
% 1.98/1.57 (~c3_1(a527)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[829, 1440])).
% 1.98/1.57 tff(1442,plain,
% 1.98/1.57 (~c1_1(a527)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[835, 1440])).
% 1.98/1.57 tff(1443,plain,
% 1.98/1.57 (c2_1(a527)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[864, 1440])).
% 1.98/1.57 tff(1444,plain,
% 1.98/1.57 (~c0_1(a527)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1328, 112, 1429, 1443, 1437, 1442, 1436, 1439, 240])).
% 1.98/1.57 tff(1445,plain,
% 1.98/1.57 (~hskp20),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1419, 1444, 1433, 1432, 1442, 1441, 1434, 1038, 1026, 1020])).
% 1.98/1.57 tff(1446,plain,
% 1.98/1.57 (hskp20 | hskp12),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1357, 112, 1443, 1442, 1441, 1126])).
% 1.98/1.57 tff(1447,plain,
% 1.98/1.57 (hskp12),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1446, 1445])).
% 1.98/1.57 tff(1448,plain,
% 1.98/1.57 (~c2_1(a514)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[541, 1447])).
% 1.98/1.57 tff(1449,plain,
% 1.98/1.57 (c3_1(a514)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[552, 1447])).
% 1.98/1.57 tff(1450,plain,
% 1.98/1.57 (c1_1(a514)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[563, 1447])).
% 1.98/1.57 tff(1451,plain,
% 1.98/1.57 ($false),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1368, 112, 1445, 1450, 1449, 1437, 1448, 1439, 521, 1438])).
% 1.98/1.57 tff(1452,plain,(hskp13 | (~c0_1(a568)) | c1_1(a568) | hskp10 | (~c3_1(a568))), inference(lemma,lemma(discharge,[]))).
% 1.98/1.57 tff(1453,plain,
% 1.98/1.57 (hskp13),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1452, 222, 252, 11, 211])).
% 1.98/1.57 tff(1454,plain,
% 1.98/1.57 (((~hskp13) | (~c3_1(a520))) <=> ((~hskp13) | (~c3_1(a520)))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1455,plain,
% 1.98/1.57 (((~c3_1(a520)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a520)))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1456,axiom,((~c3_1(a520)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 1.98/1.57 tff(1457,plain,
% 1.98/1.57 ((~hskp13) | (~c3_1(a520))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1456, 1455])).
% 1.98/1.57 tff(1458,plain,
% 1.98/1.57 ((~hskp13) | (~c3_1(a520))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1457, 1454])).
% 1.98/1.57 tff(1459,plain,
% 1.98/1.57 (~c3_1(a520)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1458, 1453])).
% 1.98/1.57 tff(1460,plain,
% 1.98/1.57 (((~hskp13) | c2_1(a520)) <=> ((~hskp13) | c2_1(a520))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1461,axiom,((~hskp13) | c2_1(a520)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 1.98/1.57 tff(1462,plain,
% 1.98/1.57 ((~hskp13) | c2_1(a520)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1461, 1460])).
% 1.98/1.57 tff(1463,plain,
% 1.98/1.57 ((~hskp13) | c2_1(a520)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1462, 1460])).
% 1.98/1.57 tff(1464,plain,
% 1.98/1.57 ((~hskp13) | c2_1(a520)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1463, 1460])).
% 1.98/1.57 tff(1465,plain,
% 1.98/1.57 ((~hskp13) | c2_1(a520)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1464, 1460])).
% 1.98/1.57 tff(1466,plain,
% 1.98/1.57 ((~hskp13) | c2_1(a520)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1465, 1460])).
% 1.98/1.57 tff(1467,plain,
% 1.98/1.57 ((~hskp13) | c2_1(a520)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1466, 1460])).
% 1.98/1.57 tff(1468,plain,
% 1.98/1.57 ((~hskp13) | c2_1(a520)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1467, 1460])).
% 1.98/1.57 tff(1469,plain,
% 1.98/1.57 ((~hskp13) | c2_1(a520)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1468, 1460])).
% 1.98/1.57 tff(1470,plain,
% 1.98/1.57 (c2_1(a520)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1469, 1453])).
% 1.98/1.57 tff(1471,plain,
% 1.98/1.57 (((~hskp13) | c0_1(a520)) <=> ((~hskp13) | c0_1(a520))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1472,axiom,((~hskp13) | c0_1(a520)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 1.98/1.57 tff(1473,plain,
% 1.98/1.57 ((~hskp13) | c0_1(a520)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1472, 1471])).
% 1.98/1.57 tff(1474,plain,
% 1.98/1.57 ((~hskp13) | c0_1(a520)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1473, 1471])).
% 1.98/1.57 tff(1475,plain,
% 1.98/1.57 ((~hskp13) | c0_1(a520)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1474, 1471])).
% 1.98/1.57 tff(1476,plain,
% 1.98/1.57 ((~hskp13) | c0_1(a520)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1475, 1471])).
% 1.98/1.57 tff(1477,plain,
% 1.98/1.57 ((~hskp13) | c0_1(a520)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1476, 1471])).
% 1.98/1.57 tff(1478,plain,
% 1.98/1.57 ((~hskp13) | c0_1(a520)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1477, 1471])).
% 1.98/1.57 tff(1479,plain,
% 1.98/1.57 ((~hskp13) | c0_1(a520)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1478, 1471])).
% 1.98/1.57 tff(1480,plain,
% 1.98/1.57 ((~hskp13) | c0_1(a520)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1479, 1471])).
% 1.98/1.57 tff(1481,plain,
% 1.98/1.57 (c0_1(a520)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1480, 1453])).
% 1.98/1.57 tff(1482,plain,
% 1.98/1.57 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c3_1(a520) | c0_1(a502) | c1_1(a502) | (~ndr1_0) | (~c2_1(a502)) | (~c0_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c3_1(a520) | c0_1(a502) | c1_1(a502) | (~ndr1_0) | (~c2_1(a502)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1483,plain,
% 1.98/1.57 ((hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | (~c2_1(a502))) <=> (hskp4 | c3_1(a520) | c0_1(a502) | c1_1(a502) | (~ndr1_0) | (~c2_1(a502)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1484,plain,
% 1.98/1.57 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | (~c2_1(a502)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c3_1(a520) | c0_1(a502) | c1_1(a502) | (~ndr1_0) | (~c2_1(a502)) | (~c0_1(a520)) | (~c2_1(a520))))),
% 1.98/1.57 inference(monotonicity,[status(thm)],[1483])).
% 1.98/1.57 tff(1485,plain,
% 1.98/1.57 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | (~c2_1(a502)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c3_1(a520) | c0_1(a502) | c1_1(a502) | (~ndr1_0) | (~c2_1(a502)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.98/1.57 inference(transitivity,[status(thm)],[1484, 1482])).
% 1.98/1.57 tff(1486,plain,
% 1.98/1.57 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | (~c2_1(a502)))),
% 1.98/1.57 inference(quant_inst,[status(thm)],[])).
% 1.98/1.57 tff(1487,plain,
% 1.98/1.57 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c3_1(a520) | c0_1(a502) | c1_1(a502) | (~ndr1_0) | (~c2_1(a502)) | (~c0_1(a520)) | (~c2_1(a520))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 1.98/1.57 tff(1488,plain,
% 1.98/1.57 (hskp4),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1487, 112, 1481, 1470, 1459, 263, 339, 400, 390])).
% 1.98/1.57 tff(1489,plain,
% 1.98/1.57 (((~hskp4) | (~c0_1(a498))) <=> ((~hskp4) | (~c0_1(a498)))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1490,plain,
% 1.98/1.57 (((~c0_1(a498)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a498)))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1491,axiom,((~c0_1(a498)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 1.98/1.57 tff(1492,plain,
% 1.98/1.57 ((~hskp4) | (~c0_1(a498))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1491, 1490])).
% 1.98/1.57 tff(1493,plain,
% 1.98/1.57 ((~hskp4) | (~c0_1(a498))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1492, 1489])).
% 1.98/1.57 tff(1494,plain,
% 1.98/1.57 (~c0_1(a498)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1493, 1488])).
% 1.98/1.57 tff(1495,plain,
% 1.98/1.57 (((~hskp4) | c1_1(a498)) <=> ((~hskp4) | c1_1(a498))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1496,axiom,((~hskp4) | c1_1(a498)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 1.98/1.57 tff(1497,plain,
% 1.98/1.57 ((~hskp4) | c1_1(a498)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1496, 1495])).
% 1.98/1.57 tff(1498,plain,
% 1.98/1.57 ((~hskp4) | c1_1(a498)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1497, 1495])).
% 1.98/1.57 tff(1499,plain,
% 1.98/1.57 ((~hskp4) | c1_1(a498)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1498, 1495])).
% 1.98/1.57 tff(1500,plain,
% 1.98/1.57 ((~hskp4) | c1_1(a498)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1499, 1495])).
% 1.98/1.57 tff(1501,plain,
% 1.98/1.57 ((~hskp4) | c1_1(a498)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1500, 1495])).
% 1.98/1.57 tff(1502,plain,
% 1.98/1.57 ((~hskp4) | c1_1(a498)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1501, 1495])).
% 1.98/1.57 tff(1503,plain,
% 1.98/1.57 ((~hskp4) | c1_1(a498)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1502, 1495])).
% 1.98/1.57 tff(1504,plain,
% 1.98/1.57 ((~hskp4) | c1_1(a498)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1503, 1495])).
% 1.98/1.57 tff(1505,plain,
% 1.98/1.57 (c1_1(a498)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1504, 1488])).
% 1.98/1.57 tff(1506,plain,
% 1.98/1.57 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c0_1(a498) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a498)) | (~c1_1(a498)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a498) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a498)) | (~c1_1(a498)))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1507,plain,
% 1.98/1.57 ((hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a498) | (~c1_1(a498)) | (~c3_1(a498))) <=> (hskp10 | c0_1(a498) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a498)) | (~c1_1(a498)))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1508,plain,
% 1.98/1.57 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a498) | (~c1_1(a498)) | (~c3_1(a498)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c0_1(a498) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a498)) | (~c1_1(a498))))),
% 1.98/1.57 inference(monotonicity,[status(thm)],[1507])).
% 1.98/1.57 tff(1509,plain,
% 1.98/1.57 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a498) | (~c1_1(a498)) | (~c3_1(a498)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a498) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a498)) | (~c1_1(a498)))),
% 1.98/1.57 inference(transitivity,[status(thm)],[1508, 1506])).
% 1.98/1.57 tff(1510,plain,
% 1.98/1.57 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c0_1(a498) | (~c1_1(a498)) | (~c3_1(a498)))),
% 1.98/1.57 inference(quant_inst,[status(thm)],[])).
% 1.98/1.57 tff(1511,plain,
% 1.98/1.57 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c0_1(a498) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a498)) | (~c1_1(a498))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1510, 1509])).
% 1.98/1.57 tff(1512,plain,
% 1.98/1.57 (~c3_1(a498)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1511, 112, 11, 1505, 1494, 382, 369, 53, 376])).
% 1.98/1.57 tff(1513,plain,
% 1.98/1.57 (((~hskp4) | (~c2_1(a498))) <=> ((~hskp4) | (~c2_1(a498)))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1514,plain,
% 1.98/1.57 (((~c2_1(a498)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a498)))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1515,axiom,((~c2_1(a498)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 1.98/1.57 tff(1516,plain,
% 1.98/1.57 ((~hskp4) | (~c2_1(a498))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 1.98/1.57 tff(1517,plain,
% 1.98/1.57 ((~hskp4) | (~c2_1(a498))),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1516, 1513])).
% 1.98/1.57 tff(1518,plain,
% 1.98/1.57 (~c2_1(a498)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1517, 1488])).
% 1.98/1.57 tff(1519,plain,
% 1.98/1.57 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1520,plain,
% 1.98/1.57 ((hskp11 | hskp10 | (~ndr1_0) | c3_1(a498) | c2_1(a498) | c0_1(a498)) <=> (hskp11 | hskp10 | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1521,plain,
% 1.98/1.57 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a498) | c2_1(a498) | c0_1(a498))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498)))),
% 1.98/1.57 inference(monotonicity,[status(thm)],[1520])).
% 1.98/1.57 tff(1522,plain,
% 1.98/1.57 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a498) | c2_1(a498) | c0_1(a498))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498))),
% 1.98/1.57 inference(transitivity,[status(thm)],[1521, 1519])).
% 1.98/1.57 tff(1523,plain,
% 1.98/1.57 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a498) | c2_1(a498) | c0_1(a498))),
% 1.98/1.57 inference(quant_inst,[status(thm)],[])).
% 1.98/1.57 tff(1524,plain,
% 1.98/1.57 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498)),
% 1.98/1.57 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 1.98/1.57 tff(1525,plain,
% 1.98/1.57 ($false),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1524, 112, 163, 11, 1494, 1518, 10, 1512])).
% 1.98/1.57 tff(1526,plain,(hskp15 | hskp10 | c0_1(a502) | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.98/1.57 tff(1527,plain,
% 1.98/1.57 (hskp15),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1526, 263, 11, 32])).
% 1.98/1.57 tff(1528,plain,
% 1.98/1.57 (hskp13),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1452, 401, 402, 11, 403])).
% 1.98/1.57 tff(1529,plain,
% 1.98/1.57 (c0_1(a520)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1480, 1528])).
% 1.98/1.57 tff(1530,plain,
% 1.98/1.57 (~c3_1(a520)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1458, 1528])).
% 1.98/1.57 tff(1531,plain,
% 1.98/1.57 (c2_1(a520)),
% 1.98/1.57 inference(unit_resolution,[status(thm)],[1469, 1528])).
% 1.98/1.57 tff(1532,assumption,(c2_1(a520)), introduced(assumption)).
% 1.98/1.57 tff(1533,assumption,(c0_1(a520)), introduced(assumption)).
% 1.98/1.57 tff(1534,plain,
% 1.98/1.57 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.98/1.57 inference(rewrite,[status(thm)],[])).
% 1.98/1.57 tff(1535,plain,
% 1.98/1.57 ((hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | c3_1(a502)) <=> (hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.98/1.58 inference(rewrite,[status(thm)],[])).
% 1.98/1.58 tff(1536,plain,
% 1.98/1.58 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520))))),
% 1.98/1.58 inference(monotonicity,[status(thm)],[1535])).
% 1.98/1.58 tff(1537,plain,
% 1.98/1.58 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.98/1.58 inference(transitivity,[status(thm)],[1536, 1534])).
% 1.98/1.58 tff(1538,plain,
% 1.98/1.58 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | c3_1(a502))),
% 1.98/1.58 inference(quant_inst,[status(thm)],[])).
% 1.98/1.58 tff(1539,plain,
% 1.98/1.58 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520))),
% 1.98/1.58 inference(modus_ponens,[status(thm)],[1538, 1537])).
% 1.98/1.58 tff(1540,plain,
% 1.98/1.58 (hskp2 | c3_1(a502) | (~c1_1(a520))),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1539, 112, 1533, 1532, 263, 1039, 320])).
% 1.98/1.58 tff(1541,plain,
% 1.98/1.58 (~c1_1(a520)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1540, 453, 1027])).
% 1.98/1.58 tff(1542,assumption,(~c3_1(a520)), introduced(assumption)).
% 1.98/1.58 tff(1543,plain,
% 1.98/1.58 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))),
% 1.98/1.58 inference(rewrite,[status(thm)],[])).
% 1.98/1.58 tff(1544,plain,
% 1.98/1.58 ((hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | c3_1(a502)) <=> (hskp1 | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))),
% 1.98/1.58 inference(rewrite,[status(thm)],[])).
% 1.98/1.58 tff(1545,plain,
% 1.98/1.58 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520))))),
% 1.98/1.58 inference(monotonicity,[status(thm)],[1544])).
% 1.98/1.58 tff(1546,plain,
% 1.98/1.58 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))),
% 1.98/1.58 inference(transitivity,[status(thm)],[1545, 1543])).
% 1.98/1.58 tff(1547,plain,
% 1.98/1.58 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a502) | c0_1(a502) | c3_1(a502))),
% 1.98/1.58 inference(quant_inst,[status(thm)],[])).
% 1.98/1.58 tff(1548,plain,
% 1.98/1.58 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520))),
% 1.98/1.58 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 1.98/1.58 tff(1549,plain,
% 1.98/1.58 (hskp1 | c3_1(a502) | c1_1(a520)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1548, 112, 1533, 1542, 263, 1039, 645])).
% 1.98/1.58 tff(1550,plain,
% 1.98/1.58 (hskp1),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1549, 1541, 1027])).
% 1.98/1.58 tff(1551,assumption,(hskp1), introduced(assumption)).
% 1.98/1.58 tff(1552,plain,
% 1.98/1.58 (~c0_1(a495)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1025, 1551])).
% 1.98/1.58 tff(1553,plain,
% 1.98/1.58 (c1_1(a495)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1037, 1551])).
% 1.98/1.58 tff(1554,plain,
% 1.98/1.58 (~c3_1(a495)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1019, 1551])).
% 1.98/1.58 tff(1555,plain,
% 1.98/1.58 ($false),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1115, 1554, 1553, 263, 1082, 1091, 1092, 1039, 1027, 1083, 1552])).
% 1.98/1.58 tff(1556,plain,((~hskp1) | c0_1(a502) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a502) | c3_1(a502) | (~hskp20)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.58 tff(1557,plain,
% 1.98/1.58 (~hskp20),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1556, 1550, 1082, 1091, 1092, 1039, 1027, 263])).
% 1.98/1.58 tff(1558,plain,
% 1.98/1.58 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)))),
% 1.98/1.58 inference(rewrite,[status(thm)],[])).
% 1.98/1.58 tff(1559,plain,
% 1.98/1.58 ((hskp20 | hskp12 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c2_1(a520))) <=> (hskp20 | hskp12 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)))),
% 1.98/1.58 inference(rewrite,[status(thm)],[])).
% 1.98/1.58 tff(1560,plain,
% 1.98/1.58 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c2_1(a520)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c2_1(a520))))),
% 1.98/1.58 inference(monotonicity,[status(thm)],[1559])).
% 1.98/1.58 tff(1561,plain,
% 1.98/1.58 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c2_1(a520)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)))),
% 1.98/1.58 inference(transitivity,[status(thm)],[1560, 1558])).
% 1.98/1.58 tff(1562,plain,
% 1.98/1.58 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c2_1(a520)))),
% 1.98/1.58 inference(quant_inst,[status(thm)],[])).
% 1.98/1.58 tff(1563,plain,
% 1.98/1.58 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c2_1(a520))),
% 1.98/1.58 inference(modus_ponens,[status(thm)],[1562, 1561])).
% 1.98/1.58 tff(1564,plain,
% 1.98/1.58 (hskp20 | hskp12 | c1_1(a520)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1563, 112, 1532, 1542, 1126])).
% 1.98/1.58 tff(1565,plain,
% 1.98/1.58 (hskp12),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1564, 1557, 1541])).
% 1.98/1.58 tff(1566,plain,
% 1.98/1.58 (c1_1(a514)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[563, 1565])).
% 1.98/1.58 tff(1567,plain,
% 1.98/1.58 (~c0_1(a495)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1025, 1550])).
% 1.98/1.58 tff(1568,plain,
% 1.98/1.58 (~c3_1(a495)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1019, 1550])).
% 1.98/1.58 tff(1569,plain,
% 1.98/1.58 (c1_1(a495)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1037, 1550])).
% 1.98/1.58 tff(1570,plain,
% 1.98/1.58 (hskp8),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1055, 112, 401, 403, 1569, 402, 1567, 1568, 1049])).
% 1.98/1.58 tff(1571,plain,
% 1.98/1.58 (~c0_1(a505)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1072, 1570])).
% 1.98/1.58 tff(1572,plain,
% 1.98/1.58 (~c2_1(a514)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[541, 1565])).
% 1.98/1.58 tff(1573,plain,
% 1.98/1.58 (c3_1(a505)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1161, 1570])).
% 1.98/1.58 tff(1574,plain,
% 1.98/1.58 (c3_1(a514)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[552, 1565])).
% 1.98/1.58 tff(1575,plain,
% 1.98/1.58 (~c0_1(a514)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[607, 112, 453, 1566, 1574, 1572, 601])).
% 1.98/1.58 tff(1576,plain,
% 1.98/1.58 (c2_1(a505)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1066, 1570])).
% 1.98/1.58 tff(1577,plain,
% 1.98/1.58 ($false),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1203, 1576, 1575, 1574, 1573, 1569, 1572, 1571, 1567, 1566])).
% 1.98/1.58 tff(1578,plain,(hskp2 | (~c0_1(a568)) | (~c3_1(a568)) | c1_1(a568) | (~c2_1(a520)) | c3_1(a520) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a502) | c3_1(a502) | c0_1(a502) | (~c0_1(a520))), inference(lemma,lemma(discharge,[]))).
% 1.98/1.58 tff(1579,plain,
% 1.98/1.58 (hskp2),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1578, 1027, 403, 402, 1531, 1530, 1082, 1091, 1092, 1039, 401, 263, 1529])).
% 1.98/1.58 tff(1580,plain,
% 1.98/1.58 (~c2_1(a496)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[368, 1579])).
% 1.98/1.58 tff(1581,plain,
% 1.98/1.58 (~c1_1(a496)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[381, 1579])).
% 1.98/1.58 tff(1582,plain,
% 1.98/1.58 (~c3_1(a496)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[362, 1579])).
% 1.98/1.58 tff(1583,assumption,(~hskp20), introduced(assumption)).
% 1.98/1.58 tff(1584,assumption,(c2_1(a568)), introduced(assumption)).
% 1.98/1.58 tff(1585,plain,
% 1.98/1.58 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.98/1.58 inference(bind,[status(th)],[])).
% 1.98/1.58 tff(1586,plain,
% 1.98/1.58 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.58 inference(quant_intro,[status(thm)],[1585])).
% 1.98/1.58 tff(1587,plain,
% 1.98/1.58 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.58 inference(rewrite,[status(thm)],[])).
% 1.98/1.58 tff(1588,plain,
% 1.98/1.58 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_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) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_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) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp20) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp20))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.98/1.58 inference(bind,[status(th)],[])).
% 1.98/1.58 tff(1589,plain,
% 1.98/1.58 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.58 inference(quant_intro,[status(thm)],[1588])).
% 1.98/1.58 tff(1590,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 1.98/1.58 tff(1591,plain,
% 1.98/1.58 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.58 inference(modus_ponens,[status(thm)],[1590, 1589])).
% 1.98/1.58 tff(1592,plain,
% 1.98/1.58 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.58 inference(modus_ponens,[status(thm)],[1591, 1587])).
% 1.98/1.58 tff(1593,plain,(
% 1.98/1.58 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.58 inference(skolemize,[status(sab)],[1592])).
% 1.98/1.58 tff(1594,plain,
% 1.98/1.58 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.58 inference(modus_ponens,[status(thm)],[1593, 1586])).
% 1.98/1.58 tff(1595,plain,
% 1.98/1.58 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | c1_1(a568) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a568)) | (~c2_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp20 | c1_1(a568) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a568)) | (~c2_1(a568)))),
% 1.98/1.58 inference(rewrite,[status(thm)],[])).
% 1.98/1.58 tff(1596,plain,
% 1.98/1.58 ((hskp20 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496))) <=> (hskp20 | c1_1(a568) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a568)) | (~c2_1(a568)))),
% 1.98/1.58 inference(rewrite,[status(thm)],[])).
% 1.98/1.58 tff(1597,plain,
% 1.98/1.58 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | c1_1(a568) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a568)) | (~c2_1(a568))))),
% 1.98/1.58 inference(monotonicity,[status(thm)],[1596])).
% 1.98/1.58 tff(1598,plain,
% 1.98/1.58 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp20 | c1_1(a568) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a568)) | (~c2_1(a568)))),
% 1.98/1.58 inference(transitivity,[status(thm)],[1597, 1595])).
% 1.98/1.58 tff(1599,plain,
% 1.98/1.58 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a568) | (~c2_1(a568)) | (~c0_1(a568)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))),
% 1.98/1.58 inference(quant_inst,[status(thm)],[])).
% 1.98/1.58 tff(1600,plain,
% 1.98/1.58 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp20 | c1_1(a568) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a568)) | (~c2_1(a568))),
% 1.98/1.58 inference(modus_ponens,[status(thm)],[1599, 1598])).
% 1.98/1.58 tff(1601,plain,
% 1.98/1.58 (hskp20 | (~c0_1(a496))),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1600, 112, 401, 402, 632, 634, 1594, 1584])).
% 1.98/1.58 tff(1602,plain,
% 1.98/1.58 (~c0_1(a496)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1601, 1583])).
% 1.98/1.58 tff(1603,plain,
% 1.98/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.98/1.58 inference(rewrite,[status(thm)],[])).
% 1.98/1.58 tff(1604,plain,
% 1.98/1.58 (((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a502) | c1_1(a502) | c0_1(a502)) <=> (c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.98/1.58 inference(rewrite,[status(thm)],[])).
% 1.98/1.58 tff(1605,plain,
% 1.98/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a502) | c1_1(a502) | c0_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520))))),
% 1.98/1.58 inference(monotonicity,[status(thm)],[1604])).
% 1.98/1.58 tff(1606,plain,
% 1.98/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a502) | c1_1(a502) | c0_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.98/1.58 inference(transitivity,[status(thm)],[1605, 1603])).
% 1.98/1.58 tff(1607,plain,
% 1.98/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a502) | c1_1(a502) | c0_1(a502))),
% 1.98/1.58 inference(quant_inst,[status(thm)],[])).
% 1.98/1.58 tff(1608,plain,
% 1.98/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520))),
% 1.98/1.58 inference(modus_ponens,[status(thm)],[1607, 1606])).
% 1.98/1.58 tff(1609,plain,
% 1.98/1.58 (c0_1(a496) | (~c1_1(a520))),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1608, 112, 1532, 1542, 263, 1039, 1027, 634, 633, 784])).
% 1.98/1.58 tff(1610,plain,
% 1.98/1.58 (~c1_1(a520)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1609, 1602])).
% 1.98/1.58 tff(1611,plain,
% 1.98/1.58 (hskp11 | c0_1(a496)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[375, 112, 11, 634, 633, 10])).
% 1.98/1.58 tff(1612,plain,
% 1.98/1.58 (hskp11),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1611, 1602])).
% 1.98/1.58 tff(1613,plain,
% 1.98/1.58 (~c2_1(a510)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[59, 1612])).
% 1.98/1.58 tff(1614,plain,
% 1.98/1.58 (~c1_1(a510)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[65, 1612])).
% 1.98/1.58 tff(1615,plain,
% 1.98/1.58 (c0_1(a510)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[76, 1612])).
% 1.98/1.58 tff(1616,plain,
% 1.98/1.58 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp20 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.98/1.58 inference(rewrite,[status(thm)],[])).
% 1.98/1.58 tff(1617,plain,
% 1.98/1.58 ((hskp20 | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510))) <=> (hskp20 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.98/1.58 inference(rewrite,[status(thm)],[])).
% 1.98/1.58 tff(1618,plain,
% 1.98/1.58 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520))))),
% 1.98/1.58 inference(monotonicity,[status(thm)],[1617])).
% 1.98/1.58 tff(1619,plain,
% 1.98/1.58 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp20 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.98/1.58 inference(transitivity,[status(thm)],[1618, 1616])).
% 1.98/1.58 tff(1620,plain,
% 1.98/1.58 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)))),
% 1.98/1.58 inference(quant_inst,[status(thm)],[])).
% 1.98/1.58 tff(1621,plain,
% 1.98/1.58 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp20 | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520))),
% 1.98/1.58 inference(modus_ponens,[status(thm)],[1620, 1619])).
% 1.98/1.58 tff(1622,plain,
% 1.98/1.58 ($false),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1621, 112, 1583, 1533, 1532, 1615, 1614, 1613, 1594, 1610])).
% 1.98/1.58 tff(1623,plain,(hskp20 | (~c0_1(a520)) | (~c2_1(a520)) | hskp10 | c2_1(a496) | c3_1(a496) | c3_1(a520) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~c0_1(a568)) | c1_1(a568) | c1_1(a496) | (~c2_1(a568))), inference(lemma,lemma(discharge,[]))).
% 1.98/1.58 tff(1624,plain,
% 1.98/1.58 (~c2_1(a568)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1623, 1583, 1531, 11, 1529, 634, 1530, 263, 1039, 1027, 401, 402, 633, 632])).
% 1.98/1.58 tff(1625,plain,
% 1.98/1.58 (hskp9),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1292, 112, 401, 1092, 1091, 402, 1082, 1282, 1624])).
% 1.98/1.58 tff(1626,plain,
% 1.98/1.58 (~c1_1(a507)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[924, 1625])).
% 1.98/1.58 tff(1627,plain,
% 1.98/1.58 (~c0_1(a507)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[930, 1625])).
% 1.98/1.58 tff(1628,plain,
% 1.98/1.58 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))))),
% 1.98/1.58 inference(bind,[status(th)],[])).
% 1.98/1.58 tff(1629,plain,
% 1.98/1.58 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.98/1.58 inference(quant_intro,[status(thm)],[1628])).
% 1.98/1.58 tff(1630,plain,
% 1.98/1.58 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.98/1.58 inference(rewrite,[status(thm)],[])).
% 1.98/1.58 tff(1631,plain,
% 1.98/1.58 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp24) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp24))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))))),
% 1.98/1.58 inference(bind,[status(th)],[])).
% 1.98/1.58 tff(1632,plain,
% 1.98/1.58 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.98/1.58 inference(quant_intro,[status(thm)],[1631])).
% 1.98/1.58 tff(1633,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 1.98/1.58 tff(1634,plain,
% 1.98/1.58 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.98/1.58 inference(modus_ponens,[status(thm)],[1633, 1632])).
% 1.98/1.58 tff(1635,plain,
% 1.98/1.58 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.98/1.58 inference(modus_ponens,[status(thm)],[1634, 1630])).
% 1.98/1.58 tff(1636,plain,(
% 1.98/1.58 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.98/1.58 inference(skolemize,[status(sab)],[1635])).
% 1.98/1.58 tff(1637,plain,
% 1.98/1.58 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.98/1.58 inference(modus_ponens,[status(thm)],[1636, 1629])).
% 1.98/1.58 tff(1638,plain,
% 1.98/1.58 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp24 | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568))),
% 1.98/1.58 inference(rewrite,[status(thm)],[])).
% 1.98/1.58 tff(1639,plain,
% 1.98/1.58 ((hskp24 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a568) | (~c0_1(a568)) | (~c3_1(a568))) <=> (hskp24 | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568))),
% 1.98/1.58 inference(rewrite,[status(thm)],[])).
% 1.98/1.58 tff(1640,plain,
% 1.98/1.58 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a568) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568)))),
% 1.98/1.58 inference(monotonicity,[status(thm)],[1639])).
% 1.98/1.58 tff(1641,plain,
% 1.98/1.58 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a568) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp24 | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568))),
% 1.98/1.58 inference(transitivity,[status(thm)],[1640, 1638])).
% 1.98/1.58 tff(1642,plain,
% 1.98/1.58 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a568) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.58 inference(quant_inst,[status(thm)],[])).
% 1.98/1.58 tff(1643,plain,
% 1.98/1.58 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp24 | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c0_1(a568)) | (~c3_1(a568)) | c2_1(a568)),
% 1.98/1.58 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 1.98/1.58 tff(1644,plain,
% 1.98/1.58 (hskp24),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1643, 112, 401, 403, 1529, 1531, 1530, 1637, 1624])).
% 1.98/1.58 tff(1645,plain,
% 1.98/1.58 (((~hskp24) | (~c2_1(a554))) <=> ((~hskp24) | (~c2_1(a554)))),
% 1.98/1.58 inference(rewrite,[status(thm)],[])).
% 1.98/1.58 tff(1646,plain,
% 1.98/1.58 (((~c2_1(a554)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a554)))),
% 1.98/1.58 inference(rewrite,[status(thm)],[])).
% 1.98/1.58 tff(1647,axiom,((~c2_1(a554)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 1.98/1.58 tff(1648,plain,
% 1.98/1.58 ((~hskp24) | (~c2_1(a554))),
% 1.98/1.58 inference(modus_ponens,[status(thm)],[1647, 1646])).
% 1.98/1.58 tff(1649,plain,
% 1.98/1.58 ((~hskp24) | (~c2_1(a554))),
% 1.98/1.58 inference(modus_ponens,[status(thm)],[1648, 1645])).
% 1.98/1.58 tff(1650,plain,
% 1.98/1.58 (~c2_1(a554)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[1649, 1644])).
% 1.98/1.58 tff(1651,plain,
% 1.98/1.58 (c3_1(a507)),
% 1.98/1.58 inference(unit_resolution,[status(thm)],[941, 1625])).
% 1.98/1.58 tff(1652,plain,
% 1.98/1.58 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a568) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.58 inference(rewrite,[status(thm)],[])).
% 1.98/1.58 tff(1653,plain,
% 1.98/1.58 ((hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507))) <=> (hskp28 | c1_1(a568) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1654,plain,
% 1.98/1.59 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a568) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.98/1.59 inference(monotonicity,[status(thm)],[1653])).
% 1.98/1.59 tff(1655,plain,
% 1.98/1.59 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.59 inference(transitivity,[status(thm)],[1654, 1652])).
% 1.98/1.59 tff(1656,plain,
% 1.98/1.59 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))),
% 1.98/1.59 inference(quant_inst,[status(thm)],[])).
% 1.98/1.59 tff(1657,plain,
% 1.98/1.59 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1656, 1655])).
% 1.98/1.59 tff(1658,plain,
% 1.98/1.59 (hskp28),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1657, 112, 401, 403, 1651, 402, 1627, 1626, 262])).
% 1.98/1.59 tff(1659,plain,
% 1.98/1.59 (c3_1(a500)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[429, 1658])).
% 1.98/1.59 tff(1660,plain,
% 1.98/1.59 (c2_1(a500)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[440, 1658])).
% 1.98/1.59 tff(1661,plain,
% 1.98/1.59 (c0_1(a500)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[451, 1658])).
% 1.98/1.59 tff(1662,plain,
% 1.98/1.59 (((~hskp24) | (~c3_1(a554))) <=> ((~hskp24) | (~c3_1(a554)))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1663,plain,
% 1.98/1.59 (((~c3_1(a554)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a554)))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1664,axiom,((~c3_1(a554)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 1.98/1.59 tff(1665,plain,
% 1.98/1.59 ((~hskp24) | (~c3_1(a554))),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1664, 1663])).
% 1.98/1.59 tff(1666,plain,
% 1.98/1.59 ((~hskp24) | (~c3_1(a554))),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1665, 1662])).
% 1.98/1.59 tff(1667,plain,
% 1.98/1.59 (~c3_1(a554)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1666, 1644])).
% 1.98/1.59 tff(1668,plain,
% 1.98/1.59 (((~hskp24) | c0_1(a554)) <=> ((~hskp24) | c0_1(a554))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1669,axiom,((~hskp24) | c0_1(a554)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 1.98/1.59 tff(1670,plain,
% 1.98/1.59 ((~hskp24) | c0_1(a554)),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1669, 1668])).
% 1.98/1.59 tff(1671,plain,
% 1.98/1.59 ((~hskp24) | c0_1(a554)),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1670, 1668])).
% 1.98/1.59 tff(1672,plain,
% 1.98/1.59 ((~hskp24) | c0_1(a554)),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1671, 1668])).
% 1.98/1.59 tff(1673,plain,
% 1.98/1.59 ((~hskp24) | c0_1(a554)),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1672, 1668])).
% 1.98/1.59 tff(1674,plain,
% 1.98/1.59 ((~hskp24) | c0_1(a554)),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1673, 1668])).
% 1.98/1.59 tff(1675,plain,
% 1.98/1.59 ((~hskp24) | c0_1(a554)),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1674, 1668])).
% 1.98/1.59 tff(1676,plain,
% 1.98/1.59 ((~hskp24) | c0_1(a554)),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1675, 1668])).
% 1.98/1.59 tff(1677,plain,
% 1.98/1.59 ((~hskp24) | c0_1(a554)),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1676, 1668])).
% 1.98/1.59 tff(1678,plain,
% 1.98/1.59 (c0_1(a554)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1677, 1644])).
% 1.98/1.59 tff(1679,plain,
% 1.98/1.59 (c1_1(a520)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1564, 1074, 1583])).
% 1.98/1.59 tff(1680,plain,
% 1.98/1.59 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.98/1.59 inference(bind,[status(th)],[])).
% 1.98/1.59 tff(1681,plain,
% 1.98/1.59 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.98/1.59 inference(quant_intro,[status(thm)],[1680])).
% 1.98/1.59 tff(1682,plain,
% 1.98/1.59 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1683,plain,
% 1.98/1.59 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_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)) | (~c1_1(V))) | (~c2_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)) | (~c1_1(V))) | (~c2_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)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp0))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.98/1.59 inference(bind,[status(th)],[])).
% 1.98/1.59 tff(1684,plain,
% 1.98/1.59 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.98/1.59 inference(quant_intro,[status(thm)],[1683])).
% 1.98/1.59 tff(1685,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 1.98/1.59 tff(1686,plain,
% 1.98/1.59 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1685, 1684])).
% 1.98/1.59 tff(1687,plain,
% 1.98/1.59 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1686, 1682])).
% 1.98/1.59 tff(1688,plain,(
% 1.98/1.59 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.98/1.59 inference(skolemize,[status(sab)],[1687])).
% 1.98/1.59 tff(1689,plain,
% 1.98/1.59 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1688, 1681])).
% 1.98/1.59 tff(1690,plain,
% 1.98/1.59 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp0 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp0 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1691,plain,
% 1.98/1.59 ((hskp0 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a520) | (~c1_1(a520)) | (~c2_1(a520))) <=> (hskp0 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1692,plain,
% 1.98/1.59 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a520) | (~c1_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp0 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c2_1(a520))))),
% 1.98/1.59 inference(monotonicity,[status(thm)],[1691])).
% 1.98/1.59 tff(1693,plain,
% 1.98/1.59 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a520) | (~c1_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp0 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.98/1.59 inference(transitivity,[status(thm)],[1692, 1690])).
% 1.98/1.59 tff(1694,plain,
% 1.98/1.59 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp0 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a520) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.98/1.59 inference(quant_inst,[status(thm)],[])).
% 1.98/1.59 tff(1695,plain,
% 1.98/1.59 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp0 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c2_1(a520))),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1694, 1693])).
% 1.98/1.59 tff(1696,plain,
% 1.98/1.59 (hskp0 | (~c1_1(a520))),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1695, 112, 495, 494, 493, 1532, 1542, 1689])).
% 1.98/1.59 tff(1697,plain,
% 1.98/1.59 (hskp0),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1696, 1679])).
% 1.98/1.59 tff(1698,plain,
% 1.98/1.59 (((~hskp0) | (~c2_1(a494))) <=> ((~hskp0) | (~c2_1(a494)))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1699,plain,
% 1.98/1.59 (((~c2_1(a494)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a494)))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1700,axiom,((~c2_1(a494)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 1.98/1.59 tff(1701,plain,
% 1.98/1.59 ((~hskp0) | (~c2_1(a494))),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1700, 1699])).
% 1.98/1.59 tff(1702,plain,
% 1.98/1.59 ((~hskp0) | (~c2_1(a494))),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1701, 1698])).
% 1.98/1.59 tff(1703,plain,
% 1.98/1.59 (~c2_1(a494)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1702, 1697])).
% 1.98/1.59 tff(1704,plain,
% 1.98/1.59 (~c0_1(a494)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[878, 1697])).
% 1.98/1.59 tff(1705,plain,
% 1.98/1.59 (~c2_1(a502)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1133, 1074, 1027, 1583])).
% 1.98/1.59 tff(1706,assumption,(~c3_1(a554)), introduced(assumption)).
% 1.98/1.59 tff(1707,assumption,(~c2_1(a554)), introduced(assumption)).
% 1.98/1.59 tff(1708,assumption,(c0_1(a554)), introduced(assumption)).
% 1.98/1.59 tff(1709,plain,
% 1.98/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a554) | c3_1(a554) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a554)) | (~c0_1(a554)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a554) | c3_1(a554) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a554)) | (~c0_1(a554)))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1710,plain,
% 1.98/1.59 (((~ndr1_0) | c3_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c2_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c3_1(a502) | c0_1(a502) | c2_1(a502)) <=> (c2_1(a554) | c3_1(a554) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a554)) | (~c0_1(a554)))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1711,plain,
% 1.98/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c2_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c3_1(a502) | c0_1(a502) | c2_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a554) | c3_1(a554) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a554)) | (~c0_1(a554))))),
% 1.98/1.59 inference(monotonicity,[status(thm)],[1710])).
% 1.98/1.59 tff(1712,plain,
% 1.98/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c2_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c3_1(a502) | c0_1(a502) | c2_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a554) | c3_1(a554) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a554)) | (~c0_1(a554)))),
% 1.98/1.59 inference(transitivity,[status(thm)],[1711, 1709])).
% 1.98/1.59 tff(1713,plain,
% 1.98/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c2_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c3_1(a502) | c0_1(a502) | c2_1(a502))),
% 1.98/1.59 inference(quant_inst,[status(thm)],[])).
% 1.98/1.59 tff(1714,plain,
% 1.98/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a554) | c3_1(a554) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a554)) | (~c0_1(a554))),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1713, 1712])).
% 1.98/1.59 tff(1715,plain,
% 1.98/1.59 (c2_1(a502) | (~c1_1(a554))),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1714, 112, 1708, 1707, 1706, 263, 1027, 996])).
% 1.98/1.59 tff(1716,plain,
% 1.98/1.59 (~c1_1(a554)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1715, 1705])).
% 1.98/1.59 tff(1717,plain,
% 1.98/1.59 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c3_1(a554) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a554) | (~c0_1(a554)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a554) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a554) | (~c0_1(a554)))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1718,plain,
% 1.98/1.59 ((hskp1 | (~ndr1_0) | c3_1(a554) | c1_1(a554) | (~c0_1(a554)) | c1_1(a502) | c0_1(a502) | c3_1(a502)) <=> (hskp1 | c3_1(a554) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a554) | (~c0_1(a554)))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1719,plain,
% 1.98/1.59 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a554) | c1_1(a554) | (~c0_1(a554)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c3_1(a554) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a554) | (~c0_1(a554))))),
% 1.98/1.59 inference(monotonicity,[status(thm)],[1718])).
% 1.98/1.59 tff(1720,plain,
% 1.98/1.59 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a554) | c1_1(a554) | (~c0_1(a554)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a554) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a554) | (~c0_1(a554)))),
% 1.98/1.59 inference(transitivity,[status(thm)],[1719, 1717])).
% 1.98/1.59 tff(1721,plain,
% 1.98/1.59 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a554) | c1_1(a554) | (~c0_1(a554)) | c1_1(a502) | c0_1(a502) | c3_1(a502))),
% 1.98/1.59 inference(quant_inst,[status(thm)],[])).
% 1.98/1.59 tff(1722,plain,
% 1.98/1.59 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a554) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~ndr1_0) | c1_1(a554) | (~c0_1(a554))),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1721, 1720])).
% 1.98/1.59 tff(1723,plain,
% 1.98/1.59 (hskp1 | c1_1(a554)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1722, 112, 1708, 1706, 263, 1039, 1027, 645])).
% 1.98/1.59 tff(1724,plain,
% 1.98/1.59 (hskp1),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1723, 1716])).
% 1.98/1.59 tff(1725,plain,
% 1.98/1.59 (~c3_1(a495)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1019, 1724])).
% 1.98/1.59 tff(1726,plain,
% 1.98/1.59 (~c0_1(a495)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1025, 1724])).
% 1.98/1.59 tff(1727,plain,
% 1.98/1.59 (c3_1(a494)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[893, 1697])).
% 1.98/1.59 tff(1728,plain,
% 1.98/1.59 (c1_1(a495)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1037, 1724])).
% 1.98/1.59 tff(1729,plain,
% 1.98/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c3_1(a528) | c0_1(a495) | c3_1(a495) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c3_1(a528) | c0_1(a495) | c3_1(a495) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1730,plain,
% 1.98/1.59 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a494) | (~c3_1(a494)) | c2_1(a494)) <=> (c3_1(a528) | c0_1(a495) | c3_1(a495) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1731,plain,
% 1.98/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a494) | (~c3_1(a494)) | c2_1(a494))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c3_1(a528) | c0_1(a495) | c3_1(a495) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528))))),
% 1.98/1.59 inference(monotonicity,[status(thm)],[1730])).
% 1.98/1.59 tff(1732,plain,
% 1.98/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a494) | (~c3_1(a494)) | c2_1(a494))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c3_1(a528) | c0_1(a495) | c3_1(a495) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.98/1.59 inference(transitivity,[status(thm)],[1731, 1729])).
% 1.98/1.59 tff(1733,plain,
% 1.98/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a495) | c3_1(a495) | (~c1_1(a495)) | c0_1(a494) | (~c3_1(a494)) | c2_1(a494))),
% 1.98/1.59 inference(quant_inst,[status(thm)],[])).
% 1.98/1.59 tff(1734,plain,
% 1.98/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c3_1(a528) | c0_1(a495) | c3_1(a495) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a495)) | (~c1_1(a528)) | (~c0_1(a528))),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1733, 1732])).
% 1.98/1.59 tff(1735,plain,
% 1.98/1.59 ($false),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1734, 112, 1092, 1091, 1728, 1727, 1082, 1726, 1725, 1704, 1703, 21])).
% 1.98/1.59 tff(1736,plain,(hskp12 | (~c0_1(a528)) | (~c1_1(a528)) | c3_1(a528) | (~c0_1(a554)) | c3_1(a554) | c0_1(a502) | c1_1(a502) | c3_1(a502) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c2_1(a520)) | c3_1(a520) | c2_1(a554) | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.98/1.59 tff(1737,plain,
% 1.98/1.59 (hskp12),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1736, 1678, 1091, 1082, 1092, 1667, 263, 1039, 1027, 1661, 1660, 1659, 1531, 1530, 1650, 1583])).
% 1.98/1.59 tff(1738,plain,
% 1.98/1.59 (~c2_1(a514)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[541, 1737])).
% 1.98/1.59 tff(1739,plain,
% 1.98/1.59 (c3_1(a514)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[552, 1737])).
% 1.98/1.59 tff(1740,plain,
% 1.98/1.59 (c1_1(a514)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[563, 1737])).
% 1.98/1.59 tff(1741,plain,
% 1.98/1.59 (c0_1(a514)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[955, 112, 1740, 1739, 1651, 1738, 1627, 1626, 618])).
% 1.98/1.59 tff(1742,plain,
% 1.98/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c2_1(a514) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a514) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1743,plain,
% 1.98/1.59 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c3_1(a502) | c0_1(a502) | c2_1(a502)) <=> (c3_1(a528) | c2_1(a514) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1744,plain,
% 1.98/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c3_1(a502) | c0_1(a502) | c2_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c2_1(a514) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528))))),
% 1.98/1.59 inference(monotonicity,[status(thm)],[1743])).
% 1.98/1.59 tff(1745,plain,
% 1.98/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c3_1(a502) | c0_1(a502) | c2_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a514) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.98/1.59 inference(transitivity,[status(thm)],[1744, 1742])).
% 1.98/1.59 tff(1746,plain,
% 1.98/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c3_1(a502) | c0_1(a502) | c2_1(a502))),
% 1.98/1.59 inference(quant_inst,[status(thm)],[])).
% 1.98/1.59 tff(1747,plain,
% 1.98/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a514) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528))),
% 1.98/1.59 inference(modus_ponens,[status(thm)],[1746, 1745])).
% 1.98/1.59 tff(1748,plain,
% 1.98/1.59 (c2_1(a502) | (~c0_1(a514))),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1747, 112, 1092, 1091, 1740, 1082, 1738, 263, 1027, 996])).
% 1.98/1.59 tff(1749,plain,
% 1.98/1.59 (c2_1(a502)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1748, 1741])).
% 1.98/1.59 tff(1750,plain,
% 1.98/1.59 (hskp4 | (~c2_1(a502))),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1487, 112, 1529, 1531, 1530, 263, 1039, 400])).
% 1.98/1.59 tff(1751,plain,
% 1.98/1.59 (hskp4),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1750, 1749])).
% 1.98/1.59 tff(1752,plain,
% 1.98/1.59 (~c0_1(a498)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1493, 1751])).
% 1.98/1.59 tff(1753,plain,
% 1.98/1.59 (c1_1(a498)),
% 1.98/1.59 inference(unit_resolution,[status(thm)],[1504, 1751])).
% 1.98/1.59 tff(1754,plain,
% 1.98/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1755,plain,
% 1.98/1.59 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a498) | (~c3_1(a498)) | (~c1_1(a498))) <=> (c1_1(a568) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.59 inference(rewrite,[status(thm)],[])).
% 1.98/1.59 tff(1756,plain,
% 1.98/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a498) | (~c3_1(a498)) | (~c1_1(a498)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.98/1.59 inference(monotonicity,[status(thm)],[1755])).
% 1.98/1.59 tff(1757,plain,
% 1.98/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a498) | (~c3_1(a498)) | (~c1_1(a498)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.60 inference(transitivity,[status(thm)],[1756, 1754])).
% 1.98/1.60 tff(1758,plain,
% 1.98/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a498) | (~c3_1(a498)) | (~c1_1(a498)))),
% 1.98/1.60 inference(quant_inst,[status(thm)],[])).
% 1.98/1.60 tff(1759,plain,
% 1.98/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.98/1.60 inference(modus_ponens,[status(thm)],[1758, 1757])).
% 1.98/1.60 tff(1760,plain,
% 1.98/1.60 (~c3_1(a498)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1759, 112, 401, 403, 1092, 1091, 1753, 402, 1082, 1752, 1398])).
% 1.98/1.60 tff(1761,plain,
% 1.98/1.60 (~c2_1(a498)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1517, 1751])).
% 1.98/1.60 tff(1762,plain,
% 1.98/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.98/1.60 inference(rewrite,[status(thm)],[])).
% 1.98/1.60 tff(1763,plain,
% 1.98/1.60 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c3_1(a496) | c0_1(a496) | c2_1(a496)) <=> (c3_1(a528) | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.98/1.60 inference(rewrite,[status(thm)],[])).
% 1.98/1.60 tff(1764,plain,
% 1.98/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528))))),
% 1.98/1.60 inference(monotonicity,[status(thm)],[1763])).
% 1.98/1.60 tff(1765,plain,
% 1.98/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.98/1.60 inference(transitivity,[status(thm)],[1764, 1762])).
% 1.98/1.60 tff(1766,plain,
% 1.98/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c3_1(a496) | c0_1(a496) | c2_1(a496))),
% 1.98/1.60 inference(quant_inst,[status(thm)],[])).
% 1.98/1.60 tff(1767,plain,
% 1.98/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a514) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a514)) | (~c0_1(a514)) | (~c1_1(a528)) | (~c0_1(a528))),
% 1.98/1.60 inference(modus_ponens,[status(thm)],[1766, 1765])).
% 1.98/1.60 tff(1768,plain,
% 1.98/1.60 (c0_1(a496) | (~c0_1(a514))),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1767, 112, 1092, 1091, 1740, 1082, 1738, 634, 633, 996])).
% 1.98/1.60 tff(1769,plain,
% 1.98/1.60 (c0_1(a496)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1768, 1741])).
% 1.98/1.60 tff(1770,plain,
% 1.98/1.60 (hskp22 | (~c0_1(a496))),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[797, 112, 632, 634, 633, 31])).
% 1.98/1.60 tff(1771,plain,
% 1.98/1.60 (hskp22),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1770, 1769])).
% 1.98/1.60 tff(1772,plain,
% 1.98/1.60 (~c0_1(a540)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[131, 1771])).
% 1.98/1.60 tff(1773,plain,
% 1.98/1.60 (c1_1(a540)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[153, 1771])).
% 1.98/1.60 tff(1774,plain,
% 1.98/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a540) | c2_1(a514) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c1_1(a498)) | (~c3_1(a514)) | (~c1_1(a514)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a540) | c2_1(a514) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c1_1(a498)) | (~c3_1(a514)) | (~c1_1(a514)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.98/1.60 inference(rewrite,[status(thm)],[])).
% 1.98/1.60 tff(1775,plain,
% 1.98/1.60 (((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c0_1(a498) | c2_1(a498) | (~c1_1(a498))) <=> (c0_1(a540) | c2_1(a514) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c1_1(a498)) | (~c3_1(a514)) | (~c1_1(a514)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.98/1.60 inference(rewrite,[status(thm)],[])).
% 1.98/1.60 tff(1776,plain,
% 1.98/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c0_1(a498) | c2_1(a498) | (~c1_1(a498)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a540) | c2_1(a514) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c1_1(a498)) | (~c3_1(a514)) | (~c1_1(a514)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 1.98/1.60 inference(monotonicity,[status(thm)],[1775])).
% 1.98/1.60 tff(1777,plain,
% 1.98/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c0_1(a498) | c2_1(a498) | (~c1_1(a498)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a540) | c2_1(a514) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c1_1(a498)) | (~c3_1(a514)) | (~c1_1(a514)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 1.98/1.60 inference(transitivity,[status(thm)],[1776, 1774])).
% 1.98/1.60 tff(1778,plain,
% 1.98/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c0_1(a498) | c2_1(a498) | (~c1_1(a498)))),
% 1.98/1.60 inference(quant_inst,[status(thm)],[])).
% 1.98/1.60 tff(1779,plain,
% 1.98/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a540) | c2_1(a514) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c1_1(a498)) | (~c3_1(a514)) | (~c1_1(a514)) | (~c1_1(a540)) | (~c2_1(a540))),
% 1.98/1.60 inference(modus_ponens,[status(thm)],[1778, 1777])).
% 1.98/1.60 tff(1780,plain,
% 1.98/1.60 (~c2_1(a540)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1779, 112, 1773, 1740, 1739, 1753, 1772, 1738, 1752, 1761, 1175])).
% 1.98/1.60 tff(1781,plain,
% 1.98/1.60 (c3_1(a540)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[142, 1771])).
% 1.98/1.60 tff(1782,plain,
% 1.98/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a540) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | c2_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a540) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | c2_1(a540))),
% 1.98/1.60 inference(rewrite,[status(thm)],[])).
% 1.98/1.60 tff(1783,plain,
% 1.98/1.60 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a498) | c3_1(a498) | (~c1_1(a498)) | c0_1(a540) | (~c3_1(a540)) | c2_1(a540)) <=> (c0_1(a540) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | c2_1(a540))),
% 1.98/1.60 inference(rewrite,[status(thm)],[])).
% 1.98/1.60 tff(1784,plain,
% 1.98/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a498) | c3_1(a498) | (~c1_1(a498)) | c0_1(a540) | (~c3_1(a540)) | c2_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a540) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | c2_1(a540)))),
% 1.98/1.60 inference(monotonicity,[status(thm)],[1783])).
% 1.98/1.60 tff(1785,plain,
% 1.98/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a498) | c3_1(a498) | (~c1_1(a498)) | c0_1(a540) | (~c3_1(a540)) | c2_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a540) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | c2_1(a540))),
% 1.98/1.60 inference(transitivity,[status(thm)],[1784, 1782])).
% 1.98/1.60 tff(1786,plain,
% 1.98/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a498) | c3_1(a498) | (~c1_1(a498)) | c0_1(a540) | (~c3_1(a540)) | c2_1(a540))),
% 1.98/1.60 inference(quant_inst,[status(thm)],[])).
% 1.98/1.60 tff(1787,plain,
% 1.98/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a540) | c3_1(a528) | c0_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a498)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | c2_1(a540)),
% 1.98/1.60 inference(modus_ponens,[status(thm)],[1786, 1785])).
% 1.98/1.60 tff(1788,plain,
% 1.98/1.60 ($false),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1787, 112, 1781, 1092, 1091, 1753, 1772, 1082, 1752, 21, 1780, 1760])).
% 1.98/1.60 tff(1789,plain,(hskp20 | (~c0_1(a528)) | (~c1_1(a528)) | c3_1(a528) | (~c0_1(a568)) | (~c3_1(a568)) | c1_1(a568) | c1_1(a496) | c2_1(a496) | c3_1(a496) | c0_1(a502) | c1_1(a502) | c3_1(a502) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.98/1.60 tff(1790,plain,
% 1.98/1.60 (hskp20),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1789, 632, 1091, 1082, 401, 403, 402, 1092, 634, 633, 263, 1039, 1027, 11])).
% 1.98/1.60 tff(1791,plain,
% 1.98/1.60 (~hskp1),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1556, 1790, 1082, 1091, 1092, 1039, 1027, 263])).
% 1.98/1.60 tff(1792,plain,
% 1.98/1.60 (hskp1 | c3_1(a502) | c1_1(a520)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1548, 112, 1529, 1530, 263, 1039, 645])).
% 1.98/1.60 tff(1793,plain,
% 1.98/1.60 (c1_1(a520)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1792, 1791, 1027])).
% 1.98/1.60 tff(1794,plain,
% 1.98/1.60 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))),
% 1.98/1.60 inference(rewrite,[status(thm)],[])).
% 1.98/1.60 tff(1795,plain,
% 1.98/1.60 ((hskp1 | (~ndr1_0) | c3_1(a496) | c1_1(a496) | (~c0_1(a496)) | c1_1(a502) | c0_1(a502) | c3_1(a502)) <=> (hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))),
% 1.98/1.60 inference(rewrite,[status(thm)],[])).
% 1.98/1.60 tff(1796,plain,
% 1.98/1.60 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a496) | c1_1(a496) | (~c0_1(a496)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496))))),
% 1.98/1.60 inference(monotonicity,[status(thm)],[1795])).
% 1.98/1.60 tff(1797,plain,
% 1.98/1.60 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a496) | c1_1(a496) | (~c0_1(a496)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))),
% 1.98/1.60 inference(transitivity,[status(thm)],[1796, 1794])).
% 1.98/1.60 tff(1798,plain,
% 1.98/1.60 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a496) | c1_1(a496) | (~c0_1(a496)) | c1_1(a502) | c0_1(a502) | c3_1(a502))),
% 1.98/1.60 inference(quant_inst,[status(thm)],[])).
% 1.98/1.60 tff(1799,plain,
% 1.98/1.60 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496))),
% 1.98/1.60 inference(modus_ponens,[status(thm)],[1798, 1797])).
% 1.98/1.60 tff(1800,plain,
% 1.98/1.60 (hskp1 | c1_1(a496) | (~c0_1(a496))),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1799, 112, 263, 1039, 1027, 633, 645])).
% 1.98/1.60 tff(1801,plain,
% 1.98/1.60 (~c0_1(a496)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1800, 1791, 632])).
% 1.98/1.60 tff(1802,plain,
% 1.98/1.60 (c3_1(a496) | c0_1(a496) | (~c1_1(a520))),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1608, 112, 1531, 1530, 263, 1039, 1027, 634, 784])).
% 1.98/1.60 tff(1803,plain,
% 1.98/1.60 ($false),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1802, 1801, 1793, 633])).
% 1.98/1.60 tff(1804,plain,(c1_1(a496) | c3_1(a496) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c2_1(a496) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)) | c1_1(a568) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.98/1.60 tff(1805,plain,
% 1.98/1.60 ($false),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1804, 1582, 1581, 263, 1039, 1027, 1580, 1082, 1091, 1092, 401, 403, 402, 11])).
% 1.98/1.60 tff(1806,plain,(c3_1(a502) | c0_1(a502) | c1_1(a502) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)) | c1_1(a568) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.98/1.60 tff(1807,plain,
% 1.98/1.60 (c1_1(a502)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1806, 1027, 263, 470, 481, 492, 401, 403, 402, 11])).
% 1.98/1.60 tff(1808,plain,
% 1.98/1.60 (~hskp7),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[338, 1807])).
% 1.98/1.60 tff(1809,plain,
% 1.98/1.60 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a568) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a568) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.60 inference(rewrite,[status(thm)],[])).
% 1.98/1.60 tff(1810,plain,
% 1.98/1.60 ((hskp8 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502))) <=> (hskp8 | c1_1(a568) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.60 inference(rewrite,[status(thm)],[])).
% 1.98/1.60 tff(1811,plain,
% 1.98/1.60 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a568) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.98/1.60 inference(monotonicity,[status(thm)],[1810])).
% 1.98/1.60 tff(1812,plain,
% 1.98/1.60 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a568) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.60 inference(transitivity,[status(thm)],[1811, 1809])).
% 1.98/1.60 tff(1813,plain,
% 1.98/1.60 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c0_1(a502) | c3_1(a502) | (~c1_1(a502)))),
% 1.98/1.60 inference(quant_inst,[status(thm)],[])).
% 1.98/1.60 tff(1814,plain,
% 1.98/1.60 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a568) | c0_1(a502) | (~c1_1(a502)) | c3_1(a502) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.98/1.60 inference(modus_ponens,[status(thm)],[1813, 1812])).
% 1.98/1.60 tff(1815,plain,
% 1.98/1.60 (hskp8 | (~c1_1(a502)) | c3_1(a502)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1814, 112, 401, 403, 402, 263, 1049])).
% 1.98/1.60 tff(1816,plain,
% 1.98/1.60 (hskp8),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1815, 1807, 1027])).
% 1.98/1.60 tff(1817,plain,
% 1.98/1.60 (~c0_1(a505)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1072, 1816])).
% 1.98/1.60 tff(1818,plain,
% 1.98/1.60 (c3_1(a505)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1161, 1816])).
% 1.98/1.60 tff(1819,plain,
% 1.98/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c3_1(a528) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c3_1(a528) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.60 inference(rewrite,[status(thm)],[])).
% 1.98/1.60 tff(1820,plain,
% 1.98/1.60 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a505) | (~c3_1(a505)) | (~c1_1(a505))) <=> (c1_1(a568) | c3_1(a528) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.60 inference(rewrite,[status(thm)],[])).
% 1.98/1.60 tff(1821,plain,
% 1.98/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a505) | (~c3_1(a505)) | (~c1_1(a505)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c3_1(a528) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.98/1.60 inference(monotonicity,[status(thm)],[1820])).
% 1.98/1.60 tff(1822,plain,
% 1.98/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a505) | (~c3_1(a505)) | (~c1_1(a505)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c3_1(a528) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.60 inference(transitivity,[status(thm)],[1821, 1819])).
% 1.98/1.60 tff(1823,plain,
% 1.98/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a505) | (~c3_1(a505)) | (~c1_1(a505)))),
% 1.98/1.60 inference(quant_inst,[status(thm)],[])).
% 1.98/1.60 tff(1824,plain,
% 1.98/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c3_1(a528) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c1_1(a505)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.98/1.60 inference(modus_ponens,[status(thm)],[1823, 1822])).
% 1.98/1.60 tff(1825,plain,
% 1.98/1.60 (~c1_1(a505)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1824, 112, 401, 403, 492, 481, 1818, 402, 470, 1817, 1398])).
% 1.98/1.60 tff(1826,plain,
% 1.98/1.60 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.60 inference(rewrite,[status(thm)],[])).
% 1.98/1.60 tff(1827,plain,
% 1.98/1.60 ((hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505))) <=> (hskp28 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.60 inference(rewrite,[status(thm)],[])).
% 1.98/1.60 tff(1828,plain,
% 1.98/1.60 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.98/1.60 inference(monotonicity,[status(thm)],[1827])).
% 1.98/1.60 tff(1829,plain,
% 1.98/1.60 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.60 inference(transitivity,[status(thm)],[1828, 1826])).
% 1.98/1.60 tff(1830,plain,
% 1.98/1.60 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))),
% 1.98/1.60 inference(quant_inst,[status(thm)],[])).
% 1.98/1.60 tff(1831,plain,
% 1.98/1.60 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | c1_1(a505) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.98/1.60 inference(modus_ponens,[status(thm)],[1830, 1829])).
% 1.98/1.60 tff(1832,plain,
% 1.98/1.60 (hskp28),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1831, 112, 401, 403, 1818, 402, 1817, 262, 1825])).
% 1.98/1.60 tff(1833,plain,
% 1.98/1.60 (c3_1(a500)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[429, 1832])).
% 1.98/1.60 tff(1834,plain,
% 1.98/1.60 (c0_1(a500)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[451, 1832])).
% 1.98/1.60 tff(1835,plain,
% 1.98/1.60 (c2_1(a500)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[440, 1832])).
% 1.98/1.60 tff(1836,plain,
% 1.98/1.60 (hskp2),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[503, 1835, 464, 1834, 1833])).
% 1.98/1.60 tff(1837,plain,
% 1.98/1.60 (~c3_1(a496)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[362, 1836])).
% 1.98/1.60 tff(1838,plain,
% 1.98/1.60 (~c2_1(a496)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[368, 1836])).
% 1.98/1.60 tff(1839,plain,
% 1.98/1.60 (~c1_1(a496)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[381, 1836])).
% 1.98/1.60 tff(1840,assumption,(hskp22), introduced(assumption)).
% 1.98/1.60 tff(1841,plain,
% 1.98/1.60 (~c0_1(a540)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[131, 1840])).
% 1.98/1.60 tff(1842,plain,
% 1.98/1.60 (c3_1(a540)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[142, 1840])).
% 1.98/1.60 tff(1843,plain,
% 1.98/1.60 (c1_1(a540)),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[153, 1840])).
% 1.98/1.60 tff(1844,plain,
% 1.98/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.60 inference(rewrite,[status(thm)],[])).
% 1.98/1.60 tff(1845,plain,
% 1.98/1.60 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540))) <=> (c1_1(a568) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.60 inference(rewrite,[status(thm)],[])).
% 1.98/1.60 tff(1846,plain,
% 1.98/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.98/1.60 inference(monotonicity,[status(thm)],[1845])).
% 1.98/1.60 tff(1847,plain,
% 1.98/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.60 inference(transitivity,[status(thm)],[1846, 1844])).
% 1.98/1.60 tff(1848,plain,
% 1.98/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))),
% 1.98/1.60 inference(quant_inst,[status(thm)],[])).
% 1.98/1.60 tff(1849,plain,
% 1.98/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.98/1.60 inference(modus_ponens,[status(thm)],[1848, 1847])).
% 1.98/1.60 tff(1850,plain,
% 1.98/1.60 ($false),
% 1.98/1.60 inference(unit_resolution,[status(thm)],[1849, 112, 401, 403, 1843, 1842, 1092, 1091, 402, 1841, 1082, 1398])).
% 1.98/1.61 tff(1851,plain,((~hskp22) | (~c0_1(a568)) | (~c3_1(a568)) | (~c0_1(a528)) | (~c1_1(a528)) | c1_1(a568) | c3_1(a528)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.61 tff(1852,plain,
% 1.98/1.61 (~hskp22),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1851, 492, 403, 401, 481, 402, 470])).
% 1.98/1.61 tff(1853,plain,
% 1.98/1.61 (~c0_1(a496)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[797, 112, 1852, 1839, 1838, 1837, 31])).
% 1.98/1.61 tff(1854,plain,
% 1.98/1.61 (~c2_1(a568)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1270, 112, 1808, 401, 1818, 402, 1817, 240, 1825])).
% 1.98/1.61 tff(1855,plain,
% 1.98/1.61 (c2_1(a505)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1066, 1816])).
% 1.98/1.61 tff(1856,plain,
% 1.98/1.61 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c3_1(a520) | c0_1(a505) | (~ndr1_0) | c1_1(a505) | (~c2_1(a505)) | (~c0_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c3_1(a520) | c0_1(a505) | (~ndr1_0) | c1_1(a505) | (~c2_1(a505)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1857,plain,
% 1.98/1.61 ((hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a505) | c0_1(a505) | (~c2_1(a505))) <=> (hskp4 | c3_1(a520) | c0_1(a505) | (~ndr1_0) | c1_1(a505) | (~c2_1(a505)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1858,plain,
% 1.98/1.61 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a505) | c0_1(a505) | (~c2_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c3_1(a520) | c0_1(a505) | (~ndr1_0) | c1_1(a505) | (~c2_1(a505)) | (~c0_1(a520)) | (~c2_1(a520))))),
% 1.98/1.61 inference(monotonicity,[status(thm)],[1857])).
% 1.98/1.61 tff(1859,plain,
% 1.98/1.61 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a505) | c0_1(a505) | (~c2_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c3_1(a520) | c0_1(a505) | (~ndr1_0) | c1_1(a505) | (~c2_1(a505)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 1.98/1.61 inference(transitivity,[status(thm)],[1858, 1856])).
% 1.98/1.61 tff(1860,plain,
% 1.98/1.61 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a505) | c0_1(a505) | (~c2_1(a505)))),
% 1.98/1.61 inference(quant_inst,[status(thm)],[])).
% 1.98/1.61 tff(1861,plain,
% 1.98/1.61 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c3_1(a520) | c0_1(a505) | (~ndr1_0) | c1_1(a505) | (~c2_1(a505)) | (~c0_1(a520)) | (~c2_1(a520))),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1860, 1859])).
% 1.98/1.61 tff(1862,plain,
% 1.98/1.61 (hskp4),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1861, 112, 1529, 1531, 1855, 1530, 1817, 400, 1825])).
% 1.98/1.61 tff(1863,plain,
% 1.98/1.61 (~c0_1(a498)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1493, 1862])).
% 1.98/1.61 tff(1864,plain,
% 1.98/1.61 (c1_1(a498)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1504, 1862])).
% 1.98/1.61 tff(1865,plain,
% 1.98/1.61 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c1_1(a568) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c0_1(a568)) | c2_1(a568))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a568) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c0_1(a568)) | c2_1(a568))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1866,plain,
% 1.98/1.61 ((hskp10 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a498) | (~c1_1(a498)) | (~c3_1(a498))) <=> (hskp10 | c1_1(a568) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c0_1(a568)) | c2_1(a568))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1867,plain,
% 1.98/1.61 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a498) | (~c1_1(a498)) | (~c3_1(a498)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | c1_1(a568) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c0_1(a568)) | c2_1(a568)))),
% 1.98/1.61 inference(monotonicity,[status(thm)],[1866])).
% 1.98/1.61 tff(1868,plain,
% 1.98/1.61 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a498) | (~c1_1(a498)) | (~c3_1(a498)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a568) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c0_1(a568)) | c2_1(a568))),
% 1.98/1.61 inference(transitivity,[status(thm)],[1867, 1865])).
% 1.98/1.61 tff(1869,plain,
% 1.98/1.61 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a568) | c1_1(a568) | (~c0_1(a568)) | c0_1(a498) | (~c1_1(a498)) | (~c3_1(a498)))),
% 1.98/1.61 inference(quant_inst,[status(thm)],[])).
% 1.98/1.61 tff(1870,plain,
% 1.98/1.61 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp10 | c1_1(a568) | c0_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c0_1(a568)) | c2_1(a568)),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1869, 1868])).
% 1.98/1.61 tff(1871,plain,
% 1.98/1.61 (~c3_1(a498)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1870, 112, 11, 401, 1864, 402, 1863, 53, 1854])).
% 1.98/1.61 tff(1872,plain,
% 1.98/1.61 (~c2_1(a498)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1517, 1862])).
% 1.98/1.61 tff(1873,plain,
% 1.98/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a520) | c0_1(a498) | c2_1(a498) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c3_1(a498) | (~c1_1(a520)) | (~c2_1(a520)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a520) | c0_1(a498) | c2_1(a498) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c3_1(a498) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1874,plain,
% 1.98/1.61 (((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a496) | c1_1(a496) | c0_1(a496)) <=> (c3_1(a520) | c0_1(a498) | c2_1(a498) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c3_1(a498) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1875,plain,
% 1.98/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a520) | c0_1(a498) | c2_1(a498) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c3_1(a498) | (~c1_1(a520)) | (~c2_1(a520))))),
% 1.98/1.61 inference(monotonicity,[status(thm)],[1874])).
% 1.98/1.61 tff(1876,plain,
% 1.98/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a520) | c0_1(a498) | c2_1(a498) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c3_1(a498) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.98/1.61 inference(transitivity,[status(thm)],[1875, 1873])).
% 1.98/1.61 tff(1877,plain,
% 1.98/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a496) | c1_1(a496) | c0_1(a496))),
% 1.98/1.61 inference(quant_inst,[status(thm)],[])).
% 1.98/1.61 tff(1878,plain,
% 1.98/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a520) | c0_1(a498) | c2_1(a498) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c3_1(a498) | (~c1_1(a520)) | (~c2_1(a520))),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1877, 1876])).
% 1.98/1.61 tff(1879,plain,
% 1.98/1.61 (c0_1(a496) | (~c1_1(a520))),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1878, 112, 1531, 1530, 1863, 1872, 1839, 1837, 784, 1871])).
% 1.98/1.61 tff(1880,plain,
% 1.98/1.61 (~c1_1(a520)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1879, 1853])).
% 1.98/1.61 tff(1881,plain,
% 1.98/1.61 (^[U: $i] : refl((hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.98/1.61 inference(bind,[status(th)],[])).
% 1.98/1.61 tff(1882,plain,
% 1.98/1.61 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.98/1.61 inference(quant_intro,[status(thm)],[1881])).
% 1.98/1.61 tff(1883,plain,
% 1.98/1.61 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1884,plain,
% 1.98/1.61 (^[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) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp5) | hskp7) <=> ((hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp7))), rewrite(((hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp7) <=> (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp5) | hskp7) <=> (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.98/1.61 inference(bind,[status(th)],[])).
% 1.98/1.61 tff(1885,plain,
% 1.98/1.61 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp5) | hskp7) <=> ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.98/1.61 inference(quant_intro,[status(thm)],[1884])).
% 1.98/1.61 tff(1886,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp5) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 1.98/1.61 tff(1887,plain,
% 1.98/1.61 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 1.98/1.61 tff(1888,plain,
% 1.98/1.61 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1887, 1883])).
% 1.98/1.61 tff(1889,plain,(
% 1.98/1.61 ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.98/1.61 inference(skolemize,[status(sab)],[1888])).
% 1.98/1.61 tff(1890,plain,
% 1.98/1.61 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1889, 1882])).
% 1.98/1.61 tff(1891,plain,
% 1.98/1.61 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp7 | hskp5 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp7 | hskp5 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1892,plain,
% 1.98/1.61 ((hskp7 | hskp5 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520))) <=> (hskp7 | hskp5 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1893,plain,
% 1.98/1.61 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp7 | hskp5 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520))))),
% 1.98/1.61 inference(monotonicity,[status(thm)],[1892])).
% 1.98/1.61 tff(1894,plain,
% 1.98/1.61 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp7 | hskp5 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))),
% 1.98/1.61 inference(transitivity,[status(thm)],[1893, 1891])).
% 1.98/1.61 tff(1895,plain,
% 1.98/1.61 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)))),
% 1.98/1.61 inference(quant_inst,[status(thm)],[])).
% 1.98/1.61 tff(1896,plain,
% 1.98/1.61 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp7 | hskp5 | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520))),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1895, 1894])).
% 1.98/1.61 tff(1897,plain,
% 1.98/1.61 (hskp7 | hskp5 | c1_1(a520)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1896, 112, 1529, 1530, 1890])).
% 1.98/1.61 tff(1898,plain,
% 1.98/1.61 (hskp5),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1897, 1880, 1808])).
% 1.98/1.61 tff(1899,plain,
% 1.98/1.61 (((~hskp5) | c0_1(a499)) <=> ((~hskp5) | c0_1(a499))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1900,axiom,((~hskp5) | c0_1(a499)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 1.98/1.61 tff(1901,plain,
% 1.98/1.61 ((~hskp5) | c0_1(a499)),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1900, 1899])).
% 1.98/1.61 tff(1902,plain,
% 1.98/1.61 ((~hskp5) | c0_1(a499)),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1901, 1899])).
% 1.98/1.61 tff(1903,plain,
% 1.98/1.61 ((~hskp5) | c0_1(a499)),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1902, 1899])).
% 1.98/1.61 tff(1904,plain,
% 1.98/1.61 ((~hskp5) | c0_1(a499)),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1903, 1899])).
% 1.98/1.61 tff(1905,plain,
% 1.98/1.61 ((~hskp5) | c0_1(a499)),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1904, 1899])).
% 1.98/1.61 tff(1906,plain,
% 1.98/1.61 ((~hskp5) | c0_1(a499)),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1905, 1899])).
% 1.98/1.61 tff(1907,plain,
% 1.98/1.61 ((~hskp5) | c0_1(a499)),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1906, 1899])).
% 1.98/1.61 tff(1908,plain,
% 1.98/1.61 ((~hskp5) | c0_1(a499)),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1907, 1899])).
% 1.98/1.61 tff(1909,plain,
% 1.98/1.61 (c0_1(a499)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1908, 1898])).
% 1.98/1.61 tff(1910,plain,
% 1.98/1.61 (((~hskp5) | c2_1(a499)) <=> ((~hskp5) | c2_1(a499))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1911,axiom,((~hskp5) | c2_1(a499)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 1.98/1.61 tff(1912,plain,
% 1.98/1.61 ((~hskp5) | c2_1(a499)),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1911, 1910])).
% 1.98/1.61 tff(1913,plain,
% 1.98/1.61 ((~hskp5) | c2_1(a499)),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1912, 1910])).
% 1.98/1.61 tff(1914,plain,
% 1.98/1.61 ((~hskp5) | c2_1(a499)),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1913, 1910])).
% 1.98/1.61 tff(1915,plain,
% 1.98/1.61 ((~hskp5) | c2_1(a499)),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1914, 1910])).
% 1.98/1.61 tff(1916,plain,
% 1.98/1.61 ((~hskp5) | c2_1(a499)),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1915, 1910])).
% 1.98/1.61 tff(1917,plain,
% 1.98/1.61 ((~hskp5) | c2_1(a499)),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1916, 1910])).
% 1.98/1.61 tff(1918,plain,
% 1.98/1.61 ((~hskp5) | c2_1(a499)),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1917, 1910])).
% 1.98/1.61 tff(1919,plain,
% 1.98/1.61 ((~hskp5) | c2_1(a499)),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1918, 1910])).
% 1.98/1.61 tff(1920,plain,
% 1.98/1.61 (c2_1(a499)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1919, 1898])).
% 1.98/1.61 tff(1921,plain,
% 1.98/1.61 (((~hskp5) | (~c1_1(a499))) <=> ((~hskp5) | (~c1_1(a499)))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1922,plain,
% 1.98/1.61 (((~c1_1(a499)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a499)))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1923,axiom,((~c1_1(a499)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 1.98/1.61 tff(1924,plain,
% 1.98/1.61 ((~hskp5) | (~c1_1(a499))),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1923, 1922])).
% 1.98/1.61 tff(1925,plain,
% 1.98/1.61 ((~hskp5) | (~c1_1(a499))),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1924, 1921])).
% 1.98/1.61 tff(1926,plain,
% 1.98/1.61 (~c1_1(a499)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1925, 1898])).
% 1.98/1.61 tff(1927,assumption,(~c1_1(a505)), introduced(assumption)).
% 1.98/1.61 tff(1928,assumption,(~c1_1(a499)), introduced(assumption)).
% 1.98/1.61 tff(1929,assumption,(c2_1(a499)), introduced(assumption)).
% 1.98/1.61 tff(1930,assumption,(c0_1(a499)), introduced(assumption)).
% 1.98/1.61 tff(1931,assumption,(~hskp7), introduced(assumption)).
% 1.98/1.61 tff(1932,plain,
% 1.98/1.61 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a505) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a505)) | c1_1(a505))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a505) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a505)) | c1_1(a505))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1933,plain,
% 1.98/1.61 ((hskp7 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505))) <=> (hskp7 | c0_1(a505) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a505)) | c1_1(a505))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1934,plain,
% 1.98/1.61 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a505) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a505)) | c1_1(a505)))),
% 1.98/1.61 inference(monotonicity,[status(thm)],[1933])).
% 1.98/1.61 tff(1935,plain,
% 1.98/1.61 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a505) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a505)) | c1_1(a505))),
% 1.98/1.61 inference(transitivity,[status(thm)],[1934, 1932])).
% 1.98/1.61 tff(1936,plain,
% 1.98/1.61 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c1_1(a505) | c0_1(a505) | (~c3_1(a505)))),
% 1.98/1.61 inference(quant_inst,[status(thm)],[])).
% 1.98/1.61 tff(1937,plain,
% 1.98/1.61 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a505) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a505)) | c1_1(a505)),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1936, 1935])).
% 1.98/1.61 tff(1938,plain,
% 1.98/1.61 ($false),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1937, 112, 1931, 1195, 1930, 1929, 1176, 1928, 240, 1927])).
% 1.98/1.61 tff(1939,plain,(c1_1(a505) | hskp7 | (~c3_1(a505)) | (~c0_1(a499)) | (~c2_1(a499)) | c0_1(a505) | c1_1(a499)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.61 tff(1940,plain,
% 1.98/1.61 ($false),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1939, 1926, 1920, 1808, 1818, 1825, 1817, 1909])).
% 1.98/1.61 tff(1941,plain,(c3_1(a502) | hskp10 | (~c0_1(a568)) | c1_1(a568) | (~hskp15) | (~c3_1(a568)) | c0_1(a502)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.61 tff(1942,plain,
% 1.98/1.61 (c3_1(a502)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1941, 1527, 222, 252, 11, 211, 263])).
% 1.98/1.61 tff(1943,plain,
% 1.98/1.61 (~c3_1(a528)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[469, 1527])).
% 1.98/1.61 tff(1944,plain,
% 1.98/1.61 (c1_1(a528)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[480, 1527])).
% 1.98/1.61 tff(1945,plain,
% 1.98/1.61 (c0_1(a528)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[491, 1527])).
% 1.98/1.61 tff(1946,plain,
% 1.98/1.61 ((~c1_1(a502)) | (~c3_1(a502))),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1404, 112, 222, 211, 1945, 1944, 252, 1943, 263, 1398])).
% 1.98/1.61 tff(1947,plain,
% 1.98/1.61 (~c1_1(a502)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1946, 1942])).
% 1.98/1.61 tff(1948,plain,
% 1.98/1.61 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a568) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1949,plain,
% 1.98/1.61 ((hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a502) | c0_1(a502) | (~c3_1(a502))) <=> (hskp28 | c1_1(a568) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1950,plain,
% 1.98/1.61 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a502) | c0_1(a502) | (~c3_1(a502)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a568) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.98/1.61 inference(monotonicity,[status(thm)],[1949])).
% 1.98/1.61 tff(1951,plain,
% 1.98/1.61 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a502) | c0_1(a502) | (~c3_1(a502)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.61 inference(transitivity,[status(thm)],[1950, 1948])).
% 1.98/1.61 tff(1952,plain,
% 1.98/1.61 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a502) | c0_1(a502) | (~c3_1(a502)))),
% 1.98/1.61 inference(quant_inst,[status(thm)],[])).
% 1.98/1.61 tff(1953,plain,
% 1.98/1.61 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a502) | c1_1(a502) | (~c3_1(a502)) | (~ndr1_0) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1952, 1951])).
% 1.98/1.61 tff(1954,plain,
% 1.98/1.61 (hskp28),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1953, 112, 222, 211, 252, 263, 1947, 1942, 262])).
% 1.98/1.61 tff(1955,plain,
% 1.98/1.61 (c3_1(a500)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[429, 1954])).
% 1.98/1.61 tff(1956,plain,
% 1.98/1.61 (c0_1(a500)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[451, 1954])).
% 1.98/1.61 tff(1957,plain,
% 1.98/1.61 (c2_1(a500)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[440, 1954])).
% 1.98/1.61 tff(1958,plain,
% 1.98/1.61 (hskp2),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[503, 1957, 1527, 1956, 1955])).
% 1.98/1.61 tff(1959,plain,
% 1.98/1.61 (~c3_1(a496)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[362, 1958])).
% 1.98/1.61 tff(1960,plain,
% 1.98/1.61 (~c2_1(a496)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[368, 1958])).
% 1.98/1.61 tff(1961,plain,
% 1.98/1.61 (~c1_1(a496)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[381, 1958])).
% 1.98/1.61 tff(1962,plain,
% 1.98/1.61 (~hskp22),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1851, 1945, 211, 222, 1944, 252, 1943])).
% 1.98/1.61 tff(1963,plain,
% 1.98/1.61 (~c0_1(a496)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[797, 112, 1962, 1961, 1960, 1959, 31])).
% 1.98/1.61 tff(1964,plain,
% 1.98/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a520) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a520) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1965,plain,
% 1.98/1.61 (((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496)) <=> (c3_1(a520) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1966,plain,
% 1.98/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a520) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520))))),
% 1.98/1.61 inference(monotonicity,[status(thm)],[1965])).
% 1.98/1.61 tff(1967,plain,
% 1.98/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a520) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))),
% 1.98/1.61 inference(transitivity,[status(thm)],[1966, 1964])).
% 1.98/1.61 tff(1968,plain,
% 1.98/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496))),
% 1.98/1.61 inference(quant_inst,[status(thm)],[])).
% 1.98/1.61 tff(1969,plain,
% 1.98/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a520) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520))),
% 1.98/1.61 inference(modus_ponens,[status(thm)],[1968, 1967])).
% 1.98/1.61 tff(1970,plain,
% 1.98/1.61 (c0_1(a496) | (~c1_1(a520))),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1969, 112, 1470, 1459, 1961, 1960, 1959, 784])).
% 1.98/1.61 tff(1971,plain,
% 1.98/1.61 (~c1_1(a520)),
% 1.98/1.61 inference(unit_resolution,[status(thm)],[1970, 1963])).
% 1.98/1.61 tff(1972,plain,
% 1.98/1.61 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c3_1(a520) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c3_1(a520) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c2_1(a520)))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1973,plain,
% 1.98/1.61 ((hskp0 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c2_1(a520)) | c2_1(a496) | c1_1(a496) | c0_1(a496)) <=> (hskp0 | c3_1(a520) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c2_1(a520)))),
% 1.98/1.61 inference(rewrite,[status(thm)],[])).
% 1.98/1.61 tff(1974,plain,
% 1.98/1.61 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c2_1(a520)) | c2_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c3_1(a520) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c2_1(a520))))),
% 1.98/1.62 inference(monotonicity,[status(thm)],[1973])).
% 1.98/1.62 tff(1975,plain,
% 1.98/1.62 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c2_1(a520)) | c2_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c3_1(a520) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c2_1(a520)))),
% 1.98/1.62 inference(transitivity,[status(thm)],[1974, 1972])).
% 1.98/1.62 tff(1976,plain,
% 1.98/1.62 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c2_1(a520)) | c2_1(a496) | c1_1(a496) | c0_1(a496))),
% 1.98/1.62 inference(quant_inst,[status(thm)],[])).
% 1.98/1.62 tff(1977,plain,
% 1.98/1.62 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c3_1(a520) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c2_1(a520))),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[1976, 1975])).
% 1.98/1.62 tff(1978,plain,
% 1.98/1.62 (hskp0 | c0_1(a496) | c1_1(a520)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[1977, 112, 1470, 1459, 1961, 1960, 854])).
% 1.98/1.62 tff(1979,plain,
% 1.98/1.62 (hskp0),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[1978, 1963, 1971])).
% 1.98/1.62 tff(1980,plain,
% 1.98/1.62 (~c2_1(a494)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[1702, 1979])).
% 1.98/1.62 tff(1981,plain,
% 1.98/1.62 (~c0_1(a494)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[878, 1979])).
% 1.98/1.62 tff(1982,plain,
% 1.98/1.62 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c3_1(a520) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a520) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c0_1(a520)))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(1983,plain,
% 1.98/1.62 ((hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a496) | c0_1(a496) | c3_1(a496)) <=> (hskp1 | c3_1(a520) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c0_1(a520)))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(1984,plain,
% 1.98/1.62 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a496) | c0_1(a496) | c3_1(a496))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c3_1(a520) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c0_1(a520))))),
% 1.98/1.62 inference(monotonicity,[status(thm)],[1983])).
% 1.98/1.62 tff(1985,plain,
% 1.98/1.62 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a496) | c0_1(a496) | c3_1(a496))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a520) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c0_1(a520)))),
% 1.98/1.62 inference(transitivity,[status(thm)],[1984, 1982])).
% 1.98/1.62 tff(1986,plain,
% 1.98/1.62 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a496) | c0_1(a496) | c3_1(a496))),
% 1.98/1.62 inference(quant_inst,[status(thm)],[])).
% 1.98/1.62 tff(1987,plain,
% 1.98/1.62 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c3_1(a520) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | c1_1(a520) | (~c0_1(a520))),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[1986, 1985])).
% 1.98/1.62 tff(1988,plain,
% 1.98/1.62 (hskp1 | c1_1(a520)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[1987, 112, 1481, 1459, 1961, 1959, 645, 1963])).
% 1.98/1.62 tff(1989,plain,
% 1.98/1.62 (hskp1),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[1988, 1971])).
% 1.98/1.62 tff(1990,plain,
% 1.98/1.62 (~c3_1(a495)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[1019, 1989])).
% 1.98/1.62 tff(1991,plain,
% 1.98/1.62 (~c0_1(a495)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[1025, 1989])).
% 1.98/1.62 tff(1992,plain,
% 1.98/1.62 (c3_1(a494)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[893, 1979])).
% 1.98/1.62 tff(1993,plain,
% 1.98/1.62 (c1_1(a495)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[1037, 1989])).
% 1.98/1.62 tff(1994,plain,
% 1.98/1.62 ($false),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[1734, 112, 1945, 1944, 1993, 1992, 1943, 1991, 1990, 1981, 1980, 21])).
% 1.98/1.62 tff(1995,plain,(c0_1(a502) | hskp10 | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.98/1.62 tff(1996,plain,
% 1.98/1.62 (c0_1(a502)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[1995, 11, 32])).
% 1.98/1.62 tff(1997,plain,
% 1.98/1.62 (~hskp7),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[709, 1996])).
% 1.98/1.62 tff(1998,plain,
% 1.98/1.62 ($false),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[326, 112, 1997, 222, 192, 252, 246, 240, 230, 199])).
% 1.98/1.62 tff(1999,plain,(hskp15 | hskp10 | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.98/1.62 tff(2000,plain,
% 1.98/1.62 (hskp15),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[1999, 11, 32])).
% 1.98/1.62 tff(2001,plain,
% 1.98/1.62 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.98/1.62 inference(bind,[status(th)],[])).
% 1.98/1.62 tff(2002,plain,
% 1.98/1.62 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.98/1.62 inference(quant_intro,[status(thm)],[2001])).
% 1.98/1.62 tff(2003,plain,
% 1.98/1.62 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2004,plain,
% 1.98/1.62 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_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) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_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) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp23))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.98/1.62 inference(bind,[status(th)],[])).
% 1.98/1.62 tff(2005,plain,
% 1.98/1.62 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.98/1.62 inference(quant_intro,[status(thm)],[2004])).
% 1.98/1.62 tff(2006,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 1.98/1.62 tff(2007,plain,
% 1.98/1.62 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2006, 2005])).
% 1.98/1.62 tff(2008,plain,
% 1.98/1.62 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2007, 2003])).
% 1.98/1.62 tff(2009,plain,(
% 1.98/1.62 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.98/1.62 inference(skolemize,[status(sab)],[2008])).
% 1.98/1.62 tff(2010,plain,
% 1.98/1.62 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2009, 2002])).
% 1.98/1.62 tff(2011,assumption,(hskp28), introduced(assumption)).
% 1.98/1.62 tff(2012,plain,
% 1.98/1.62 (c3_1(a500)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[429, 2011])).
% 1.98/1.62 tff(2013,plain,
% 1.98/1.62 (c0_1(a500)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[451, 2011])).
% 1.98/1.62 tff(2014,plain,
% 1.98/1.62 (c2_1(a500)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[440, 2011])).
% 1.98/1.62 tff(2015,plain,
% 1.98/1.62 ($false),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[503, 2014, 2013, 464, 453, 2012])).
% 1.98/1.62 tff(2016,plain,((~hskp28) | (~hskp15) | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.98/1.62 tff(2017,plain,
% 1.98/1.62 (~hskp28),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[2016, 453, 464])).
% 1.98/1.62 tff(2018,plain,
% 1.98/1.62 (~c1_1(a536)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[576, 1083])).
% 1.98/1.62 tff(2019,assumption,(~hskp28), introduced(assumption)).
% 1.98/1.62 tff(2020,plain,
% 1.98/1.62 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a568) | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c3_1(a536)) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c3_1(a536)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2021,plain,
% 1.98/1.62 ((hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a536) | c0_1(a536) | (~c3_1(a536))) <=> (hskp28 | c1_1(a568) | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c3_1(a536)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2022,plain,
% 1.98/1.62 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a536) | c0_1(a536) | (~c3_1(a536)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a568) | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c3_1(a536)) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.98/1.62 inference(monotonicity,[status(thm)],[2021])).
% 1.98/1.62 tff(2023,plain,
% 1.98/1.62 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a536) | c0_1(a536) | (~c3_1(a536)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c3_1(a536)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.62 inference(transitivity,[status(thm)],[2022, 2020])).
% 1.98/1.62 tff(2024,plain,
% 1.98/1.62 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a568) | (~c3_1(a568)) | (~c0_1(a568)) | c1_1(a536) | c0_1(a536) | (~c3_1(a536)))),
% 1.98/1.62 inference(quant_inst,[status(thm)],[])).
% 1.98/1.62 tff(2025,plain,
% 1.98/1.62 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a568) | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c3_1(a536)) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2024, 2023])).
% 1.98/1.62 tff(2026,plain,
% 1.98/1.62 (~c3_1(a536)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[2025, 112, 2019, 401, 403, 402, 1090, 2018, 262])).
% 1.98/1.62 tff(2027,plain,
% 1.98/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a536) | c1_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a536) | c1_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2028,plain,
% 1.98/1.62 (((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a536) | c1_1(a536) | c0_1(a536)) <=> (c0_1(a536) | c1_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2029,plain,
% 1.98/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a536) | c1_1(a536) | c0_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a536) | c1_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536)))),
% 1.98/1.62 inference(monotonicity,[status(thm)],[2028])).
% 1.98/1.62 tff(2030,plain,
% 1.98/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a536) | c1_1(a536) | c0_1(a536))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a536) | c1_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536))),
% 1.98/1.62 inference(transitivity,[status(thm)],[2029, 2027])).
% 1.98/1.62 tff(2031,plain,
% 1.98/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a536) | c0_1(a536) | c3_1(a536) | c3_1(a536) | c1_1(a536) | c0_1(a536))),
% 1.98/1.62 inference(quant_inst,[status(thm)],[])).
% 1.98/1.62 tff(2032,plain,
% 1.98/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a536) | c1_1(a536) | c2_1(a536) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c3_1(a536)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 1.98/1.62 tff(2033,plain,
% 1.98/1.62 (~c2_1(a528)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[2032, 112, 1091, 1090, 2018, 1089, 1082, 784, 2026])).
% 1.98/1.62 tff(2034,plain,
% 1.98/1.62 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)) | c3_1(a536))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)) | c3_1(a536))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2035,plain,
% 1.98/1.62 ((hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a536) | c0_1(a536) | c3_1(a536)) <=> (hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)) | c3_1(a536))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2036,plain,
% 1.98/1.62 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a536) | c0_1(a536) | c3_1(a536))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)) | c3_1(a536)))),
% 1.98/1.62 inference(monotonicity,[status(thm)],[2035])).
% 1.98/1.62 tff(2037,plain,
% 1.98/1.62 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a536) | c0_1(a536) | c3_1(a536))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)) | c3_1(a536))),
% 1.98/1.62 inference(transitivity,[status(thm)],[2036, 2034])).
% 1.98/1.62 tff(2038,plain,
% 1.98/1.62 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a536) | c0_1(a536) | c3_1(a536))),
% 1.98/1.62 inference(quant_inst,[status(thm)],[])).
% 1.98/1.62 tff(2039,plain,
% 1.98/1.62 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a536) | c1_1(a536) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)) | c3_1(a536)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2038, 2037])).
% 1.98/1.62 tff(2040,plain,
% 1.98/1.62 (~c1_1(a520)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[2039, 112, 453, 1533, 1532, 1090, 2018, 320, 2026])).
% 1.98/1.62 tff(2041,plain,
% 1.98/1.62 (~hskp22),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[1851, 1092, 403, 401, 1091, 402, 1082])).
% 1.98/1.62 tff(2042,plain,
% 1.98/1.62 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a528)) | c2_1(a528))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a528)) | c2_1(a528))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2043,plain,
% 1.98/1.62 ((hskp22 | (~ndr1_0) | c3_1(a528) | c2_1(a528) | (~c0_1(a528)) | c1_1(a520) | c3_1(a520) | (~c0_1(a520))) <=> (hskp22 | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a528)) | c2_1(a528))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2044,plain,
% 1.98/1.62 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a528) | c2_1(a528) | (~c0_1(a528)) | c1_1(a520) | c3_1(a520) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a528)) | c2_1(a528)))),
% 1.98/1.62 inference(monotonicity,[status(thm)],[2043])).
% 1.98/1.62 tff(2045,plain,
% 1.98/1.62 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a528) | c2_1(a528) | (~c0_1(a528)) | c1_1(a520) | c3_1(a520) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a528)) | c2_1(a528))),
% 1.98/1.62 inference(transitivity,[status(thm)],[2044, 2042])).
% 1.98/1.62 tff(2046,plain,
% 1.98/1.62 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a528) | c2_1(a528) | (~c0_1(a528)) | c1_1(a520) | c3_1(a520) | (~c0_1(a520)))),
% 1.98/1.62 inference(quant_inst,[status(thm)],[])).
% 1.98/1.62 tff(2047,plain,
% 1.98/1.62 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a528)) | c2_1(a528)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2046, 2045])).
% 1.98/1.62 tff(2048,plain,
% 1.98/1.62 ($false),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[2047, 112, 2041, 1092, 1533, 1082, 1542, 31, 2040, 2033])).
% 1.98/1.62 tff(2049,plain,((~hskp20) | (~c0_1(a528)) | (~c0_1(a520)) | c3_1(a528) | c3_1(a520) | (~c1_1(a528)) | hskp2 | (~c2_1(a520)) | hskp28 | (~c0_1(a568)) | (~c3_1(a568)) | c1_1(a568)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.62 tff(2050,plain,
% 1.98/1.62 (~hskp20),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[2049, 453, 1533, 470, 1542, 481, 492, 1532, 2017, 401, 403, 402])).
% 1.98/1.62 tff(2051,plain,
% 1.98/1.62 ((hskp28 | hskp21 | hskp20) <=> (hskp28 | hskp21 | hskp20)),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2052,plain,
% 1.98/1.62 (((hskp28 | hskp21) | hskp20) <=> (hskp28 | hskp21 | hskp20)),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2053,plain,
% 1.98/1.62 ((hskp28 | hskp21) <=> (hskp28 | hskp21)),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2054,plain,
% 1.98/1.62 (((hskp28 | hskp21) | hskp20) <=> ((hskp28 | hskp21) | hskp20)),
% 1.98/1.62 inference(monotonicity,[status(thm)],[2053])).
% 1.98/1.62 tff(2055,plain,
% 1.98/1.62 (((hskp28 | hskp21) | hskp20) <=> (hskp28 | hskp21 | hskp20)),
% 1.98/1.62 inference(transitivity,[status(thm)],[2054, 2052])).
% 1.98/1.62 tff(2056,axiom,((hskp28 | hskp21) | hskp20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 1.98/1.62 tff(2057,plain,
% 1.98/1.62 (hskp28 | hskp21 | hskp20),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2056, 2055])).
% 1.98/1.62 tff(2058,plain,
% 1.98/1.62 (hskp28 | hskp21 | hskp20),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2057, 2051])).
% 1.98/1.62 tff(2059,plain,
% 1.98/1.62 (hskp28 | hskp21 | hskp20),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2058, 2051])).
% 1.98/1.62 tff(2060,plain,
% 1.98/1.62 (hskp28 | hskp21 | hskp20),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2059, 2051])).
% 1.98/1.62 tff(2061,plain,
% 1.98/1.62 (hskp28 | hskp21 | hskp20),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2060, 2051])).
% 1.98/1.62 tff(2062,plain,
% 1.98/1.62 (hskp28 | hskp21 | hskp20),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2061, 2051])).
% 1.98/1.62 tff(2063,plain,
% 1.98/1.62 (hskp28 | hskp21 | hskp20),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2062, 2051])).
% 1.98/1.62 tff(2064,plain,
% 1.98/1.62 (hskp28 | hskp21 | hskp20),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2063, 2051])).
% 1.98/1.62 tff(2065,plain,
% 1.98/1.62 (hskp21),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[2064, 2050, 2017])).
% 1.98/1.62 tff(2066,plain,
% 1.98/1.62 (((~hskp21) | (~c3_1(a538))) <=> ((~hskp21) | (~c3_1(a538)))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2067,plain,
% 1.98/1.62 (((~c3_1(a538)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a538)))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2068,axiom,((~c3_1(a538)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 1.98/1.62 tff(2069,plain,
% 1.98/1.62 ((~hskp21) | (~c3_1(a538))),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2068, 2067])).
% 1.98/1.62 tff(2070,plain,
% 1.98/1.62 ((~hskp21) | (~c3_1(a538))),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2069, 2066])).
% 1.98/1.62 tff(2071,plain,
% 1.98/1.62 (~c3_1(a538)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[2070, 2065])).
% 1.98/1.62 tff(2072,plain,
% 1.98/1.62 (((~hskp21) | (~c1_1(a538))) <=> ((~hskp21) | (~c1_1(a538)))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2073,plain,
% 1.98/1.62 (((~c1_1(a538)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a538)))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2074,axiom,((~c1_1(a538)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 1.98/1.62 tff(2075,plain,
% 1.98/1.62 ((~hskp21) | (~c1_1(a538))),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2074, 2073])).
% 1.98/1.62 tff(2076,plain,
% 1.98/1.62 ((~hskp21) | (~c1_1(a538))),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2075, 2072])).
% 1.98/1.62 tff(2077,plain,
% 1.98/1.62 (~c1_1(a538)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[2076, 2065])).
% 1.98/1.62 tff(2078,plain,
% 1.98/1.62 (((~hskp21) | c0_1(a538)) <=> ((~hskp21) | c0_1(a538))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2079,axiom,((~hskp21) | c0_1(a538)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 1.98/1.62 tff(2080,plain,
% 1.98/1.62 ((~hskp21) | c0_1(a538)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2079, 2078])).
% 1.98/1.62 tff(2081,plain,
% 1.98/1.62 ((~hskp21) | c0_1(a538)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2080, 2078])).
% 1.98/1.62 tff(2082,plain,
% 1.98/1.62 ((~hskp21) | c0_1(a538)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2081, 2078])).
% 1.98/1.62 tff(2083,plain,
% 1.98/1.62 ((~hskp21) | c0_1(a538)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2082, 2078])).
% 1.98/1.62 tff(2084,plain,
% 1.98/1.62 ((~hskp21) | c0_1(a538)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2083, 2078])).
% 1.98/1.62 tff(2085,plain,
% 1.98/1.62 ((~hskp21) | c0_1(a538)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2084, 2078])).
% 1.98/1.62 tff(2086,plain,
% 1.98/1.62 ((~hskp21) | c0_1(a538)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2085, 2078])).
% 1.98/1.62 tff(2087,plain,
% 1.98/1.62 ((~hskp21) | c0_1(a538)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2086, 2078])).
% 1.98/1.62 tff(2088,plain,
% 1.98/1.62 (c0_1(a538)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[2087, 2065])).
% 1.98/1.62 tff(2089,plain,
% 1.98/1.62 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a538) | c3_1(a538) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a538)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a538) | c3_1(a538) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a538)))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2090,plain,
% 1.98/1.62 ((hskp23 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538))) <=> (hskp23 | c1_1(a538) | c3_1(a538) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a538)))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2091,plain,
% 1.98/1.62 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c1_1(a538) | c3_1(a538) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a538))))),
% 1.98/1.62 inference(monotonicity,[status(thm)],[2090])).
% 1.98/1.62 tff(2092,plain,
% 1.98/1.62 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a538) | c3_1(a538) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a538)))),
% 1.98/1.62 inference(transitivity,[status(thm)],[2091, 2089])).
% 1.98/1.62 tff(2093,plain,
% 1.98/1.62 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538)))),
% 1.98/1.62 inference(quant_inst,[status(thm)],[])).
% 1.98/1.62 tff(2094,plain,
% 1.98/1.62 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c1_1(a538) | c3_1(a538) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | (~c0_1(a538))),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2093, 2092])).
% 1.98/1.62 tff(2095,plain,
% 1.98/1.62 (hskp23),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[2094, 112, 2088, 492, 481, 2077, 2071, 470, 2010])).
% 1.98/1.62 tff(2096,plain,
% 1.98/1.62 (((~hskp23) | (~c2_1(a541))) <=> ((~hskp23) | (~c2_1(a541)))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2097,plain,
% 1.98/1.62 (((~c2_1(a541)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a541)))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2098,axiom,((~c2_1(a541)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 1.98/1.62 tff(2099,plain,
% 1.98/1.62 ((~hskp23) | (~c2_1(a541))),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2098, 2097])).
% 1.98/1.62 tff(2100,plain,
% 1.98/1.62 ((~hskp23) | (~c2_1(a541))),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2099, 2096])).
% 1.98/1.62 tff(2101,plain,
% 1.98/1.62 (~c2_1(a541)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[2100, 2095])).
% 1.98/1.62 tff(2102,plain,
% 1.98/1.62 (((~hskp23) | c1_1(a541)) <=> ((~hskp23) | c1_1(a541))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2103,axiom,((~hskp23) | c1_1(a541)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 1.98/1.62 tff(2104,plain,
% 1.98/1.62 ((~hskp23) | c1_1(a541)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2103, 2102])).
% 1.98/1.62 tff(2105,plain,
% 1.98/1.62 ((~hskp23) | c1_1(a541)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2104, 2102])).
% 1.98/1.62 tff(2106,plain,
% 1.98/1.62 ((~hskp23) | c1_1(a541)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2105, 2102])).
% 1.98/1.62 tff(2107,plain,
% 1.98/1.62 ((~hskp23) | c1_1(a541)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2106, 2102])).
% 1.98/1.62 tff(2108,plain,
% 1.98/1.62 ((~hskp23) | c1_1(a541)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2107, 2102])).
% 1.98/1.62 tff(2109,plain,
% 1.98/1.62 ((~hskp23) | c1_1(a541)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2108, 2102])).
% 1.98/1.62 tff(2110,plain,
% 1.98/1.62 ((~hskp23) | c1_1(a541)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2109, 2102])).
% 1.98/1.62 tff(2111,plain,
% 1.98/1.62 ((~hskp23) | c1_1(a541)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2110, 2102])).
% 1.98/1.62 tff(2112,plain,
% 1.98/1.62 (c1_1(a541)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[2111, 2095])).
% 1.98/1.62 tff(2113,plain,
% 1.98/1.62 (((~hskp23) | c0_1(a541)) <=> ((~hskp23) | c0_1(a541))),
% 1.98/1.62 inference(rewrite,[status(thm)],[])).
% 1.98/1.62 tff(2114,axiom,((~hskp23) | c0_1(a541)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 1.98/1.62 tff(2115,plain,
% 1.98/1.62 ((~hskp23) | c0_1(a541)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2114, 2113])).
% 1.98/1.62 tff(2116,plain,
% 1.98/1.62 ((~hskp23) | c0_1(a541)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2115, 2113])).
% 1.98/1.62 tff(2117,plain,
% 1.98/1.62 ((~hskp23) | c0_1(a541)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2116, 2113])).
% 1.98/1.62 tff(2118,plain,
% 1.98/1.62 ((~hskp23) | c0_1(a541)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2117, 2113])).
% 1.98/1.62 tff(2119,plain,
% 1.98/1.62 ((~hskp23) | c0_1(a541)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2118, 2113])).
% 1.98/1.62 tff(2120,plain,
% 1.98/1.62 ((~hskp23) | c0_1(a541)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2119, 2113])).
% 1.98/1.62 tff(2121,plain,
% 1.98/1.62 ((~hskp23) | c0_1(a541)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2120, 2113])).
% 1.98/1.62 tff(2122,plain,
% 1.98/1.62 ((~hskp23) | c0_1(a541)),
% 1.98/1.62 inference(modus_ponens,[status(thm)],[2121, 2113])).
% 1.98/1.62 tff(2123,plain,
% 1.98/1.62 (c0_1(a541)),
% 1.98/1.62 inference(unit_resolution,[status(thm)],[2122, 2095])).
% 1.98/1.62 tff(2124,plain,
% 1.98/1.62 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a541) | (~ndr1_0) | (~c3_1(a541)) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a541) | (~ndr1_0) | (~c3_1(a541)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2125,plain,
% 1.98/1.63 ((hskp2 | (~ndr1_0) | c2_1(a541) | (~c3_1(a541)) | (~c0_1(a541)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541))) <=> (hskp2 | c2_1(a541) | (~ndr1_0) | (~c3_1(a541)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2126,plain,
% 1.98/1.63 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a541) | (~c3_1(a541)) | (~c0_1(a541)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a541) | (~ndr1_0) | (~c3_1(a541)) | (~c1_1(a541)) | (~c0_1(a541))))),
% 1.98/1.63 inference(monotonicity,[status(thm)],[2125])).
% 1.98/1.63 tff(2127,plain,
% 1.98/1.63 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a541) | (~c3_1(a541)) | (~c0_1(a541)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a541) | (~ndr1_0) | (~c3_1(a541)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.98/1.63 inference(transitivity,[status(thm)],[2126, 2124])).
% 1.98/1.63 tff(2128,plain,
% 1.98/1.63 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a541) | (~c3_1(a541)) | (~c0_1(a541)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.98/1.63 inference(quant_inst,[status(thm)],[])).
% 1.98/1.63 tff(2129,plain,
% 1.98/1.63 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a541) | (~ndr1_0) | (~c3_1(a541)) | (~c1_1(a541)) | (~c0_1(a541))),
% 1.98/1.63 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 1.98/1.63 tff(2130,plain,
% 1.98/1.63 (~c3_1(a541)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2129, 112, 453, 2123, 2112, 2101, 601])).
% 1.98/1.63 tff(2131,plain,
% 1.98/1.63 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c0_1(a538)) | c2_1(a538))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c0_1(a538)) | c2_1(a538))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2132,plain,
% 1.98/1.63 ((hskp22 | (~ndr1_0) | c3_1(a538) | c2_1(a538) | (~c0_1(a538)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538))) <=> (hskp22 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c0_1(a538)) | c2_1(a538))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2133,plain,
% 1.98/1.63 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a538) | c2_1(a538) | (~c0_1(a538)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c0_1(a538)) | c2_1(a538)))),
% 1.98/1.63 inference(monotonicity,[status(thm)],[2132])).
% 1.98/1.63 tff(2134,plain,
% 1.98/1.63 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a538) | c2_1(a538) | (~c0_1(a538)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c0_1(a538)) | c2_1(a538))),
% 1.98/1.63 inference(transitivity,[status(thm)],[2133, 2131])).
% 1.98/1.63 tff(2135,plain,
% 1.98/1.63 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a538) | c2_1(a538) | (~c0_1(a538)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538)))),
% 1.98/1.63 inference(quant_inst,[status(thm)],[])).
% 1.98/1.63 tff(2136,plain,
% 1.98/1.63 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c0_1(a538)) | c2_1(a538)),
% 1.98/1.63 inference(modus_ponens,[status(thm)],[2135, 2134])).
% 1.98/1.63 tff(2137,plain,
% 1.98/1.63 (c2_1(a538)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2136, 112, 1852, 2088, 2077, 2071, 31])).
% 1.98/1.63 tff(2138,plain,
% 1.98/1.63 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c2_1(a538)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c2_1(a538)))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2139,plain,
% 1.98/1.63 ((hskp20 | hskp12 | (~ndr1_0) | c3_1(a538) | c1_1(a538) | (~c2_1(a538))) <=> (hskp20 | hskp12 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c2_1(a538)))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2140,plain,
% 1.98/1.63 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a538) | c1_1(a538) | (~c2_1(a538)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c2_1(a538))))),
% 1.98/1.63 inference(monotonicity,[status(thm)],[2139])).
% 1.98/1.63 tff(2141,plain,
% 1.98/1.63 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a538) | c1_1(a538) | (~c2_1(a538)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c2_1(a538)))),
% 1.98/1.63 inference(transitivity,[status(thm)],[2140, 2138])).
% 1.98/1.63 tff(2142,plain,
% 1.98/1.63 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a538) | c1_1(a538) | (~c2_1(a538)))),
% 1.98/1.63 inference(quant_inst,[status(thm)],[])).
% 1.98/1.63 tff(2143,plain,
% 1.98/1.63 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a538) | c3_1(a538) | (~ndr1_0) | (~c2_1(a538))),
% 1.98/1.63 inference(modus_ponens,[status(thm)],[2142, 2141])).
% 1.98/1.63 tff(2144,plain,
% 1.98/1.63 (hskp12),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2143, 112, 2050, 2077, 2071, 1126, 2137])).
% 1.98/1.63 tff(2145,plain,
% 1.98/1.63 (~c2_1(a514)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[541, 2144])).
% 1.98/1.63 tff(2146,plain,
% 1.98/1.63 (c3_1(a514)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[552, 2144])).
% 1.98/1.63 tff(2147,plain,
% 1.98/1.63 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a541) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a541) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2148,plain,
% 1.98/1.63 ((hskp2 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541))) <=> (hskp2 | c2_1(a541) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2149,plain,
% 1.98/1.63 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a541) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)) | (~c1_1(a541)) | (~c0_1(a541))))),
% 1.98/1.63 inference(monotonicity,[status(thm)],[2148])).
% 1.98/1.63 tff(2150,plain,
% 1.98/1.63 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a541) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.98/1.63 inference(transitivity,[status(thm)],[2149, 2147])).
% 1.98/1.63 tff(2151,plain,
% 1.98/1.63 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a514) | (~c3_1(a514)) | (~c0_1(a514)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)))),
% 1.98/1.63 inference(quant_inst,[status(thm)],[])).
% 1.98/1.63 tff(2152,plain,
% 1.98/1.63 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a541) | c2_1(a514) | (~ndr1_0) | (~c3_1(a514)) | (~c0_1(a514)) | (~c1_1(a541)) | (~c0_1(a541))),
% 1.98/1.63 inference(modus_ponens,[status(thm)],[2151, 2150])).
% 1.98/1.63 tff(2153,plain,
% 1.98/1.63 (~c0_1(a514)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2152, 112, 453, 2123, 2112, 2146, 2101, 2145, 601])).
% 1.98/1.63 tff(2154,plain,
% 1.98/1.63 (c1_1(a514)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[563, 2144])).
% 1.98/1.63 tff(2155,plain,
% 1.98/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2156,plain,
% 1.98/1.63 (((~ndr1_0) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a514) | (~c3_1(a514)) | (~c1_1(a514))) <=> (c1_1(a568) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2157,plain,
% 1.98/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a514) | (~c3_1(a514)) | (~c1_1(a514)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | (~c0_1(a568)) | (~c3_1(a568))))),
% 1.98/1.63 inference(monotonicity,[status(thm)],[2156])).
% 1.98/1.63 tff(2158,plain,
% 1.98/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a514) | (~c3_1(a514)) | (~c1_1(a514)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 1.98/1.63 inference(transitivity,[status(thm)],[2157, 2155])).
% 1.98/1.63 tff(2159,plain,
% 1.98/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a514) | (~c3_1(a514)) | (~c1_1(a514)))),
% 1.98/1.63 inference(quant_inst,[status(thm)],[])).
% 1.98/1.63 tff(2160,plain,
% 1.98/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | (~ndr1_0) | (~c3_1(a514)) | (~c1_1(a514)) | c0_1(a514) | c3_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | (~c0_1(a568)) | (~c3_1(a568))),
% 1.98/1.63 inference(modus_ponens,[status(thm)],[2159, 2158])).
% 1.98/1.63 tff(2161,plain,
% 1.98/1.63 ($false),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2160, 112, 401, 403, 2123, 2112, 2154, 2146, 402, 1398, 2153, 2130])).
% 1.98/1.63 tff(2162,plain,(hskp2 | (~c0_1(a568)) | (~c3_1(a568)) | c1_1(a568) | (~c0_1(a520)) | c3_1(a520) | (~c2_1(a520)) | (~hskp15)), inference(lemma,lemma(discharge,[]))).
% 1.98/1.63 tff(2163,plain,
% 1.98/1.63 (hskp2),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2162, 222, 211, 252, 1481, 1459, 1470, 2000])).
% 1.98/1.63 tff(2164,plain,
% 1.98/1.63 (~c3_1(a496)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[362, 2163])).
% 1.98/1.63 tff(2165,plain,
% 1.98/1.63 (~c2_1(a496)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[368, 2163])).
% 1.98/1.63 tff(2166,plain,
% 1.98/1.63 (~c1_1(a496)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[381, 2163])).
% 1.98/1.63 tff(2167,plain,
% 1.98/1.63 (~c3_1(a528)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[469, 2000])).
% 1.98/1.63 tff(2168,plain,
% 1.98/1.63 (c1_1(a528)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[480, 2000])).
% 1.98/1.63 tff(2169,plain,
% 1.98/1.63 (c0_1(a528)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[491, 2000])).
% 1.98/1.63 tff(2170,plain,
% 1.98/1.63 (~hskp22),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[1851, 2169, 211, 222, 2168, 252, 2167])).
% 1.98/1.63 tff(2171,plain,
% 1.98/1.63 (~c0_1(a496)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[797, 112, 2170, 2166, 2165, 2164, 31])).
% 1.98/1.63 tff(2172,plain,
% 1.98/1.63 (c0_1(a496) | (~c1_1(a520))),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[1969, 112, 1470, 1459, 2166, 2165, 2164, 784])).
% 1.98/1.63 tff(2173,plain,
% 1.98/1.63 (~c1_1(a520)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2172, 2171])).
% 1.98/1.63 tff(2174,plain,
% 1.98/1.63 (hskp0 | c1_1(a520)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[1977, 112, 1470, 1459, 2166, 2165, 854, 2171])).
% 1.98/1.63 tff(2175,plain,
% 1.98/1.63 (hskp0),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2174, 2173])).
% 1.98/1.63 tff(2176,plain,
% 1.98/1.63 (~c2_1(a494)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[1702, 2175])).
% 1.98/1.63 tff(2177,plain,
% 1.98/1.63 (~c0_1(a494)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[878, 2175])).
% 1.98/1.63 tff(2178,plain,
% 1.98/1.63 (hskp1 | c1_1(a520)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[1987, 112, 1481, 1459, 2166, 2164, 645, 2171])).
% 1.98/1.63 tff(2179,plain,
% 1.98/1.63 (hskp1),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2178, 2173])).
% 1.98/1.63 tff(2180,plain,
% 1.98/1.63 (~c3_1(a495)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[1019, 2179])).
% 1.98/1.63 tff(2181,plain,
% 1.98/1.63 (~c0_1(a495)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[1025, 2179])).
% 1.98/1.63 tff(2182,plain,
% 1.98/1.63 (c3_1(a494)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[893, 2175])).
% 1.98/1.63 tff(2183,plain,
% 1.98/1.63 (c1_1(a495)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[1037, 2179])).
% 1.98/1.63 tff(2184,plain,
% 1.98/1.63 ($false),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[1734, 112, 2169, 2168, 2183, 2182, 2167, 2181, 2180, 2177, 2176, 21])).
% 1.98/1.63 tff(2185,plain,(hskp10 | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.98/1.63 tff(2186,plain,
% 1.98/1.63 (hskp26),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2185, 11])).
% 1.98/1.63 tff(2187,plain,
% 1.98/1.63 (((~hskp26) | (~c3_1(a559))) <=> ((~hskp26) | (~c3_1(a559)))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2188,plain,
% 1.98/1.63 (((~c3_1(a559)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a559)))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2189,axiom,((~c3_1(a559)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 1.98/1.63 tff(2190,plain,
% 1.98/1.63 ((~hskp26) | (~c3_1(a559))),
% 1.98/1.63 inference(modus_ponens,[status(thm)],[2189, 2188])).
% 1.98/1.63 tff(2191,plain,
% 1.98/1.63 ((~hskp26) | (~c3_1(a559))),
% 1.98/1.63 inference(modus_ponens,[status(thm)],[2190, 2187])).
% 1.98/1.63 tff(2192,plain,
% 1.98/1.63 (~c3_1(a559)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2191, 2186])).
% 1.98/1.63 tff(2193,plain,
% 1.98/1.63 (((~hskp26) | (~c2_1(a559))) <=> ((~hskp26) | (~c2_1(a559)))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2194,plain,
% 1.98/1.63 (((~c2_1(a559)) | (~hskp26)) <=> ((~hskp26) | (~c2_1(a559)))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2195,axiom,((~c2_1(a559)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 1.98/1.63 tff(2196,plain,
% 1.98/1.63 ((~hskp26) | (~c2_1(a559))),
% 1.98/1.63 inference(modus_ponens,[status(thm)],[2195, 2194])).
% 1.98/1.63 tff(2197,plain,
% 1.98/1.63 ((~hskp26) | (~c2_1(a559))),
% 1.98/1.63 inference(modus_ponens,[status(thm)],[2196, 2193])).
% 1.98/1.63 tff(2198,plain,
% 1.98/1.63 (~c2_1(a559)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2197, 2186])).
% 1.98/1.63 tff(2199,plain,
% 1.98/1.63 (((~hskp26) | (~c0_1(a559))) <=> ((~hskp26) | (~c0_1(a559)))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2200,plain,
% 1.98/1.63 (((~c0_1(a559)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a559)))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2201,axiom,((~c0_1(a559)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 1.98/1.63 tff(2202,plain,
% 1.98/1.63 ((~hskp26) | (~c0_1(a559))),
% 1.98/1.63 inference(modus_ponens,[status(thm)],[2201, 2200])).
% 1.98/1.63 tff(2203,plain,
% 1.98/1.63 ((~hskp26) | (~c0_1(a559))),
% 1.98/1.63 inference(modus_ponens,[status(thm)],[2202, 2199])).
% 1.98/1.63 tff(2204,plain,
% 1.98/1.63 (~c0_1(a559)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2203, 2186])).
% 1.98/1.63 tff(2205,plain,
% 1.98/1.63 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | c0_1(a559) | c2_1(a559) | c3_1(a559) | (~ndr1_0))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c0_1(a559) | c2_1(a559) | c3_1(a559) | (~ndr1_0))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2206,plain,
% 1.98/1.63 ((hskp11 | hskp10 | (~ndr1_0) | c3_1(a559) | c2_1(a559) | c0_1(a559)) <=> (hskp11 | hskp10 | c0_1(a559) | c2_1(a559) | c3_1(a559) | (~ndr1_0))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2207,plain,
% 1.98/1.63 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a559) | c2_1(a559) | c0_1(a559))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | c0_1(a559) | c2_1(a559) | c3_1(a559) | (~ndr1_0)))),
% 1.98/1.63 inference(monotonicity,[status(thm)],[2206])).
% 1.98/1.63 tff(2208,plain,
% 1.98/1.63 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a559) | c2_1(a559) | c0_1(a559))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c0_1(a559) | c2_1(a559) | c3_1(a559) | (~ndr1_0))),
% 1.98/1.63 inference(transitivity,[status(thm)],[2207, 2205])).
% 1.98/1.63 tff(2209,plain,
% 1.98/1.63 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp11 | hskp10 | (~ndr1_0) | c3_1(a559) | c2_1(a559) | c0_1(a559))),
% 1.98/1.63 inference(quant_inst,[status(thm)],[])).
% 1.98/1.63 tff(2210,plain,
% 1.98/1.63 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp11 | hskp10 | c0_1(a559) | c2_1(a559) | c3_1(a559) | (~ndr1_0)),
% 1.98/1.63 inference(modus_ponens,[status(thm)],[2209, 2208])).
% 1.98/1.63 tff(2211,plain,
% 1.98/1.63 (hskp11),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2210, 112, 11, 2204, 2198, 2192, 10])).
% 1.98/1.63 tff(2212,plain,
% 1.98/1.63 (~c2_1(a510)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[59, 2211])).
% 1.98/1.63 tff(2213,plain,
% 1.98/1.63 (~c1_1(a510)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[65, 2211])).
% 1.98/1.63 tff(2214,plain,
% 1.98/1.63 (c0_1(a510)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[76, 2211])).
% 1.98/1.63 tff(2215,plain,
% 1.98/1.63 (hskp15),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[162, 2211, 11])).
% 1.98/1.63 tff(2216,plain,
% 1.98/1.63 (~c3_1(a528)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[469, 2215])).
% 1.98/1.63 tff(2217,plain,
% 1.98/1.63 (c1_1(a528)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[480, 2215])).
% 1.98/1.63 tff(2218,plain,
% 1.98/1.63 (c0_1(a528)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[491, 2215])).
% 1.98/1.63 tff(2219,assumption,(c2_1(a528)), introduced(assumption)).
% 1.98/1.63 tff(2220,assumption,(~c3_1(a559)), introduced(assumption)).
% 1.98/1.63 tff(2221,assumption,(~c2_1(a559)), introduced(assumption)).
% 1.98/1.63 tff(2222,assumption,(~c0_1(a559)), introduced(assumption)).
% 1.98/1.63 tff(2223,plain,
% 1.98/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c1_1(a559))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c1_1(a559))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2224,plain,
% 1.98/1.63 (((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a559) | c0_1(a559) | c3_1(a559) | c3_1(a559) | c1_1(a559) | c0_1(a559)) <=> (c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c1_1(a559))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2225,plain,
% 1.98/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a559) | c0_1(a559) | c3_1(a559) | c3_1(a559) | c1_1(a559) | c0_1(a559))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c1_1(a559)))),
% 1.98/1.63 inference(monotonicity,[status(thm)],[2224])).
% 1.98/1.63 tff(2226,plain,
% 1.98/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a559) | c0_1(a559) | c3_1(a559) | c3_1(a559) | c1_1(a559) | c0_1(a559))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c1_1(a559))),
% 1.98/1.63 inference(transitivity,[status(thm)],[2225, 2223])).
% 1.98/1.63 tff(2227,plain,
% 1.98/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a559) | c0_1(a559) | c3_1(a559) | c3_1(a559) | c1_1(a559) | c0_1(a559))),
% 1.98/1.63 inference(quant_inst,[status(thm)],[])).
% 1.98/1.63 tff(2228,plain,
% 1.98/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c2_1(a528)) | c1_1(a559)),
% 1.98/1.63 inference(modus_ponens,[status(thm)],[2227, 2226])).
% 1.98/1.63 tff(2229,plain,
% 1.98/1.63 ((~c2_1(a528)) | c1_1(a559)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2228, 112, 1091, 2222, 2221, 2220, 1082, 784])).
% 1.98/1.63 tff(2230,plain,
% 1.98/1.63 (c1_1(a559)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2229, 2219])).
% 1.98/1.63 tff(2231,assumption,(~c2_1(a510)), introduced(assumption)).
% 1.98/1.63 tff(2232,assumption,(~c1_1(a510)), introduced(assumption)).
% 1.98/1.63 tff(2233,assumption,(c0_1(a510)), introduced(assumption)).
% 1.98/1.63 tff(2234,plain,
% 1.98/1.63 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2235,plain,
% 1.98/1.63 ((hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510))) <=> (hskp9 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2236,plain,
% 1.98/1.63 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c0_1(a528))))),
% 1.98/1.63 inference(monotonicity,[status(thm)],[2235])).
% 1.98/1.63 tff(2237,plain,
% 1.98/1.63 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 1.98/1.63 inference(transitivity,[status(thm)],[2236, 2234])).
% 1.98/1.63 tff(2238,plain,
% 1.98/1.63 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)))),
% 1.98/1.63 inference(quant_inst,[status(thm)],[])).
% 1.98/1.63 tff(2239,plain,
% 1.98/1.63 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c0_1(a528))),
% 1.98/1.63 inference(modus_ponens,[status(thm)],[2238, 2237])).
% 1.98/1.63 tff(2240,plain,
% 1.98/1.63 (hskp9),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2239, 112, 1092, 1091, 2233, 1082, 2232, 2231, 1282])).
% 1.98/1.63 tff(2241,plain,
% 1.98/1.63 (~c0_1(a507)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[930, 2240])).
% 1.98/1.63 tff(2242,plain,
% 1.98/1.63 (c3_1(a507)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[941, 2240])).
% 1.98/1.63 tff(2243,plain,
% 1.98/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a559) | c3_1(a559) | c3_1(a528) | c0_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a559)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a559) | c3_1(a559) | c3_1(a528) | c0_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a559)))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2244,plain,
% 1.98/1.63 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a559) | c3_1(a559) | (~c1_1(a559)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507)) <=> (c0_1(a559) | c3_1(a559) | c3_1(a528) | c0_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a559)))),
% 1.98/1.63 inference(rewrite,[status(thm)],[])).
% 1.98/1.63 tff(2245,plain,
% 1.98/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a559) | c3_1(a559) | (~c1_1(a559)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a559) | c3_1(a559) | c3_1(a528) | c0_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a559))))),
% 1.98/1.63 inference(monotonicity,[status(thm)],[2244])).
% 1.98/1.63 tff(2246,plain,
% 1.98/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a559) | c3_1(a559) | (~c1_1(a559)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a559) | c3_1(a559) | c3_1(a528) | c0_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a559)))),
% 1.98/1.63 inference(transitivity,[status(thm)],[2245, 2243])).
% 1.98/1.63 tff(2247,plain,
% 1.98/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c0_1(a559) | c3_1(a559) | (~c1_1(a559)) | c0_1(a507) | (~c3_1(a507)) | c2_1(a507))),
% 1.98/1.63 inference(quant_inst,[status(thm)],[])).
% 1.98/1.63 tff(2248,plain,
% 1.98/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a559) | c3_1(a559) | c3_1(a528) | c0_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c2_1(a507) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a559))),
% 1.98/1.63 inference(modus_ponens,[status(thm)],[2247, 2246])).
% 1.98/1.63 tff(2249,plain,
% 1.98/1.63 (c2_1(a507) | (~c1_1(a559))),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2248, 112, 1092, 1091, 2242, 2222, 2220, 1082, 2241, 21])).
% 1.98/1.63 tff(2250,plain,
% 1.98/1.63 (c2_1(a507)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[2249, 2230])).
% 1.98/1.63 tff(2251,plain,
% 1.98/1.63 (~c1_1(a507)),
% 1.98/1.63 inference(unit_resolution,[status(thm)],[924, 2240])).
% 1.98/1.63 tff(2252,plain,
% 1.98/1.63 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c3_1(a528) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c2_1(a507)) | (~c0_1(a528)) | (~c2_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c3_1(a528) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c2_1(a507)) | (~c0_1(a528)) | (~c2_1(a528)))),
% 1.98/1.64 inference(rewrite,[status(thm)],[])).
% 1.98/1.64 tff(2253,plain,
% 1.98/1.64 ((hskp4 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c0_1(a528)) | c1_1(a507) | c0_1(a507) | (~c2_1(a507))) <=> (hskp4 | c3_1(a528) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c2_1(a507)) | (~c0_1(a528)) | (~c2_1(a528)))),
% 1.98/1.64 inference(rewrite,[status(thm)],[])).
% 1.98/1.64 tff(2254,plain,
% 1.98/1.64 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c0_1(a528)) | c1_1(a507) | c0_1(a507) | (~c2_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c3_1(a528) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c2_1(a507)) | (~c0_1(a528)) | (~c2_1(a528))))),
% 1.98/1.64 inference(monotonicity,[status(thm)],[2253])).
% 1.98/1.64 tff(2255,plain,
% 1.98/1.64 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c0_1(a528)) | c1_1(a507) | c0_1(a507) | (~c2_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c3_1(a528) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c2_1(a507)) | (~c0_1(a528)) | (~c2_1(a528)))),
% 1.98/1.64 inference(transitivity,[status(thm)],[2254, 2252])).
% 1.98/1.64 tff(2256,plain,
% 1.98/1.64 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c0_1(a528)) | c1_1(a507) | c0_1(a507) | (~c2_1(a507)))),
% 1.98/1.64 inference(quant_inst,[status(thm)],[])).
% 1.98/1.64 tff(2257,plain,
% 1.98/1.64 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c3_1(a528) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c2_1(a507)) | (~c0_1(a528)) | (~c2_1(a528))),
% 1.98/1.64 inference(modus_ponens,[status(thm)],[2256, 2255])).
% 1.98/1.64 tff(2258,plain,
% 1.98/1.64 (hskp4 | (~c2_1(a507)) | (~c2_1(a528))),
% 1.98/1.64 inference(unit_resolution,[status(thm)],[2257, 112, 1092, 1082, 2241, 2251, 400])).
% 1.98/1.64 tff(2259,plain,
% 1.98/1.64 (hskp4),
% 1.98/1.64 inference(unit_resolution,[status(thm)],[2258, 2250, 2219])).
% 1.98/1.64 tff(2260,plain,
% 1.98/1.64 (~c2_1(a498)),
% 1.98/1.64 inference(unit_resolution,[status(thm)],[1517, 2259])).
% 1.98/1.64 tff(2261,plain,
% 1.98/1.64 (~c0_1(a498)),
% 1.98/1.64 inference(unit_resolution,[status(thm)],[1493, 2259])).
% 1.98/1.64 tff(2262,plain,
% 1.98/1.64 (c1_1(a498)),
% 1.98/1.64 inference(unit_resolution,[status(thm)],[1504, 2259])).
% 1.98/1.64 tff(2263,plain,
% 1.98/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a507) | c1_1(a507) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c3_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a507) | c1_1(a507) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c3_1(a507)))),
% 1.98/1.64 inference(rewrite,[status(thm)],[])).
% 1.98/1.64 tff(2264,plain,
% 1.98/1.64 (((~ndr1_0) | c2_1(a498) | (~c3_1(a498)) | (~c1_1(a498)) | c2_1(a498) | c0_1(a498) | (~c1_1(a498)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507))) <=> (c0_1(a507) | c1_1(a507) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c3_1(a507)))),
% 1.98/1.64 inference(rewrite,[status(thm)],[])).
% 1.98/1.64 tff(2265,plain,
% 1.98/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a498) | (~c3_1(a498)) | (~c1_1(a498)) | c2_1(a498) | c0_1(a498) | (~c1_1(a498)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a507) | c1_1(a507) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c3_1(a507))))),
% 1.98/1.64 inference(monotonicity,[status(thm)],[2264])).
% 1.98/1.64 tff(2266,plain,
% 1.98/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a498) | (~c3_1(a498)) | (~c1_1(a498)) | c2_1(a498) | c0_1(a498) | (~c1_1(a498)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a507) | c1_1(a507) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c3_1(a507)))),
% 1.98/1.64 inference(transitivity,[status(thm)],[2265, 2263])).
% 1.98/1.64 tff(2267,plain,
% 1.98/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a498) | (~c3_1(a498)) | (~c1_1(a498)) | c2_1(a498) | c0_1(a498) | (~c1_1(a498)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))),
% 1.98/1.64 inference(quant_inst,[status(thm)],[])).
% 1.98/1.64 tff(2268,plain,
% 1.98/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a507) | c1_1(a507) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c3_1(a507))),
% 1.98/1.64 inference(modus_ponens,[status(thm)],[2267, 2266])).
% 1.98/1.64 tff(2269,plain,
% 1.98/1.64 (~c3_1(a498)),
% 1.98/1.64 inference(unit_resolution,[status(thm)],[2268, 112, 2242, 2262, 2241, 2251, 2261, 2260, 618])).
% 1.98/1.64 tff(2270,plain,
% 1.98/1.64 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.98/1.64 inference(bind,[status(th)],[])).
% 1.98/1.64 tff(2271,plain,
% 1.98/1.64 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.64 inference(quant_intro,[status(thm)],[2270])).
% 1.98/1.64 tff(2272,plain,
% 1.98/1.64 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.64 inference(rewrite,[status(thm)],[])).
% 1.98/1.64 tff(2273,plain,
% 1.98/1.64 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | 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)) | (~c0_1(V))) | c3_1(U)) | 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)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.98/1.64 inference(bind,[status(th)],[])).
% 1.98/1.64 tff(2274,plain,
% 1.98/1.64 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.64 inference(quant_intro,[status(thm)],[2273])).
% 1.98/1.64 tff(2275,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 1.98/1.64 tff(2276,plain,
% 1.98/1.64 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.64 inference(modus_ponens,[status(thm)],[2275, 2274])).
% 1.98/1.64 tff(2277,plain,
% 1.98/1.64 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.64 inference(modus_ponens,[status(thm)],[2276, 2272])).
% 1.98/1.64 tff(2278,plain,(
% 1.98/1.64 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.64 inference(skolemize,[status(sab)],[2277])).
% 1.98/1.64 tff(2279,plain,
% 1.98/1.64 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.98/1.64 inference(modus_ponens,[status(thm)],[2278, 2271])).
% 1.98/1.64 tff(2280,plain,
% 1.98/1.64 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c2_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.98/1.64 inference(rewrite,[status(thm)],[])).
% 1.98/1.64 tff(2281,plain,
% 1.98/1.64 ((hskp21 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510))) <=> (hskp21 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.98/1.64 inference(rewrite,[status(thm)],[])).
% 1.98/1.64 tff(2282,plain,
% 1.98/1.64 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c2_1(a528))))),
% 1.98/1.64 inference(monotonicity,[status(thm)],[2281])).
% 1.98/1.64 tff(2283,plain,
% 1.98/1.64 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c2_1(a528)))),
% 1.98/1.64 inference(transitivity,[status(thm)],[2282, 2280])).
% 2.07/1.64 tff(2284,plain,
% 2.07/1.64 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a510) | c1_1(a510) | (~c0_1(a510)))),
% 2.07/1.64 inference(quant_inst,[status(thm)],[])).
% 2.07/1.64 tff(2285,plain,
% 2.07/1.64 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a528) | c1_1(a510) | c2_1(a510) | (~ndr1_0) | (~c0_1(a510)) | (~c1_1(a528)) | (~c2_1(a528))),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2284, 2283])).
% 2.07/1.64 tff(2286,plain,
% 2.07/1.64 (hskp21 | (~c2_1(a528))),
% 2.07/1.64 inference(unit_resolution,[status(thm)],[2285, 112, 1091, 2233, 1082, 2232, 2231, 2279])).
% 2.07/1.64 tff(2287,plain,
% 2.07/1.64 (hskp21),
% 2.07/1.64 inference(unit_resolution,[status(thm)],[2286, 2219])).
% 2.07/1.64 tff(2288,plain,
% 2.07/1.64 (~c3_1(a538)),
% 2.07/1.64 inference(unit_resolution,[status(thm)],[2070, 2287])).
% 2.07/1.64 tff(2289,plain,
% 2.07/1.64 (~c1_1(a538)),
% 2.07/1.64 inference(unit_resolution,[status(thm)],[2076, 2287])).
% 2.07/1.64 tff(2290,plain,
% 2.07/1.64 (c0_1(a538)),
% 2.07/1.64 inference(unit_resolution,[status(thm)],[2087, 2287])).
% 2.07/1.64 tff(2291,plain,
% 2.07/1.64 (hskp23),
% 2.07/1.64 inference(unit_resolution,[status(thm)],[2094, 112, 2290, 1092, 1091, 2289, 2288, 1082, 2010])).
% 2.07/1.64 tff(2292,plain,
% 2.07/1.64 (~c2_1(a541)),
% 2.07/1.64 inference(unit_resolution,[status(thm)],[2100, 2291])).
% 2.07/1.64 tff(2293,plain,
% 2.07/1.64 (c1_1(a541)),
% 2.07/1.64 inference(unit_resolution,[status(thm)],[2111, 2291])).
% 2.07/1.64 tff(2294,plain,
% 2.07/1.64 (c0_1(a541)),
% 2.07/1.64 inference(unit_resolution,[status(thm)],[2122, 2291])).
% 2.07/1.64 tff(2295,plain,
% 2.07/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a541) | c3_1(a528) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a541) | c3_1(a528) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 2.07/1.64 inference(rewrite,[status(thm)],[])).
% 2.07/1.64 tff(2296,plain,
% 2.07/1.64 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c3_1(a498) | c0_1(a498) | c2_1(a498)) <=> (c2_1(a541) | c3_1(a528) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 2.07/1.64 inference(rewrite,[status(thm)],[])).
% 2.07/1.64 tff(2297,plain,
% 2.07/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c3_1(a498) | c0_1(a498) | c2_1(a498))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a541) | c3_1(a528) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541))))),
% 2.07/1.64 inference(monotonicity,[status(thm)],[2296])).
% 2.07/1.64 tff(2298,plain,
% 2.07/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c3_1(a498) | c0_1(a498) | c2_1(a498))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a541) | c3_1(a528) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 2.07/1.64 inference(transitivity,[status(thm)],[2297, 2295])).
% 2.07/1.64 tff(2299,plain,
% 2.07/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c3_1(a498) | c0_1(a498) | c2_1(a498))),
% 2.07/1.64 inference(quant_inst,[status(thm)],[])).
% 2.07/1.64 tff(2300,plain,
% 2.07/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a541) | c3_1(a528) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | c3_1(a498) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541))),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2299, 2298])).
% 2.07/1.64 tff(2301,plain,
% 2.07/1.64 ($false),
% 2.07/1.64 inference(unit_resolution,[status(thm)],[2300, 112, 2294, 2293, 1092, 1091, 2292, 1082, 2261, 2260, 996, 2269])).
% 2.07/1.64 tff(2302,plain,((~c2_1(a528)) | (~c0_1(a528)) | (~c1_1(a528)) | c3_1(a528) | c0_1(a559) | c3_1(a559) | c2_1(a559) | (~c0_1(a510)) | c1_1(a510) | c2_1(a510)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.64 tff(2303,plain,
% 2.07/1.64 (~c2_1(a528)),
% 2.07/1.64 inference(unit_resolution,[status(thm)],[2302, 2218, 2217, 2216, 2204, 2192, 2198, 2214, 2213, 2212])).
% 2.07/1.64 tff(2304,plain,
% 2.07/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))),
% 2.07/1.64 inference(rewrite,[status(thm)],[])).
% 2.07/1.64 tff(2305,plain,
% 2.07/1.64 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a559) | c0_1(a559) | c2_1(a559)) <=> (c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))),
% 2.07/1.64 inference(rewrite,[status(thm)],[])).
% 2.07/1.64 tff(2306,plain,
% 2.07/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a559) | c0_1(a559) | c2_1(a559))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528)))),
% 2.07/1.64 inference(monotonicity,[status(thm)],[2305])).
% 2.07/1.64 tff(2307,plain,
% 2.07/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a559) | c0_1(a559) | c2_1(a559))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528))),
% 2.07/1.64 inference(transitivity,[status(thm)],[2306, 2304])).
% 2.07/1.64 tff(2308,plain,
% 2.07/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a559) | c0_1(a559) | c2_1(a559))),
% 2.07/1.64 inference(quant_inst,[status(thm)],[])).
% 2.07/1.64 tff(2309,plain,
% 2.07/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528)),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2308, 2307])).
% 2.07/1.64 tff(2310,plain,
% 2.07/1.64 ($false),
% 2.07/1.64 inference(unit_resolution,[status(thm)],[2309, 112, 2218, 2217, 2204, 2198, 2192, 2216, 996, 2303])).
% 2.07/1.64 tff(2311,plain,(hskp10), inference(lemma,lemma(discharge,[]))).
% 2.07/1.64 tff(2312,plain,
% 2.07/1.64 (((~hskp10) | (~c2_1(a509))) <=> ((~hskp10) | (~c2_1(a509)))),
% 2.07/1.64 inference(rewrite,[status(thm)],[])).
% 2.07/1.64 tff(2313,plain,
% 2.07/1.64 (((~c2_1(a509)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a509)))),
% 2.07/1.64 inference(rewrite,[status(thm)],[])).
% 2.07/1.64 tff(2314,axiom,((~c2_1(a509)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 2.07/1.64 tff(2315,plain,
% 2.07/1.64 ((~hskp10) | (~c2_1(a509))),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2314, 2313])).
% 2.07/1.64 tff(2316,plain,
% 2.07/1.64 ((~hskp10) | (~c2_1(a509))),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2315, 2312])).
% 2.07/1.64 tff(2317,plain,
% 2.07/1.64 (~c2_1(a509)),
% 2.07/1.64 inference(unit_resolution,[status(thm)],[2316, 2311])).
% 2.07/1.64 tff(2318,plain,
% 2.07/1.64 (((~hskp10) | c3_1(a509)) <=> ((~hskp10) | c3_1(a509))),
% 2.07/1.64 inference(rewrite,[status(thm)],[])).
% 2.07/1.64 tff(2319,axiom,((~hskp10) | c3_1(a509)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 2.07/1.64 tff(2320,plain,
% 2.07/1.64 ((~hskp10) | c3_1(a509)),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2319, 2318])).
% 2.07/1.64 tff(2321,plain,
% 2.07/1.64 ((~hskp10) | c3_1(a509)),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2320, 2318])).
% 2.07/1.64 tff(2322,plain,
% 2.07/1.64 ((~hskp10) | c3_1(a509)),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2321, 2318])).
% 2.07/1.64 tff(2323,plain,
% 2.07/1.64 ((~hskp10) | c3_1(a509)),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2322, 2318])).
% 2.07/1.64 tff(2324,plain,
% 2.07/1.64 ((~hskp10) | c3_1(a509)),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2323, 2318])).
% 2.07/1.64 tff(2325,plain,
% 2.07/1.64 ((~hskp10) | c3_1(a509)),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2324, 2318])).
% 2.07/1.64 tff(2326,plain,
% 2.07/1.64 ((~hskp10) | c3_1(a509)),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2325, 2318])).
% 2.07/1.64 tff(2327,plain,
% 2.07/1.64 ((~hskp10) | c3_1(a509)),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2326, 2318])).
% 2.07/1.64 tff(2328,plain,
% 2.07/1.64 (c3_1(a509)),
% 2.07/1.64 inference(unit_resolution,[status(thm)],[2327, 2311])).
% 2.07/1.64 tff(2329,plain,
% 2.07/1.64 (((~hskp10) | c0_1(a509)) <=> ((~hskp10) | c0_1(a509))),
% 2.07/1.64 inference(rewrite,[status(thm)],[])).
% 2.07/1.64 tff(2330,axiom,((~hskp10) | c0_1(a509)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 2.07/1.64 tff(2331,plain,
% 2.07/1.64 ((~hskp10) | c0_1(a509)),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2330, 2329])).
% 2.07/1.64 tff(2332,plain,
% 2.07/1.64 ((~hskp10) | c0_1(a509)),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2331, 2329])).
% 2.07/1.64 tff(2333,plain,
% 2.07/1.64 ((~hskp10) | c0_1(a509)),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2332, 2329])).
% 2.07/1.64 tff(2334,plain,
% 2.07/1.64 ((~hskp10) | c0_1(a509)),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2333, 2329])).
% 2.07/1.64 tff(2335,plain,
% 2.07/1.64 ((~hskp10) | c0_1(a509)),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2334, 2329])).
% 2.07/1.64 tff(2336,plain,
% 2.07/1.64 ((~hskp10) | c0_1(a509)),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2335, 2329])).
% 2.07/1.64 tff(2337,plain,
% 2.07/1.64 ((~hskp10) | c0_1(a509)),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2336, 2329])).
% 2.07/1.64 tff(2338,plain,
% 2.07/1.64 ((~hskp10) | c0_1(a509)),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2337, 2329])).
% 2.07/1.64 tff(2339,plain,
% 2.07/1.64 (c0_1(a509)),
% 2.07/1.64 inference(unit_resolution,[status(thm)],[2338, 2311])).
% 2.07/1.64 tff(2340,plain,
% 2.07/1.64 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c0_1(a509)))),
% 2.07/1.64 inference(rewrite,[status(thm)],[])).
% 2.07/1.64 tff(2341,plain,
% 2.07/1.64 ((hskp2 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509))) <=> (hskp2 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c0_1(a509)))),
% 2.07/1.64 inference(rewrite,[status(thm)],[])).
% 2.07/1.64 tff(2342,plain,
% 2.07/1.64 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c0_1(a509))))),
% 2.07/1.64 inference(monotonicity,[status(thm)],[2341])).
% 2.07/1.64 tff(2343,plain,
% 2.07/1.64 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c0_1(a509)))),
% 2.07/1.64 inference(transitivity,[status(thm)],[2342, 2340])).
% 2.07/1.64 tff(2344,plain,
% 2.07/1.64 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)))),
% 2.07/1.64 inference(quant_inst,[status(thm)],[])).
% 2.07/1.64 tff(2345,plain,
% 2.07/1.64 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c0_1(a509))),
% 2.07/1.64 inference(modus_ponens,[status(thm)],[2344, 2343])).
% 2.07/1.64 tff(2346,plain,
% 2.07/1.64 (hskp2 | (~c1_1(a509))),
% 2.07/1.64 inference(unit_resolution,[status(thm)],[2345, 112, 2339, 2328, 2317, 601])).
% 2.07/1.64 tff(2347,plain,
% 2.07/1.64 (~c1_1(a509)),
% 2.07/1.64 inference(unit_resolution,[status(thm)],[2346, 453])).
% 2.07/1.64 tff(2348,plain,
% 2.07/1.64 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 2.07/1.64 inference(bind,[status(th)],[])).
% 2.07/1.64 tff(2349,plain,
% 2.07/1.64 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.64 inference(quant_intro,[status(thm)],[2348])).
% 2.07/1.64 tff(2350,plain,
% 2.07/1.64 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.64 inference(rewrite,[status(thm)],[])).
% 2.07/1.64 tff(2351,plain,
% 2.07/1.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | 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)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 2.07/1.65 inference(bind,[status(th)],[])).
% 2.07/1.65 tff(2352,plain,
% 2.07/1.65 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.65 inference(quant_intro,[status(thm)],[2351])).
% 2.07/1.65 tff(2353,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 2.07/1.65 tff(2354,plain,
% 2.07/1.65 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.65 inference(modus_ponens,[status(thm)],[2353, 2352])).
% 2.07/1.65 tff(2355,plain,
% 2.07/1.65 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.65 inference(modus_ponens,[status(thm)],[2354, 2350])).
% 2.07/1.65 tff(2356,plain,(
% 2.07/1.65 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.65 inference(skolemize,[status(sab)],[2355])).
% 2.07/1.65 tff(2357,plain,
% 2.07/1.65 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.65 inference(modus_ponens,[status(thm)],[2356, 2349])).
% 2.07/1.65 tff(2358,plain,
% 2.07/1.65 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)))),
% 2.07/1.65 inference(rewrite,[status(thm)],[])).
% 2.07/1.65 tff(2359,plain,
% 2.07/1.65 ((hskp9 | (~ndr1_0) | c2_1(a509) | c1_1(a509) | (~c3_1(a509)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509))) <=> (hskp9 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)))),
% 2.07/1.65 inference(rewrite,[status(thm)],[])).
% 2.07/1.65 tff(2360,plain,
% 2.07/1.65 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a509) | c1_1(a509) | (~c3_1(a509)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509))))),
% 2.07/1.65 inference(monotonicity,[status(thm)],[2359])).
% 2.07/1.65 tff(2361,plain,
% 2.07/1.65 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a509) | c1_1(a509) | (~c3_1(a509)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)))),
% 2.07/1.65 inference(transitivity,[status(thm)],[2360, 2358])).
% 2.07/1.65 tff(2362,plain,
% 2.07/1.65 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a509) | c1_1(a509) | (~c3_1(a509)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)))),
% 2.07/1.65 inference(quant_inst,[status(thm)],[])).
% 2.07/1.65 tff(2363,plain,
% 2.07/1.65 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509))),
% 2.07/1.65 inference(modus_ponens,[status(thm)],[2362, 2361])).
% 2.07/1.65 tff(2364,plain,
% 2.07/1.65 (hskp9 | c1_1(a509)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[2363, 112, 2339, 2328, 2317, 2357])).
% 2.07/1.65 tff(2365,plain,
% 2.07/1.65 (hskp9),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[2364, 2347])).
% 2.07/1.65 tff(2366,plain,
% 2.07/1.65 (~c1_1(a507)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[924, 2365])).
% 2.07/1.65 tff(2367,plain,
% 2.07/1.65 (~c0_1(a507)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[930, 2365])).
% 2.07/1.65 tff(2368,plain,
% 2.07/1.65 (c3_1(a507)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[941, 2365])).
% 2.07/1.65 tff(2369,plain,
% 2.07/1.65 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)))),
% 2.07/1.65 inference(rewrite,[status(thm)],[])).
% 2.07/1.65 tff(2370,plain,
% 2.07/1.65 ((hskp28 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507))) <=> (hskp28 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)))),
% 2.07/1.65 inference(rewrite,[status(thm)],[])).
% 2.07/1.65 tff(2371,plain,
% 2.07/1.65 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509))))),
% 2.07/1.65 inference(monotonicity,[status(thm)],[2370])).
% 2.07/1.65 tff(2372,plain,
% 2.07/1.65 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)))),
% 2.07/1.65 inference(transitivity,[status(thm)],[2371, 2369])).
% 2.07/1.65 tff(2373,plain,
% 2.07/1.65 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))),
% 2.07/1.65 inference(quant_inst,[status(thm)],[])).
% 2.07/1.65 tff(2374,plain,
% 2.07/1.65 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509))),
% 2.07/1.65 inference(modus_ponens,[status(thm)],[2373, 2372])).
% 2.07/1.65 tff(2375,plain,
% 2.07/1.65 (hskp28),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[2374, 112, 2339, 2328, 2368, 2367, 2366, 262, 2347])).
% 2.07/1.65 tff(2376,plain,
% 2.07/1.65 (c0_1(a500)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[451, 2375])).
% 2.07/1.65 tff(2377,plain,
% 2.07/1.65 (c3_1(a500)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[429, 2375])).
% 2.07/1.65 tff(2378,plain,
% 2.07/1.65 (c2_1(a500)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[440, 2375])).
% 2.07/1.65 tff(2379,plain,
% 2.07/1.65 (~hskp15),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[2016, 2375, 453])).
% 2.07/1.65 tff(2380,plain,
% 2.07/1.65 ($false),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[607, 112, 453, 949, 948, 946, 601, 956])).
% 2.07/1.65 tff(2381,plain,((~hskp12) | hskp2 | (~c3_1(a507)) | c0_1(a507) | c1_1(a507)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.65 tff(2382,plain,
% 2.07/1.65 (~hskp12),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[2381, 453, 947, 944, 943])).
% 2.07/1.65 tff(2383,plain,
% 2.07/1.65 (hskp13),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[535, 2382, 43])).
% 2.07/1.65 tff(2384,plain,
% 2.07/1.65 (~c3_1(a520)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[1458, 2383])).
% 2.07/1.65 tff(2385,plain,
% 2.07/1.65 (c0_1(a520)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[1480, 2383])).
% 2.07/1.65 tff(2386,plain,
% 2.07/1.65 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c0_1(a520)))),
% 2.07/1.65 inference(rewrite,[status(thm)],[])).
% 2.07/1.65 tff(2387,plain,
% 2.07/1.65 ((hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520))) <=> (hskp2 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c0_1(a520)))),
% 2.07/1.65 inference(rewrite,[status(thm)],[])).
% 2.07/1.65 tff(2388,plain,
% 2.07/1.65 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c0_1(a520))))),
% 2.07/1.65 inference(monotonicity,[status(thm)],[2387])).
% 2.07/1.65 tff(2389,plain,
% 2.07/1.65 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c0_1(a520)))),
% 2.07/1.65 inference(transitivity,[status(thm)],[2388, 2386])).
% 2.07/1.65 tff(2390,plain,
% 2.07/1.65 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a500)) | (~c3_1(a500)) | (~c0_1(a500)) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)))),
% 2.07/1.65 inference(quant_inst,[status(thm)],[])).
% 2.07/1.65 tff(2391,plain,
% 2.07/1.65 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c3_1(a520) | (~ndr1_0) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | (~c1_1(a520)) | (~c0_1(a520))),
% 2.07/1.65 inference(modus_ponens,[status(thm)],[2390, 2389])).
% 2.07/1.65 tff(2392,plain,
% 2.07/1.65 (~c1_1(a520)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[2391, 112, 453, 495, 494, 493, 2385, 2384, 463])).
% 2.07/1.65 tff(2393,assumption,(~c2_1(a509)), introduced(assumption)).
% 2.07/1.65 tff(2394,assumption,(c3_1(a509)), introduced(assumption)).
% 2.07/1.65 tff(2395,assumption,(c0_1(a509)), introduced(assumption)).
% 2.07/1.65 tff(2396,plain,
% 2.07/1.65 (c2_1(a520)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[1469, 2383])).
% 2.07/1.65 tff(2397,plain,
% 2.07/1.65 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | c3_1(a520) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp24 | c3_1(a520) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 2.07/1.65 inference(rewrite,[status(thm)],[])).
% 2.07/1.65 tff(2398,plain,
% 2.07/1.65 ((hskp24 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a509) | (~c0_1(a509)) | (~c3_1(a509))) <=> (hskp24 | c3_1(a520) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 2.07/1.65 inference(rewrite,[status(thm)],[])).
% 2.07/1.65 tff(2399,plain,
% 2.07/1.65 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a509) | (~c0_1(a509)) | (~c3_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | c3_1(a520) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a520)) | (~c2_1(a520))))),
% 2.07/1.65 inference(monotonicity,[status(thm)],[2398])).
% 2.07/1.65 tff(2400,plain,
% 2.07/1.65 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a509) | (~c0_1(a509)) | (~c3_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp24 | c3_1(a520) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 2.07/1.65 inference(transitivity,[status(thm)],[2399, 2397])).
% 2.07/1.65 tff(2401,plain,
% 2.07/1.65 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c2_1(a509) | (~c0_1(a509)) | (~c3_1(a509)))),
% 2.07/1.65 inference(quant_inst,[status(thm)],[])).
% 2.07/1.65 tff(2402,plain,
% 2.07/1.65 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp24 | c3_1(a520) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a520)) | (~c2_1(a520))),
% 2.07/1.65 inference(modus_ponens,[status(thm)],[2401, 2400])).
% 2.07/1.65 tff(2403,plain,
% 2.07/1.65 (hskp24),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[2402, 112, 2385, 2396, 2395, 2394, 2384, 2393, 1637])).
% 2.07/1.65 tff(2404,plain,
% 2.07/1.65 (~c3_1(a554)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[1666, 2403])).
% 2.07/1.65 tff(2405,plain,
% 2.07/1.65 (~c2_1(a554)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[1649, 2403])).
% 2.07/1.65 tff(2406,plain,
% 2.07/1.65 (c0_1(a554)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[1677, 2403])).
% 2.07/1.65 tff(2407,assumption,(~hskp22), introduced(assumption)).
% 2.07/1.65 tff(2408,plain,
% 2.07/1.65 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a554) | c3_1(a554) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a554)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a554) | c3_1(a554) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a554)))),
% 2.07/1.65 inference(rewrite,[status(thm)],[])).
% 2.07/1.65 tff(2409,plain,
% 2.07/1.65 ((hskp22 | (~ndr1_0) | c3_1(a554) | c2_1(a554) | (~c0_1(a554)) | c1_1(a520) | c3_1(a520) | (~c0_1(a520))) <=> (hskp22 | c2_1(a554) | c3_1(a554) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a554)))),
% 2.07/1.65 inference(rewrite,[status(thm)],[])).
% 2.07/1.65 tff(2410,plain,
% 2.07/1.65 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a554) | c2_1(a554) | (~c0_1(a554)) | c1_1(a520) | c3_1(a520) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a554) | c3_1(a554) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a554))))),
% 2.07/1.65 inference(monotonicity,[status(thm)],[2409])).
% 2.07/1.65 tff(2411,plain,
% 2.07/1.65 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a554) | c2_1(a554) | (~c0_1(a554)) | c1_1(a520) | c3_1(a520) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a554) | c3_1(a554) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a554)))),
% 2.07/1.65 inference(transitivity,[status(thm)],[2410, 2408])).
% 2.07/1.65 tff(2412,plain,
% 2.07/1.65 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a554) | c2_1(a554) | (~c0_1(a554)) | c1_1(a520) | c3_1(a520) | (~c0_1(a520)))),
% 2.07/1.65 inference(quant_inst,[status(thm)],[])).
% 2.07/1.65 tff(2413,plain,
% 2.07/1.65 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a554) | c3_1(a554) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)) | (~c0_1(a554))),
% 2.07/1.65 inference(modus_ponens,[status(thm)],[2412, 2411])).
% 2.07/1.65 tff(2414,plain,
% 2.07/1.65 ($false),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[2413, 112, 2407, 2406, 2385, 2405, 2404, 2384, 31, 2392])).
% 2.07/1.65 tff(2415,plain,(hskp2 | hskp22 | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | hskp15 | (~c3_1(a507)) | c0_1(a507) | c1_1(a507)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.65 tff(2416,plain,
% 2.07/1.65 (hskp22),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[2415, 2379, 2339, 2328, 2317, 453, 2378, 2377, 2376, 2368, 2367, 2366])).
% 2.07/1.65 tff(2417,plain,
% 2.07/1.65 (c3_1(a540)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[142, 2416])).
% 2.07/1.65 tff(2418,plain,
% 2.07/1.65 (c1_1(a540)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[153, 2416])).
% 2.07/1.65 tff(2419,plain,
% 2.07/1.65 (~c0_1(a540)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[131, 2416])).
% 2.07/1.65 tff(2420,assumption,(c1_1(a540)), introduced(assumption)).
% 2.07/1.65 tff(2421,assumption,(hskp9), introduced(assumption)).
% 2.07/1.65 tff(2422,plain,
% 2.07/1.65 (~c0_1(a507)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[930, 2421])).
% 2.07/1.65 tff(2423,assumption,(~c0_1(a540)), introduced(assumption)).
% 2.07/1.65 tff(2424,plain,
% 2.07/1.65 (c3_1(a507)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[941, 2421])).
% 2.07/1.65 tff(2425,assumption,(c3_1(a540)), introduced(assumption)).
% 2.07/1.65 tff(2426,plain,
% 2.07/1.65 (~c1_1(a507)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[924, 2421])).
% 2.07/1.65 tff(2427,assumption,(~c2_1(a540)), introduced(assumption)).
% 2.07/1.65 tff(2428,plain,
% 2.07/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a540) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a540) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540))),
% 2.07/1.65 inference(rewrite,[status(thm)],[])).
% 2.07/1.65 tff(2429,plain,
% 2.07/1.65 (((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | c0_1(a540) | (~c1_1(a540)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507))) <=> (c0_1(a540) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540))),
% 2.07/1.65 inference(rewrite,[status(thm)],[])).
% 2.07/1.65 tff(2430,plain,
% 2.07/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | c0_1(a540) | (~c1_1(a540)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a540) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540)))),
% 2.07/1.65 inference(monotonicity,[status(thm)],[2429])).
% 2.07/1.65 tff(2431,plain,
% 2.07/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | c0_1(a540) | (~c1_1(a540)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a540) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540))),
% 2.07/1.65 inference(transitivity,[status(thm)],[2430, 2428])).
% 2.07/1.65 tff(2432,plain,
% 2.07/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | c0_1(a540) | (~c1_1(a540)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))),
% 2.07/1.65 inference(quant_inst,[status(thm)],[])).
% 2.07/1.65 tff(2433,plain,
% 2.07/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a540) | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540)),
% 2.07/1.65 inference(modus_ponens,[status(thm)],[2432, 2431])).
% 2.07/1.65 tff(2434,plain,
% 2.07/1.65 ($false),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[2433, 112, 2420, 2425, 947, 2423, 944, 943, 618, 2427])).
% 2.07/1.65 tff(2435,plain,(c2_1(a540) | (~c1_1(a540)) | (~c3_1(a540)) | (~c3_1(a507)) | c0_1(a540) | c0_1(a507) | c1_1(a507)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.65 tff(2436,plain,
% 2.07/1.65 (c2_1(a540)),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[2435, 2426, 2425, 2424, 2423, 2422, 2420])).
% 2.07/1.65 tff(2437,plain,
% 2.07/1.65 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 2.07/1.65 inference(bind,[status(th)],[])).
% 2.07/1.65 tff(2438,plain,
% 2.07/1.65 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.07/1.65 inference(quant_intro,[status(thm)],[2437])).
% 2.07/1.65 tff(2439,plain,
% 2.07/1.65 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.07/1.65 inference(rewrite,[status(thm)],[])).
% 2.07/1.65 tff(2440,plain,
% 2.07/1.65 (^[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))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_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))) | c2_1(U)) <=> ((~ndr1_0) | c2_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))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_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))) | c2_1(U)) | c0_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 2.07/1.65 inference(bind,[status(th)],[])).
% 2.07/1.65 tff(2441,plain,
% 2.07/1.65 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.07/1.65 inference(quant_intro,[status(thm)],[2440])).
% 2.07/1.65 tff(2442,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 2.07/1.65 tff(2443,plain,
% 2.07/1.65 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.07/1.65 inference(modus_ponens,[status(thm)],[2442, 2441])).
% 2.07/1.65 tff(2444,plain,
% 2.07/1.65 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.07/1.65 inference(modus_ponens,[status(thm)],[2443, 2439])).
% 2.07/1.65 tff(2445,plain,(
% 2.07/1.65 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.07/1.65 inference(skolemize,[status(sab)],[2444])).
% 2.07/1.65 tff(2446,plain,
% 2.07/1.65 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.07/1.65 inference(modus_ponens,[status(thm)],[2445, 2438])).
% 2.07/1.65 tff(2447,plain,
% 2.07/1.65 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c3_1(a540)) | (~c2_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c3_1(a540)) | (~c2_1(a540)))),
% 2.07/1.65 inference(rewrite,[status(thm)],[])).
% 2.07/1.65 tff(2448,plain,
% 2.07/1.65 ((hskp15 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540))) <=> (hskp15 | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c3_1(a540)) | (~c2_1(a540)))),
% 2.07/1.65 inference(rewrite,[status(thm)],[])).
% 2.07/1.65 tff(2449,plain,
% 2.07/1.65 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c3_1(a540)) | (~c2_1(a540))))),
% 2.07/1.65 inference(monotonicity,[status(thm)],[2448])).
% 2.07/1.65 tff(2450,plain,
% 2.07/1.65 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c3_1(a540)) | (~c2_1(a540)))),
% 2.07/1.65 inference(transitivity,[status(thm)],[2449, 2447])).
% 2.07/1.65 tff(2451,plain,
% 2.07/1.65 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540)))),
% 2.07/1.65 inference(quant_inst,[status(thm)],[])).
% 2.07/1.65 tff(2452,plain,
% 2.07/1.65 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c3_1(a540)) | (~c2_1(a540))),
% 2.07/1.65 inference(modus_ponens,[status(thm)],[2451, 2450])).
% 2.07/1.65 tff(2453,plain,
% 2.07/1.65 ((~c1_1(a509)) | (~c2_1(a540))),
% 2.07/1.65 inference(unit_resolution,[status(thm)],[2452, 112, 43, 2425, 2395, 2423, 2393, 2446])).
% 2.07/1.65 tff(2454,plain,
% 2.07/1.66 (~c1_1(a509)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[2453, 2436])).
% 2.07/1.66 tff(2455,plain,
% 2.07/1.66 (c2_1(a540)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[2435, 943, 2425, 947, 2423, 944, 2420])).
% 2.07/1.66 tff(2456,assumption,(~c1_1(a509)), introduced(assumption)).
% 2.07/1.66 tff(2457,assumption,(hskp13), introduced(assumption)).
% 2.07/1.66 tff(2458,plain,
% 2.07/1.66 (~c3_1(a520)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[1458, 2457])).
% 2.07/1.66 tff(2459,plain,
% 2.07/1.66 (c0_1(a520)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[1480, 2457])).
% 2.07/1.66 tff(2460,plain,
% 2.07/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a540) | c3_1(a520) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a540) | c3_1(a520) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 2.07/1.66 inference(rewrite,[status(thm)],[])).
% 2.07/1.66 tff(2461,plain,
% 2.07/1.66 (((~ndr1_0) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540))) <=> (c0_1(a540) | c3_1(a520) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 2.07/1.66 inference(rewrite,[status(thm)],[])).
% 2.07/1.66 tff(2462,plain,
% 2.07/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a540) | c3_1(a520) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c3_1(a540)) | (~c1_1(a540))))),
% 2.07/1.66 inference(monotonicity,[status(thm)],[2461])).
% 2.07/1.66 tff(2463,plain,
% 2.07/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a540) | c3_1(a520) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 2.07/1.66 inference(transitivity,[status(thm)],[2462, 2460])).
% 2.07/1.66 tff(2464,plain,
% 2.07/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))),
% 2.07/1.66 inference(quant_inst,[status(thm)],[])).
% 2.07/1.66 tff(2465,plain,
% 2.07/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a540) | c3_1(a520) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c3_1(a540)) | (~c1_1(a540))),
% 2.07/1.66 inference(modus_ponens,[status(thm)],[2464, 2463])).
% 2.07/1.66 tff(2466,plain,
% 2.07/1.66 (~c1_1(a520)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[2465, 112, 2420, 2425, 2459, 2395, 2394, 2423, 2458, 1398, 2456])).
% 2.07/1.66 tff(2467,plain,
% 2.07/1.66 (c2_1(a520)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[1469, 2457])).
% 2.07/1.66 tff(2468,plain,
% 2.07/1.66 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520)))),
% 2.07/1.66 inference(rewrite,[status(thm)],[])).
% 2.07/1.66 tff(2469,plain,
% 2.07/1.66 ((hskp7 | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507))) <=> (hskp7 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520)))),
% 2.07/1.66 inference(rewrite,[status(thm)],[])).
% 2.07/1.66 tff(2470,plain,
% 2.07/1.66 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520))))),
% 2.07/1.66 inference(monotonicity,[status(thm)],[2469])).
% 2.07/1.66 tff(2471,plain,
% 2.07/1.66 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520)))),
% 2.07/1.66 inference(transitivity,[status(thm)],[2470, 2468])).
% 2.07/1.66 tff(2472,plain,
% 2.07/1.66 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))),
% 2.07/1.66 inference(quant_inst,[status(thm)],[])).
% 2.07/1.66 tff(2473,plain,
% 2.07/1.66 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a507) | c1_1(a507) | (~ndr1_0) | (~c3_1(a507)) | c1_1(a520) | (~c0_1(a520)) | (~c2_1(a520))),
% 2.07/1.66 inference(modus_ponens,[status(thm)],[2472, 2471])).
% 2.07/1.66 tff(2474,plain,
% 2.07/1.66 (hskp7),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[2473, 112, 2459, 2467, 947, 944, 943, 240, 2466])).
% 2.07/1.66 tff(2475,plain,
% 2.07/1.66 (~c3_1(a502)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[332, 2474])).
% 2.07/1.66 tff(2476,plain,
% 2.07/1.66 (~c0_1(a502)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[709, 2474])).
% 2.07/1.66 tff(2477,plain,
% 2.07/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a540) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.07/1.66 inference(rewrite,[status(thm)],[])).
% 2.07/1.66 tff(2478,plain,
% 2.07/1.66 (((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a502) | c0_1(a502) | c2_1(a502)) <=> (c0_1(a540) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.07/1.66 inference(rewrite,[status(thm)],[])).
% 2.07/1.66 tff(2479,plain,
% 2.07/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a502) | c0_1(a502) | c2_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a540) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 2.07/1.66 inference(monotonicity,[status(thm)],[2478])).
% 2.07/1.66 tff(2480,plain,
% 2.07/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a502) | c0_1(a502) | c2_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.07/1.66 inference(transitivity,[status(thm)],[2479, 2477])).
% 2.07/1.66 tff(2481,plain,
% 2.07/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a502) | c0_1(a502) | c2_1(a502))),
% 2.07/1.66 inference(quant_inst,[status(thm)],[])).
% 2.07/1.66 tff(2482,plain,
% 2.07/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c0_1(a502) | c3_1(a502) | (~ndr1_0) | c2_1(a502) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))),
% 2.07/1.66 inference(modus_ponens,[status(thm)],[2481, 2480])).
% 2.07/1.66 tff(2483,plain,
% 2.07/1.66 (c2_1(a502)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[2482, 112, 2420, 2425, 2423, 2476, 2475, 1246, 2455])).
% 2.07/1.66 tff(2484,plain,
% 2.07/1.66 (~c1_1(a502)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[338, 2474])).
% 2.07/1.66 tff(2485,plain,
% 2.07/1.66 (hskp4 | (~c2_1(a502))),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[1487, 112, 2459, 2467, 2458, 2476, 2484, 400])).
% 2.07/1.66 tff(2486,plain,
% 2.07/1.66 (hskp4),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[2485, 2483])).
% 2.07/1.66 tff(2487,plain,
% 2.07/1.66 (~c2_1(a498)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[1517, 2486])).
% 2.07/1.66 tff(2488,plain,
% 2.07/1.66 (~c0_1(a498)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[1493, 2486])).
% 2.07/1.66 tff(2489,plain,
% 2.07/1.66 (c1_1(a498)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[1504, 2486])).
% 2.07/1.66 tff(2490,plain,
% 2.07/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a540) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a540) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.07/1.66 inference(rewrite,[status(thm)],[])).
% 2.07/1.66 tff(2491,plain,
% 2.07/1.66 (((~ndr1_0) | c2_1(a498) | (~c3_1(a498)) | (~c1_1(a498)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c0_1(a498) | c2_1(a498) | (~c1_1(a498))) <=> (c0_1(a540) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.07/1.66 inference(rewrite,[status(thm)],[])).
% 2.07/1.66 tff(2492,plain,
% 2.07/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a498) | (~c3_1(a498)) | (~c1_1(a498)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c0_1(a498) | c2_1(a498) | (~c1_1(a498)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a540) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 2.07/1.66 inference(monotonicity,[status(thm)],[2491])).
% 2.07/1.66 tff(2493,plain,
% 2.07/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a498) | (~c3_1(a498)) | (~c1_1(a498)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c0_1(a498) | c2_1(a498) | (~c1_1(a498)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a540) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.07/1.66 inference(transitivity,[status(thm)],[2492, 2490])).
% 2.07/1.66 tff(2494,plain,
% 2.07/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a498) | (~c3_1(a498)) | (~c1_1(a498)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c0_1(a498) | c2_1(a498) | (~c1_1(a498)))),
% 2.07/1.66 inference(quant_inst,[status(thm)],[])).
% 2.07/1.66 tff(2495,plain,
% 2.07/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a540) | c0_1(a498) | c2_1(a498) | (~ndr1_0) | (~c3_1(a498)) | (~c1_1(a498)) | (~c1_1(a540)) | (~c2_1(a540))),
% 2.07/1.66 inference(modus_ponens,[status(thm)],[2494, 2493])).
% 2.07/1.66 tff(2496,plain,
% 2.07/1.66 (~c3_1(a498)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[2495, 112, 2420, 2489, 2423, 2488, 2487, 1175, 2455])).
% 2.07/1.66 tff(2497,plain,
% 2.07/1.66 (hskp24),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[2402, 112, 2459, 2467, 2395, 2394, 2458, 2393, 1637])).
% 2.07/1.66 tff(2498,plain,
% 2.07/1.66 (~c3_1(a554)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[1666, 2497])).
% 2.07/1.66 tff(2499,plain,
% 2.07/1.66 (c0_1(a554)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[1677, 2497])).
% 2.07/1.66 tff(2500,plain,
% 2.07/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a554) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c1_1(a554)) | (~c0_1(a554)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a554) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c1_1(a554)) | (~c0_1(a554)))),
% 2.07/1.66 inference(rewrite,[status(thm)],[])).
% 2.07/1.66 tff(2501,plain,
% 2.07/1.66 (((~ndr1_0) | c3_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540))) <=> (c3_1(a554) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c1_1(a554)) | (~c0_1(a554)))),
% 2.07/1.66 inference(rewrite,[status(thm)],[])).
% 2.07/1.66 tff(2502,plain,
% 2.07/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a554) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c1_1(a554)) | (~c0_1(a554))))),
% 2.07/1.66 inference(monotonicity,[status(thm)],[2501])).
% 2.07/1.66 tff(2503,plain,
% 2.07/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a554) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c1_1(a554)) | (~c0_1(a554)))),
% 2.07/1.66 inference(transitivity,[status(thm)],[2502, 2500])).
% 2.07/1.66 tff(2504,plain,
% 2.07/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a554) | (~c1_1(a554)) | (~c0_1(a554)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))),
% 2.07/1.66 inference(quant_inst,[status(thm)],[])).
% 2.07/1.66 tff(2505,plain,
% 2.07/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a554) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c1_1(a554)) | (~c0_1(a554))),
% 2.07/1.66 inference(modus_ponens,[status(thm)],[2504, 2503])).
% 2.07/1.66 tff(2506,plain,
% 2.07/1.66 (~c1_1(a554)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[2505, 112, 2499, 2420, 2425, 2395, 2394, 2498, 2423, 1398, 2456])).
% 2.07/1.66 tff(2507,plain,
% 2.07/1.66 (hskp1),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[1722, 112, 2499, 2498, 2476, 2484, 2475, 645, 2506])).
% 2.07/1.66 tff(2508,plain,
% 2.07/1.66 (~c3_1(a495)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[1019, 2507])).
% 2.07/1.66 tff(2509,plain,
% 2.07/1.66 (c1_1(a495)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[1037, 2507])).
% 2.07/1.66 tff(2510,plain,
% 2.07/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a502) | c1_1(a502) | c3_1(a502) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498))),
% 2.07/1.66 inference(rewrite,[status(thm)],[])).
% 2.07/1.66 tff(2511,plain,
% 2.07/1.66 (((~ndr1_0) | c3_1(a495) | (~c2_1(a495)) | (~c1_1(a495)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a502) | c1_1(a502) | c0_1(a502)) <=> (c0_1(a502) | c1_1(a502) | c3_1(a502) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498))),
% 2.07/1.66 inference(rewrite,[status(thm)],[])).
% 2.07/1.66 tff(2512,plain,
% 2.07/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a495) | (~c2_1(a495)) | (~c1_1(a495)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a502) | c1_1(a502) | c0_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a502) | c1_1(a502) | c3_1(a502) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498)))),
% 2.07/1.66 inference(monotonicity,[status(thm)],[2511])).
% 2.07/1.66 tff(2513,plain,
% 2.07/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a495) | (~c2_1(a495)) | (~c1_1(a495)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a502) | c1_1(a502) | c0_1(a502))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498))),
% 2.07/1.66 inference(transitivity,[status(thm)],[2512, 2510])).
% 2.07/1.66 tff(2514,plain,
% 2.07/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a495) | (~c2_1(a495)) | (~c1_1(a495)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a502) | c1_1(a502) | c0_1(a502))),
% 2.07/1.66 inference(quant_inst,[status(thm)],[])).
% 2.07/1.66 tff(2515,plain,
% 2.07/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a502) | c1_1(a502) | c3_1(a502) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498)),
% 2.07/1.66 inference(modus_ponens,[status(thm)],[2514, 2513])).
% 2.07/1.66 tff(2516,plain,
% 2.07/1.66 (~c2_1(a495)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[2515, 112, 2509, 2476, 2484, 2475, 2488, 2487, 2508, 784, 2496])).
% 2.07/1.66 tff(2517,plain,
% 2.07/1.66 (~c0_1(a495)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[1025, 2507])).
% 2.07/1.66 tff(2518,plain,
% 2.07/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a540) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | c2_1(a495) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | c2_1(a495) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.07/1.66 inference(rewrite,[status(thm)],[])).
% 2.07/1.66 tff(2519,plain,
% 2.07/1.66 (((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a495) | c0_1(a495) | c2_1(a495)) <=> (c0_1(a540) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | c2_1(a495) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.07/1.66 inference(rewrite,[status(thm)],[])).
% 2.07/1.66 tff(2520,plain,
% 2.07/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a495) | c0_1(a495) | c2_1(a495))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a540) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | c2_1(a495) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 2.07/1.66 inference(monotonicity,[status(thm)],[2519])).
% 2.07/1.66 tff(2521,plain,
% 2.07/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a495) | c0_1(a495) | c2_1(a495))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | c2_1(a495) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.07/1.66 inference(transitivity,[status(thm)],[2520, 2518])).
% 2.07/1.66 tff(2522,plain,
% 2.07/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a495) | c0_1(a495) | c2_1(a495))),
% 2.07/1.66 inference(quant_inst,[status(thm)],[])).
% 2.07/1.66 tff(2523,plain,
% 2.07/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c0_1(a495) | c3_1(a495) | (~ndr1_0) | c2_1(a495) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))),
% 2.07/1.66 inference(modus_ponens,[status(thm)],[2522, 2521])).
% 2.07/1.66 tff(2524,plain,
% 2.07/1.66 ($false),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[2523, 112, 2420, 2425, 2423, 2517, 2508, 1246, 2455, 2516])).
% 2.07/1.66 tff(2525,plain,((~hskp13) | (~c1_1(a540)) | (~c3_1(a540)) | c0_1(a540) | (~c0_1(a509)) | (~c3_1(a509)) | c1_1(a509) | (~c3_1(a507)) | c0_1(a507) | c1_1(a507) | c2_1(a509)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.66 tff(2526,plain,
% 2.07/1.66 (~hskp13),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[2525, 2454, 2425, 2423, 2395, 2394, 2420, 2424, 2422, 2426, 2393])).
% 2.07/1.66 tff(2527,plain,
% 2.07/1.66 (hskp12),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[535, 2526, 43])).
% 2.07/1.66 tff(2528,plain,
% 2.07/1.66 (~c2_1(a514)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[541, 2527])).
% 2.07/1.66 tff(2529,plain,
% 2.07/1.66 (c3_1(a514)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[552, 2527])).
% 2.07/1.66 tff(2530,plain,
% 2.07/1.66 (c1_1(a514)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[563, 2527])).
% 2.07/1.66 tff(2531,plain,
% 2.07/1.66 (c0_1(a514)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[955, 112, 2530, 2529, 2424, 2528, 2422, 2426, 618])).
% 2.07/1.66 tff(2532,plain,
% 2.07/1.66 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a540) | c2_1(a514) | (~ndr1_0) | (~c1_1(a514)) | (~c0_1(a514)) | (~c3_1(a540)) | (~c2_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a540) | c2_1(a514) | (~ndr1_0) | (~c1_1(a514)) | (~c0_1(a514)) | (~c3_1(a540)) | (~c2_1(a540)))),
% 2.07/1.66 inference(rewrite,[status(thm)],[])).
% 2.07/1.66 tff(2533,plain,
% 2.07/1.66 ((hskp15 | (~ndr1_0) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540))) <=> (hskp15 | c0_1(a540) | c2_1(a514) | (~ndr1_0) | (~c1_1(a514)) | (~c0_1(a514)) | (~c3_1(a540)) | (~c2_1(a540)))),
% 2.07/1.66 inference(rewrite,[status(thm)],[])).
% 2.07/1.66 tff(2534,plain,
% 2.07/1.66 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a540) | c2_1(a514) | (~ndr1_0) | (~c1_1(a514)) | (~c0_1(a514)) | (~c3_1(a540)) | (~c2_1(a540))))),
% 2.07/1.66 inference(monotonicity,[status(thm)],[2533])).
% 2.07/1.66 tff(2535,plain,
% 2.07/1.66 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a540) | c2_1(a514) | (~ndr1_0) | (~c1_1(a514)) | (~c0_1(a514)) | (~c3_1(a540)) | (~c2_1(a540)))),
% 2.07/1.66 inference(transitivity,[status(thm)],[2534, 2532])).
% 2.07/1.66 tff(2536,plain,
% 2.07/1.66 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a514) | (~c1_1(a514)) | (~c0_1(a514)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540)))),
% 2.07/1.66 inference(quant_inst,[status(thm)],[])).
% 2.07/1.66 tff(2537,plain,
% 2.07/1.66 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a540) | c2_1(a514) | (~ndr1_0) | (~c1_1(a514)) | (~c0_1(a514)) | (~c3_1(a540)) | (~c2_1(a540))),
% 2.07/1.66 inference(modus_ponens,[status(thm)],[2536, 2535])).
% 2.07/1.66 tff(2538,plain,
% 2.07/1.66 ($false),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[2537, 112, 43, 2425, 2530, 2423, 2528, 2446, 2531, 2436])).
% 2.07/1.66 tff(2539,plain,((~hskp9) | hskp15 | (~c3_1(a540)) | c0_1(a540) | (~c0_1(a509)) | (~c3_1(a509)) | (~c1_1(a540)) | c2_1(a509)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.66 tff(2540,plain,
% 2.07/1.66 ($false),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[2539, 2419, 2418, 2379, 2365, 2339, 2328, 2417, 2317])).
% 2.07/1.66 tff(2541,plain,(hskp2), inference(lemma,lemma(discharge,[]))).
% 2.07/1.66 tff(2542,plain,
% 2.07/1.66 (~c2_1(a496)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[368, 2541])).
% 2.07/1.66 tff(2543,plain,
% 2.07/1.66 (~c3_1(a496)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[362, 2541])).
% 2.07/1.66 tff(2544,plain,
% 2.07/1.66 (~hskp9),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[2539, 1843, 43, 1841, 2339, 2328, 1842, 2317])).
% 2.07/1.66 tff(2545,plain,
% 2.07/1.66 (c1_1(a509)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[2364, 2544])).
% 2.07/1.66 tff(2546,plain,
% 2.07/1.66 (~c2_1(a540)),
% 2.07/1.66 inference(unit_resolution,[status(thm)],[2452, 112, 43, 1842, 2339, 1841, 2317, 2446, 2545])).
% 2.07/1.66 tff(2547,assumption,(c1_1(a509)), introduced(assumption)).
% 2.07/1.66 tff(2548,plain,
% 2.07/1.66 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)))),
% 2.07/1.66 inference(rewrite,[status(thm)],[])).
% 2.07/1.66 tff(2549,plain,
% 2.07/1.66 ((hskp6 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c2_1(a496) | c0_1(a496) | c3_1(a496)) <=> (hskp6 | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)))),
% 2.07/1.66 inference(rewrite,[status(thm)],[])).
% 2.07/1.66 tff(2550,plain,
% 2.07/1.66 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c2_1(a496) | c0_1(a496) | c3_1(a496))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509))))),
% 2.07/1.67 inference(monotonicity,[status(thm)],[2549])).
% 2.07/1.67 tff(2551,plain,
% 2.07/1.67 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c2_1(a496) | c0_1(a496) | c3_1(a496))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)))),
% 2.07/1.67 inference(transitivity,[status(thm)],[2550, 2548])).
% 2.07/1.67 tff(2552,plain,
% 2.07/1.67 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c2_1(a496) | c0_1(a496) | c3_1(a496))),
% 2.07/1.67 inference(quant_inst,[status(thm)],[])).
% 2.07/1.67 tff(2553,plain,
% 2.07/1.67 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp6 | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509))),
% 2.07/1.67 inference(modus_ponens,[status(thm)],[2552, 2551])).
% 2.07/1.67 tff(2554,plain,
% 2.07/1.67 (hskp6 | c3_1(a496) | c0_1(a496) | (~c1_1(a509))),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2553, 112, 2395, 2393, 634, 966])).
% 2.07/1.67 tff(2555,plain,
% 2.07/1.67 (hskp6),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2554, 2547, 633, 635])).
% 2.07/1.67 tff(2556,plain,
% 2.07/1.67 (hskp2 | (~c1_1(a509))),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2345, 112, 2395, 2394, 2393, 601])).
% 2.07/1.67 tff(2557,plain,
% 2.07/1.67 (hskp2),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2556, 2547])).
% 2.07/1.67 tff(2558,plain,
% 2.07/1.67 (~c1_1(a496)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[381, 2557])).
% 2.07/1.67 tff(2559,plain,
% 2.07/1.67 ($false),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[790, 112, 674, 663, 652, 632, 634, 633, 784, 635])).
% 2.07/1.67 tff(2560,plain,((~hskp6) | c1_1(a496) | c2_1(a496) | c3_1(a496) | c0_1(a496)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.67 tff(2561,plain,
% 2.07/1.67 ($false),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2560, 2558, 2555, 634, 633, 635])).
% 2.07/1.67 tff(2562,plain,((~c1_1(a509)) | c2_1(a496) | c3_1(a496) | c0_1(a496) | (~c0_1(a509)) | c2_1(a509) | (~c3_1(a509))), inference(lemma,lemma(discharge,[]))).
% 2.07/1.67 tff(2563,plain,
% 2.07/1.67 (~c1_1(a509)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2562, 635, 633, 634, 2395, 2393, 2394])).
% 2.07/1.67 tff(2564,plain,
% 2.07/1.67 (hskp9 | c1_1(a509)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2363, 112, 2395, 2394, 2393, 2357])).
% 2.07/1.67 tff(2565,plain,
% 2.07/1.67 (hskp9),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2564, 2563])).
% 2.07/1.67 tff(2566,plain,
% 2.07/1.67 (c3_1(a507)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[941, 2565])).
% 2.07/1.67 tff(2567,plain,
% 2.07/1.67 (~c0_1(a507)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[930, 2565])).
% 2.07/1.67 tff(2568,plain,
% 2.07/1.67 (~c1_1(a507)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[924, 2565])).
% 2.07/1.67 tff(2569,plain,
% 2.07/1.67 (c2_1(a540)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2435, 2568, 2420, 2425, 2423, 2567, 2566])).
% 2.07/1.67 tff(2570,plain,
% 2.07/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.07/1.67 inference(rewrite,[status(thm)],[])).
% 2.07/1.67 tff(2571,plain,
% 2.07/1.67 (((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a496) | c0_1(a496) | c2_1(a496)) <=> (c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.07/1.67 inference(rewrite,[status(thm)],[])).
% 2.07/1.67 tff(2572,plain,
% 2.07/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 2.07/1.67 inference(monotonicity,[status(thm)],[2571])).
% 2.07/1.67 tff(2573,plain,
% 2.07/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.07/1.67 inference(transitivity,[status(thm)],[2572, 2570])).
% 2.07/1.67 tff(2574,plain,
% 2.07/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a496) | c0_1(a496) | c2_1(a496))),
% 2.07/1.67 inference(quant_inst,[status(thm)],[])).
% 2.07/1.67 tff(2575,plain,
% 2.07/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))),
% 2.07/1.67 inference(modus_ponens,[status(thm)],[2574, 2573])).
% 2.07/1.67 tff(2576,plain,
% 2.07/1.67 ($false),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2575, 112, 2420, 2425, 2423, 634, 633, 1246, 635, 2569])).
% 2.07/1.67 tff(2577,plain,(c0_1(a496) | (~c1_1(a540)) | (~c3_1(a540)) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.67 tff(2578,plain,
% 2.07/1.67 (c0_1(a496)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2577, 1841, 2317, 2339, 634, 633, 1842, 2328, 1843])).
% 2.07/1.67 tff(2579,plain,
% 2.07/1.67 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 2.07/1.67 inference(bind,[status(th)],[])).
% 2.07/1.67 tff(2580,plain,
% 2.07/1.67 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.07/1.67 inference(quant_intro,[status(thm)],[2579])).
% 2.07/1.67 tff(2581,plain,
% 2.07/1.67 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.07/1.67 inference(rewrite,[status(thm)],[])).
% 2.07/1.67 tff(2582,plain,
% 2.07/1.67 (^[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)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_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) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_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) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 2.07/1.67 inference(bind,[status(th)],[])).
% 2.07/1.67 tff(2583,plain,
% 2.07/1.67 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.07/1.67 inference(quant_intro,[status(thm)],[2582])).
% 2.07/1.67 tff(2584,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 2.07/1.67 tff(2585,plain,
% 2.07/1.67 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.07/1.67 inference(modus_ponens,[status(thm)],[2584, 2583])).
% 2.07/1.67 tff(2586,plain,
% 2.07/1.67 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.07/1.67 inference(modus_ponens,[status(thm)],[2585, 2581])).
% 2.07/1.67 tff(2587,plain,(
% 2.07/1.67 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.07/1.67 inference(skolemize,[status(sab)],[2586])).
% 2.07/1.67 tff(2588,plain,
% 2.07/1.67 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.07/1.67 inference(modus_ponens,[status(thm)],[2587, 2580])).
% 2.07/1.67 tff(2589,plain,
% 2.07/1.67 (hskp2),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2346, 2545])).
% 2.07/1.67 tff(2590,plain,
% 2.07/1.67 (~c1_1(a496)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[381, 2589])).
% 2.07/1.67 tff(2591,plain,
% 2.07/1.67 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a540)) | c2_1(a540))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a540)) | c2_1(a540))),
% 2.07/1.67 inference(rewrite,[status(thm)],[])).
% 2.07/1.67 tff(2592,plain,
% 2.07/1.67 ((hskp9 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c2_1(a540) | c0_1(a540) | (~c1_1(a540))) <=> (hskp9 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a540)) | c2_1(a540))),
% 2.07/1.67 inference(rewrite,[status(thm)],[])).
% 2.07/1.67 tff(2593,plain,
% 2.07/1.67 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c2_1(a540) | c0_1(a540) | (~c1_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a540)) | c2_1(a540)))),
% 2.07/1.67 inference(monotonicity,[status(thm)],[2592])).
% 2.07/1.67 tff(2594,plain,
% 2.07/1.67 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c2_1(a540) | c0_1(a540) | (~c1_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a540)) | c2_1(a540))),
% 2.07/1.67 inference(transitivity,[status(thm)],[2593, 2591])).
% 2.07/1.67 tff(2595,plain,
% 2.07/1.67 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c2_1(a540) | c0_1(a540) | (~c1_1(a540)))),
% 2.07/1.67 inference(quant_inst,[status(thm)],[])).
% 2.07/1.67 tff(2596,plain,
% 2.07/1.67 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a540) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a540)) | c2_1(a540)),
% 2.07/1.67 inference(modus_ponens,[status(thm)],[2595, 2594])).
% 2.07/1.67 tff(2597,plain,
% 2.07/1.67 ($false),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2596, 112, 2544, 1843, 1841, 2590, 634, 2588, 2578, 2546])).
% 2.07/1.67 tff(2598,plain,((~hskp22) | c2_1(a496) | hskp15 | c3_1(a496)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.67 tff(2599,plain,
% 2.07/1.67 (~hskp22),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2598, 43, 634, 633])).
% 2.07/1.67 tff(2600,assumption,(c0_1(a496)), introduced(assumption)).
% 2.07/1.67 tff(2601,plain,
% 2.07/1.67 ($false),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[797, 112, 2407, 632, 634, 633, 31, 2600])).
% 2.07/1.67 tff(2602,plain,(c1_1(a496) | hskp22 | c2_1(a496) | c3_1(a496) | (~c0_1(a496))), inference(lemma,lemma(discharge,[]))).
% 2.07/1.67 tff(2603,plain,
% 2.07/1.67 (c1_1(a496)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2602, 2600, 634, 633, 2407])).
% 2.07/1.67 tff(2604,plain,
% 2.07/1.67 (~hskp2),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[381, 2603])).
% 2.07/1.67 tff(2605,plain,
% 2.07/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a509)) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a509)) | (~c0_1(a509)))),
% 2.07/1.67 inference(rewrite,[status(thm)],[])).
% 2.07/1.67 tff(2606,plain,
% 2.07/1.67 ((hskp2 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c2_1(a496) | (~c1_1(a496)) | (~c0_1(a496))) <=> (hskp2 | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a509)) | (~c0_1(a509)))),
% 2.07/1.67 inference(rewrite,[status(thm)],[])).
% 2.07/1.67 tff(2607,plain,
% 2.07/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c2_1(a496) | (~c1_1(a496)) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a509)) | (~c0_1(a509))))),
% 2.07/1.67 inference(monotonicity,[status(thm)],[2606])).
% 2.07/1.67 tff(2608,plain,
% 2.07/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c2_1(a496) | (~c1_1(a496)) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a509)) | (~c0_1(a509)))),
% 2.07/1.67 inference(transitivity,[status(thm)],[2607, 2605])).
% 2.07/1.67 tff(2609,plain,
% 2.07/1.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c2_1(a496) | (~c1_1(a496)) | (~c0_1(a496)))),
% 2.07/1.67 inference(quant_inst,[status(thm)],[])).
% 2.07/1.67 tff(2610,plain,
% 2.07/1.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp2 | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a509)) | (~c0_1(a509))),
% 2.07/1.67 inference(modus_ponens,[status(thm)],[2609, 2608])).
% 2.07/1.67 tff(2611,plain,
% 2.07/1.67 (hskp2 | (~c1_1(a496)) | (~c0_1(a496))),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2610, 112, 2395, 2394, 2393, 634, 601])).
% 2.07/1.67 tff(2612,plain,
% 2.07/1.67 ($false),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2611, 2604, 2603, 2600])).
% 2.07/1.67 tff(2613,plain,((~c0_1(a496)) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | c2_1(a496) | c3_1(a496) | hskp22), inference(lemma,lemma(discharge,[]))).
% 2.07/1.67 tff(2614,plain,
% 2.07/1.67 (~c0_1(a496)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2613, 2599, 2328, 2317, 634, 633, 2339])).
% 2.07/1.67 tff(2615,plain,
% 2.07/1.67 (~c1_1(a509)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2562, 2614, 2328, 633, 2339, 2317, 634])).
% 2.07/1.67 tff(2616,plain,
% 2.07/1.67 (hskp9),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2364, 2615])).
% 2.07/1.67 tff(2617,plain,
% 2.07/1.67 (~c1_1(a507)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[924, 2616])).
% 2.07/1.67 tff(2618,plain,
% 2.07/1.67 (~c0_1(a507)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[930, 2616])).
% 2.07/1.67 tff(2619,plain,
% 2.07/1.67 (c3_1(a507)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[941, 2616])).
% 2.07/1.67 tff(2620,plain,
% 2.07/1.67 (hskp28),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2374, 112, 2339, 2328, 2619, 2618, 2617, 262, 2615])).
% 2.07/1.67 tff(2621,plain,
% 2.07/1.67 (c3_1(a500)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[429, 2620])).
% 2.07/1.67 tff(2622,plain,
% 2.07/1.67 (c2_1(a500)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[440, 2620])).
% 2.07/1.67 tff(2623,plain,
% 2.07/1.67 (c0_1(a500)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[451, 2620])).
% 2.07/1.67 tff(2624,plain,
% 2.07/1.67 (hskp2),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2415, 2623, 2339, 2328, 2317, 43, 2622, 2621, 2599, 2619, 2618, 2617])).
% 2.07/1.67 tff(2625,plain,
% 2.07/1.67 (~c1_1(a496)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[381, 2624])).
% 2.07/1.67 tff(2626,plain,
% 2.07/1.67 (~hskp6),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2560, 2625, 634, 633, 2614])).
% 2.07/1.67 tff(2627,plain,
% 2.07/1.67 (~hskp12),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[975, 2626, 2614, 634, 633, 2619, 2618, 2617])).
% 2.07/1.67 tff(2628,plain,
% 2.07/1.67 (hskp13),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[535, 2627, 43])).
% 2.07/1.67 tff(2629,plain,
% 2.07/1.67 (~c3_1(a520)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[1458, 2628])).
% 2.07/1.67 tff(2630,plain,
% 2.07/1.67 (c2_1(a520)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[1469, 2628])).
% 2.07/1.67 tff(2631,plain,
% 2.07/1.67 (~c1_1(a520)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[1969, 112, 2630, 2629, 2625, 634, 633, 784, 2614])).
% 2.07/1.67 tff(2632,plain,
% 2.07/1.67 (c0_1(a520)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[1480, 2628])).
% 2.07/1.67 tff(2633,plain,
% 2.07/1.67 (hskp24),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2402, 112, 2632, 2630, 2339, 2328, 2629, 2317, 1637])).
% 2.07/1.67 tff(2634,plain,
% 2.07/1.67 (~c3_1(a554)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[1666, 2633])).
% 2.07/1.67 tff(2635,plain,
% 2.07/1.67 (~c2_1(a554)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[1649, 2633])).
% 2.07/1.67 tff(2636,plain,
% 2.07/1.67 (c0_1(a554)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[1677, 2633])).
% 2.07/1.67 tff(2637,plain,
% 2.07/1.67 ($false),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2413, 112, 2599, 2636, 2632, 2635, 2634, 2629, 31, 2631])).
% 2.07/1.67 tff(2638,plain,(hskp15 | c2_1(a496) | c3_1(a496)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.67 tff(2639,plain,
% 2.07/1.67 (hskp15),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2638, 633, 634])).
% 2.07/1.67 tff(2640,plain,
% 2.07/1.67 (c1_1(a528)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[480, 2639])).
% 2.07/1.67 tff(2641,plain,
% 2.07/1.67 (c0_1(a528)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[491, 2639])).
% 2.07/1.67 tff(2642,plain,
% 2.07/1.67 (~c3_1(a528)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[469, 2639])).
% 2.07/1.67 tff(2643,plain,
% 2.07/1.67 (hskp10),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2185, 32])).
% 2.07/1.67 tff(2644,plain,
% 2.07/1.67 (c3_1(a509)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2327, 2643])).
% 2.07/1.67 tff(2645,plain,
% 2.07/1.67 (~c2_1(a509)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2316, 2643])).
% 2.07/1.67 tff(2646,plain,
% 2.07/1.67 (c0_1(a509)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2338, 2643])).
% 2.07/1.67 tff(2647,plain,
% 2.07/1.67 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 2.07/1.67 inference(bind,[status(th)],[])).
% 2.07/1.67 tff(2648,plain,
% 2.07/1.67 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.07/1.67 inference(quant_intro,[status(thm)],[2647])).
% 2.07/1.67 tff(2649,plain,
% 2.07/1.67 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.07/1.67 inference(rewrite,[status(thm)],[])).
% 2.07/1.67 tff(2650,plain,
% 2.07/1.67 (^[V: $i, U: $i] : 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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | 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)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~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)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 2.07/1.67 inference(bind,[status(th)],[])).
% 2.07/1.67 tff(2651,plain,
% 2.07/1.67 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.07/1.67 inference(quant_intro,[status(thm)],[2650])).
% 2.07/1.67 tff(2652,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 2.07/1.67 tff(2653,plain,
% 2.07/1.67 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.07/1.67 inference(modus_ponens,[status(thm)],[2652, 2651])).
% 2.07/1.67 tff(2654,plain,
% 2.07/1.67 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.07/1.67 inference(modus_ponens,[status(thm)],[2653, 2649])).
% 2.07/1.67 tff(2655,plain,(
% 2.07/1.67 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.07/1.67 inference(skolemize,[status(sab)],[2654])).
% 2.07/1.67 tff(2656,plain,
% 2.07/1.67 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.07/1.67 inference(modus_ponens,[status(thm)],[2655, 2648])).
% 2.07/1.67 tff(2657,assumption,(~c1_1(a528)), introduced(assumption)).
% 2.07/1.67 tff(2658,plain,
% 2.07/1.67 (~hskp15),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[480, 2657])).
% 2.07/1.67 tff(2659,assumption,(~c0_1(a528)), introduced(assumption)).
% 2.07/1.67 tff(2660,plain,
% 2.07/1.67 (~c1_1(a509)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2556, 453])).
% 2.07/1.67 tff(2661,plain,
% 2.07/1.67 (hskp9),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2564, 2660])).
% 2.07/1.67 tff(2662,plain,
% 2.07/1.67 (~c1_1(a507)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[924, 2661])).
% 2.07/1.67 tff(2663,plain,
% 2.07/1.67 (~c0_1(a507)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[930, 2661])).
% 2.07/1.67 tff(2664,plain,
% 2.07/1.67 (c3_1(a507)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[941, 2661])).
% 2.07/1.67 tff(2665,plain,
% 2.07/1.67 (~hskp12),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2381, 453, 2664, 2663, 2662])).
% 2.07/1.67 tff(2666,plain,
% 2.07/1.67 (hskp13),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[535, 2665, 2658])).
% 2.07/1.67 tff(2667,plain,
% 2.07/1.67 (c2_1(a520)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[1469, 2666])).
% 2.07/1.67 tff(2668,plain,
% 2.07/1.67 (c0_1(a520)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[1480, 2666])).
% 2.07/1.67 tff(2669,plain,
% 2.07/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a528) | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a528) | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 2.07/1.67 inference(rewrite,[status(thm)],[])).
% 2.07/1.67 tff(2670,plain,
% 2.07/1.67 ((hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | c3_1(a528)) <=> (hskp2 | c0_1(a528) | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 2.07/1.67 inference(rewrite,[status(thm)],[])).
% 2.07/1.67 tff(2671,plain,
% 2.07/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | c3_1(a528))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a528) | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520))))),
% 2.07/1.67 inference(monotonicity,[status(thm)],[2670])).
% 2.07/1.67 tff(2672,plain,
% 2.07/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | c3_1(a528))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a528) | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 2.07/1.67 inference(transitivity,[status(thm)],[2671, 2669])).
% 2.07/1.67 tff(2673,plain,
% 2.07/1.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | c3_1(a528))),
% 2.07/1.67 inference(quant_inst,[status(thm)],[])).
% 2.07/1.67 tff(2674,plain,
% 2.07/1.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a528) | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520))),
% 2.07/1.67 inference(modus_ponens,[status(thm)],[2673, 2672])).
% 2.07/1.67 tff(2675,plain,
% 2.07/1.67 (~c1_1(a520)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2674, 112, 453, 2659, 2657, 2668, 2667, 1082, 320])).
% 2.07/1.67 tff(2676,plain,
% 2.07/1.67 (~c3_1(a520)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[1458, 2666])).
% 2.07/1.67 tff(2677,plain,
% 2.07/1.67 (hskp24),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2402, 112, 2668, 2667, 2395, 2394, 2676, 2393, 1637])).
% 2.07/1.67 tff(2678,plain,
% 2.07/1.67 (~c3_1(a554)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[1666, 2677])).
% 2.07/1.67 tff(2679,plain,
% 2.07/1.67 (~c2_1(a554)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[1649, 2677])).
% 2.07/1.67 tff(2680,plain,
% 2.07/1.67 (c0_1(a554)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[1677, 2677])).
% 2.07/1.67 tff(2681,plain,
% 2.07/1.67 (hskp22),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2413, 112, 2680, 2668, 2679, 2678, 2676, 31, 2675])).
% 2.07/1.67 tff(2682,plain,
% 2.07/1.67 (~c0_1(a540)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[131, 2681])).
% 2.07/1.67 tff(2683,plain,
% 2.07/1.67 (c1_1(a540)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[153, 2681])).
% 2.07/1.67 tff(2684,plain,
% 2.07/1.67 (c3_1(a540)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[142, 2681])).
% 2.07/1.67 tff(2685,plain,
% 2.07/1.67 (c2_1(a540)),
% 2.07/1.67 inference(unit_resolution,[status(thm)],[2435, 2684, 2662, 2664, 2682, 2663, 2683])).
% 2.07/1.67 tff(2686,plain,
% 2.07/1.67 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))),
% 2.07/1.67 inference(rewrite,[status(thm)],[])).
% 2.07/1.67 tff(2687,plain,
% 2.07/1.67 ((hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | c3_1(a528)) <=> (hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))),
% 2.07/1.67 inference(rewrite,[status(thm)],[])).
% 2.07/1.67 tff(2688,plain,
% 2.07/1.67 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | c3_1(a528))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520))))),
% 2.07/1.67 inference(monotonicity,[status(thm)],[2687])).
% 2.07/1.67 tff(2689,plain,
% 2.07/1.67 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | c3_1(a528))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520)))),
% 2.07/1.67 inference(transitivity,[status(thm)],[2688, 2686])).
% 2.07/1.67 tff(2690,plain,
% 2.07/1.67 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a520) | c1_1(a520) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | c3_1(a528))),
% 2.07/1.67 inference(quant_inst,[status(thm)],[])).
% 2.07/1.67 tff(2691,plain,
% 2.07/1.67 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | (~ndr1_0) | c1_1(a520) | (~c0_1(a520))),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2690, 2689])).
% 2.07/1.68 tff(2692,plain,
% 2.07/1.68 (hskp1),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2691, 112, 2659, 2657, 2668, 1082, 2676, 645, 2675])).
% 2.07/1.68 tff(2693,plain,
% 2.07/1.68 (~c3_1(a495)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[1019, 2692])).
% 2.07/1.68 tff(2694,plain,
% 2.07/1.68 (c1_1(a495)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[1037, 2692])).
% 2.07/1.68 tff(2695,plain,
% 2.07/1.68 (~c0_1(a495)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[1025, 2692])).
% 2.07/1.68 tff(2696,plain,
% 2.07/1.68 (c2_1(a495)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2523, 112, 2683, 2684, 2682, 2695, 2693, 1246, 2685])).
% 2.07/1.68 tff(2697,plain,
% 2.07/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a528) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | c2_1(a528) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a528) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | c2_1(a528) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2698,plain,
% 2.07/1.68 (((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a528) | c0_1(a528) | c2_1(a528)) <=> (c0_1(a528) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | c2_1(a528) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2699,plain,
% 2.07/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a528) | c0_1(a528) | c2_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a528) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | c2_1(a528) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 2.07/1.68 inference(monotonicity,[status(thm)],[2698])).
% 2.07/1.68 tff(2700,plain,
% 2.07/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a528) | c0_1(a528) | c2_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a528) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | c2_1(a528) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.07/1.68 inference(transitivity,[status(thm)],[2699, 2697])).
% 2.07/1.68 tff(2701,plain,
% 2.07/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a528) | c0_1(a528) | c2_1(a528))),
% 2.07/1.68 inference(quant_inst,[status(thm)],[])).
% 2.07/1.68 tff(2702,plain,
% 2.07/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a528) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | c2_1(a528) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2701, 2700])).
% 2.07/1.68 tff(2703,plain,
% 2.07/1.68 (c2_1(a528)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2702, 112, 2683, 2684, 2659, 2682, 1082, 1246, 2685])).
% 2.07/1.68 tff(2704,assumption,(~hskp4), introduced(assumption)).
% 2.07/1.68 tff(2705,plain,
% 2.07/1.68 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a528) | c1_1(a528) | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c2_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a528) | c1_1(a528) | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c2_1(a528)))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2706,plain,
% 2.07/1.68 ((hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | (~c2_1(a528))) <=> (hskp4 | c0_1(a528) | c1_1(a528) | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c2_1(a528)))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2707,plain,
% 2.07/1.68 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | (~c2_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a528) | c1_1(a528) | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c2_1(a528))))),
% 2.07/1.68 inference(monotonicity,[status(thm)],[2706])).
% 2.07/1.68 tff(2708,plain,
% 2.07/1.68 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | (~c2_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a528) | c1_1(a528) | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c2_1(a528)))),
% 2.07/1.68 inference(transitivity,[status(thm)],[2707, 2705])).
% 2.07/1.68 tff(2709,plain,
% 2.07/1.68 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c0_1(a520)) | c1_1(a528) | c0_1(a528) | (~c2_1(a528)))),
% 2.07/1.68 inference(quant_inst,[status(thm)],[])).
% 2.07/1.68 tff(2710,plain,
% 2.07/1.68 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a528) | c1_1(a528) | c3_1(a520) | (~ndr1_0) | (~c0_1(a520)) | (~c2_1(a520)) | (~c2_1(a528))),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2709, 2708])).
% 2.07/1.68 tff(2711,plain,
% 2.07/1.68 ($false),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2710, 112, 2704, 2659, 2657, 2459, 2467, 2458, 400, 2219])).
% 2.07/1.68 tff(2712,plain,((~hskp13) | hskp4 | c0_1(a528) | c1_1(a528) | (~c2_1(a528))), inference(lemma,lemma(discharge,[]))).
% 2.07/1.68 tff(2713,plain,
% 2.07/1.68 (hskp4),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2712, 2703, 2659, 2657, 2666])).
% 2.07/1.68 tff(2714,assumption,(c2_1(a540)), introduced(assumption)).
% 2.07/1.68 tff(2715,assumption,(hskp4), introduced(assumption)).
% 2.07/1.68 tff(2716,plain,
% 2.07/1.68 (~c2_1(a498)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[1517, 2715])).
% 2.07/1.68 tff(2717,plain,
% 2.07/1.68 (~c0_1(a498)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[1493, 2715])).
% 2.07/1.68 tff(2718,plain,
% 2.07/1.68 (c1_1(a498)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[1504, 2715])).
% 2.07/1.68 tff(2719,plain,
% 2.07/1.68 (~c3_1(a498)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2495, 112, 2420, 2718, 2423, 2717, 2716, 1175, 2714])).
% 2.07/1.68 tff(2720,assumption,(c2_1(a495)), introduced(assumption)).
% 2.07/1.68 tff(2721,plain,
% 2.07/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a528) | c1_1(a528) | c3_1(a528) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2722,plain,
% 2.07/1.68 (((~ndr1_0) | c3_1(a495) | (~c2_1(a495)) | (~c1_1(a495)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a528) | c1_1(a528) | c0_1(a528)) <=> (c0_1(a528) | c1_1(a528) | c3_1(a528) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2723,plain,
% 2.07/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a495) | (~c2_1(a495)) | (~c1_1(a495)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a528) | c1_1(a528) | c0_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a528) | c1_1(a528) | c3_1(a528) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498)))),
% 2.07/1.68 inference(monotonicity,[status(thm)],[2722])).
% 2.07/1.68 tff(2724,plain,
% 2.07/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a495) | (~c2_1(a495)) | (~c1_1(a495)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a528) | c1_1(a528) | c0_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498))),
% 2.07/1.68 inference(transitivity,[status(thm)],[2723, 2721])).
% 2.07/1.68 tff(2725,plain,
% 2.07/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a495) | (~c2_1(a495)) | (~c1_1(a495)) | c2_1(a498) | c0_1(a498) | c3_1(a498) | c3_1(a528) | c1_1(a528) | c0_1(a528))),
% 2.07/1.68 inference(quant_inst,[status(thm)],[])).
% 2.07/1.68 tff(2726,plain,
% 2.07/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c0_1(a498) | c2_1(a498) | c3_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a498)),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2725, 2724])).
% 2.07/1.68 tff(2727,plain,
% 2.07/1.68 ($false),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2726, 112, 2659, 2657, 1077, 1082, 2717, 2716, 1075, 784, 2720, 2719])).
% 2.07/1.68 tff(2728,plain,((~hskp4) | c0_1(a528) | c1_1(a528) | (~c1_1(a495)) | c3_1(a528) | c3_1(a495) | (~c2_1(a495)) | (~c1_1(a540)) | c0_1(a540) | (~c2_1(a540))), inference(lemma,lemma(discharge,[]))).
% 2.07/1.68 tff(2729,plain,
% 2.07/1.68 ($false),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2728, 2713, 2696, 2657, 2694, 1082, 2693, 2685, 2683, 2682, 2659])).
% 2.07/1.68 tff(2730,plain,(hskp2 | c1_1(a528) | c3_1(a528) | c0_1(a528) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.68 tff(2731,plain,
% 2.07/1.68 (hskp2),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2730, 2659, 1082, 2657, 2395, 2394, 2393])).
% 2.07/1.68 tff(2732,plain,
% 2.07/1.68 (~c2_1(a496)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[368, 2731])).
% 2.07/1.68 tff(2733,plain,
% 2.07/1.68 (~c3_1(a496)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[362, 2731])).
% 2.07/1.68 tff(2734,plain,
% 2.07/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2735,plain,
% 2.07/1.68 (((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a528) | c1_1(a528) | c0_1(a528)) <=> (c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2736,plain,
% 2.07/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a528) | c1_1(a528) | c0_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501))))),
% 2.07/1.68 inference(monotonicity,[status(thm)],[2735])).
% 2.07/1.68 tff(2737,plain,
% 2.07/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a528) | c1_1(a528) | c0_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))),
% 2.07/1.68 inference(transitivity,[status(thm)],[2736, 2734])).
% 2.07/1.68 tff(2738,plain,
% 2.07/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a528) | c1_1(a528) | c0_1(a528))),
% 2.07/1.68 inference(quant_inst,[status(thm)],[])).
% 2.07/1.68 tff(2739,plain,
% 2.07/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501))),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2738, 2737])).
% 2.07/1.68 tff(2740,plain,
% 2.07/1.68 ($false),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2739, 112, 2659, 2657, 674, 663, 1082, 652, 634, 633, 784, 635])).
% 2.07/1.68 tff(2741,plain,((~hskp6) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c2_1(a496) | c3_1(a496) | c0_1(a496)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.68 tff(2742,plain,
% 2.07/1.68 (~hskp6),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2741, 635, 2657, 1082, 634, 633, 2659])).
% 2.07/1.68 tff(2743,plain,
% 2.07/1.68 (~c1_1(a509)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2554, 635, 633, 2742])).
% 2.07/1.68 tff(2744,plain,
% 2.07/1.68 (hskp9),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2564, 2743])).
% 2.07/1.68 tff(2745,plain,
% 2.07/1.68 (~c1_1(a507)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[924, 2744])).
% 2.07/1.68 tff(2746,plain,
% 2.07/1.68 (~c0_1(a507)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[930, 2744])).
% 2.07/1.68 tff(2747,plain,
% 2.07/1.68 (~c0_1(a496)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2613, 2407, 2394, 2393, 634, 633, 2395])).
% 2.07/1.68 tff(2748,plain,
% 2.07/1.68 (~hskp6),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2741, 2747, 2657, 1082, 634, 633, 2659])).
% 2.07/1.68 tff(2749,plain,
% 2.07/1.68 (~c1_1(a509)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2554, 2748, 633, 2747])).
% 2.07/1.68 tff(2750,plain,
% 2.07/1.68 (hskp9),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2564, 2749])).
% 2.07/1.68 tff(2751,plain,
% 2.07/1.68 (~c1_1(a507)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[924, 2750])).
% 2.07/1.68 tff(2752,plain,
% 2.07/1.68 (~c0_1(a507)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[930, 2750])).
% 2.07/1.68 tff(2753,plain,
% 2.07/1.68 (c3_1(a507)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[941, 2750])).
% 2.07/1.68 tff(2754,plain,
% 2.07/1.68 (~hskp12),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[975, 2753, 634, 633, 2747, 2748, 2752, 2751])).
% 2.07/1.68 tff(2755,plain,
% 2.07/1.68 (hskp13),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[535, 2754, 2658])).
% 2.07/1.68 tff(2756,plain,
% 2.07/1.68 (~c3_1(a520)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[1458, 2755])).
% 2.07/1.68 tff(2757,plain,
% 2.07/1.68 (c2_1(a520)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[1469, 2755])).
% 2.07/1.68 tff(2758,plain,
% 2.07/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2759,plain,
% 2.07/1.68 (((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a528) | c1_1(a528) | c0_1(a528)) <=> (c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2760,plain,
% 2.07/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a528) | c1_1(a528) | c0_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520))))),
% 2.07/1.68 inference(monotonicity,[status(thm)],[2759])).
% 2.07/1.68 tff(2761,plain,
% 2.07/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a528) | c1_1(a528) | c0_1(a528))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520)))),
% 2.07/1.68 inference(transitivity,[status(thm)],[2760, 2758])).
% 2.07/1.68 tff(2762,plain,
% 2.07/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c2_1(a520)) | (~c1_1(a520)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a528) | c1_1(a528) | c0_1(a528))),
% 2.07/1.68 inference(quant_inst,[status(thm)],[])).
% 2.07/1.68 tff(2763,plain,
% 2.07/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a520) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a520)) | (~c2_1(a520))),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2762, 2761])).
% 2.07/1.68 tff(2764,plain,
% 2.07/1.68 (~c1_1(a520)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2763, 112, 2659, 2657, 2757, 1082, 2756, 634, 633, 784, 2747])).
% 2.07/1.68 tff(2765,plain,
% 2.07/1.68 (c0_1(a520)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[1480, 2755])).
% 2.07/1.68 tff(2766,plain,
% 2.07/1.68 (hskp24),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2402, 112, 2765, 2757, 2395, 2394, 2756, 2393, 1637])).
% 2.07/1.68 tff(2767,plain,
% 2.07/1.68 (~c3_1(a554)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[1666, 2766])).
% 2.07/1.68 tff(2768,plain,
% 2.07/1.68 (~c2_1(a554)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[1649, 2766])).
% 2.07/1.68 tff(2769,plain,
% 2.07/1.68 (c0_1(a554)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[1677, 2766])).
% 2.07/1.68 tff(2770,plain,
% 2.07/1.68 ($false),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2413, 112, 2407, 2769, 2765, 2768, 2767, 2756, 31, 2764])).
% 2.07/1.68 tff(2771,plain,(hskp22 | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c2_1(a496) | c3_1(a496)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.68 tff(2772,plain,
% 2.07/1.68 (hskp22),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2771, 633, 2394, 2393, 2659, 2657, 1082, 634, 2395])).
% 2.07/1.68 tff(2773,plain,
% 2.07/1.68 (~c0_1(a540)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[131, 2772])).
% 2.07/1.68 tff(2774,plain,
% 2.07/1.68 (c1_1(a540)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[153, 2772])).
% 2.07/1.68 tff(2775,plain,
% 2.07/1.68 (c3_1(a540)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[142, 2772])).
% 2.07/1.68 tff(2776,plain,
% 2.07/1.68 (c3_1(a507)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[941, 2744])).
% 2.07/1.68 tff(2777,plain,
% 2.07/1.68 (c2_1(a540)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2435, 2776, 2775, 2774, 2773, 2746, 2745])).
% 2.07/1.68 tff(2778,plain,
% 2.07/1.68 ($false),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2575, 112, 2774, 2775, 2773, 634, 633, 1246, 635, 2777])).
% 2.07/1.68 tff(2779,plain,(c0_1(a496) | c2_1(a496) | c3_1(a496) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | c1_1(a528) | c3_1(a528) | c0_1(a528)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.68 tff(2780,plain,
% 2.07/1.68 (c0_1(a496)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2779, 633, 634, 2395, 2394, 2393, 2657, 1082, 2659])).
% 2.07/1.68 tff(2781,assumption,(~hskp27), introduced(assumption)).
% 2.07/1.68 tff(2782,assumption,(~hskp19), introduced(assumption)).
% 2.07/1.68 tff(2783,plain,
% 2.07/1.68 (^[U: $i] : refl((hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 2.07/1.68 inference(bind,[status(th)],[])).
% 2.07/1.68 tff(2784,plain,
% 2.07/1.68 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.07/1.68 inference(quant_intro,[status(thm)],[2783])).
% 2.07/1.68 tff(2785,plain,
% 2.07/1.68 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2786,plain,
% 2.07/1.68 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp19) <=> ((hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp19))), rewrite(((hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp19) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp19) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 2.07/1.68 inference(bind,[status(th)],[])).
% 2.07/1.68 tff(2787,plain,
% 2.07/1.68 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp19) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.07/1.68 inference(quant_intro,[status(thm)],[2786])).
% 2.07/1.68 tff(2788,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 2.07/1.68 tff(2789,plain,
% 2.07/1.68 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2788, 2787])).
% 2.07/1.68 tff(2790,plain,
% 2.07/1.68 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2789, 2785])).
% 2.07/1.68 tff(2791,plain,(
% 2.07/1.68 ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.07/1.68 inference(skolemize,[status(sab)],[2790])).
% 2.07/1.68 tff(2792,plain,
% 2.07/1.68 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2791, 2784])).
% 2.07/1.68 tff(2793,plain,
% 2.07/1.68 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2794,plain,
% 2.07/1.68 ((hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540))) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2795,plain,
% 2.07/1.68 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 2.07/1.68 inference(monotonicity,[status(thm)],[2794])).
% 2.07/1.68 tff(2796,plain,
% 2.07/1.68 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.07/1.68 inference(transitivity,[status(thm)],[2795, 2793])).
% 2.07/1.68 tff(2797,plain,
% 2.07/1.68 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 2.07/1.68 inference(quant_inst,[status(thm)],[])).
% 2.07/1.68 tff(2798,plain,
% 2.07/1.68 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2797, 2796])).
% 2.07/1.68 tff(2799,plain,
% 2.07/1.68 (hskp27 | hskp19 | (~c2_1(a540))),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2798, 112, 2420, 2425, 2792])).
% 2.07/1.68 tff(2800,plain,
% 2.07/1.68 (~c2_1(a540)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2799, 2782, 2781])).
% 2.07/1.68 tff(2801,plain,
% 2.07/1.68 (^[U: $i] : refl((hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))),
% 2.07/1.68 inference(bind,[status(th)],[])).
% 2.07/1.68 tff(2802,plain,
% 2.07/1.68 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 2.07/1.68 inference(quant_intro,[status(thm)],[2801])).
% 2.07/1.68 tff(2803,plain,
% 2.07/1.68 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2804,plain,
% 2.07/1.68 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp18))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp19) <=> ((hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp19))), rewrite(((hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp19) <=> (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp19) <=> (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))))),
% 2.07/1.68 inference(bind,[status(th)],[])).
% 2.07/1.68 tff(2805,plain,
% 2.07/1.68 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp19) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 2.07/1.68 inference(quant_intro,[status(thm)],[2804])).
% 2.07/1.68 tff(2806,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 2.07/1.68 tff(2807,plain,
% 2.07/1.68 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2806, 2805])).
% 2.07/1.68 tff(2808,plain,
% 2.07/1.68 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2807, 2803])).
% 2.07/1.68 tff(2809,plain,(
% 2.07/1.68 ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 2.07/1.68 inference(skolemize,[status(sab)],[2808])).
% 2.07/1.68 tff(2810,plain,
% 2.07/1.68 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2809, 2802])).
% 2.07/1.68 tff(2811,plain,
% 2.07/1.68 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp18 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp19 | hskp18 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2812,plain,
% 2.07/1.68 ((hskp19 | hskp18 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | c1_1(a496)) <=> (hskp19 | hskp18 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2813,plain,
% 2.07/1.68 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp18 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | c1_1(a496))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp18 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0)))),
% 2.07/1.68 inference(monotonicity,[status(thm)],[2812])).
% 2.07/1.68 tff(2814,plain,
% 2.07/1.68 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp18 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | c1_1(a496))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp19 | hskp18 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0))),
% 2.07/1.68 inference(transitivity,[status(thm)],[2813, 2811])).
% 2.07/1.68 tff(2815,plain,
% 2.07/1.68 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp19 | hskp18 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | c1_1(a496))),
% 2.07/1.68 inference(quant_inst,[status(thm)],[])).
% 2.07/1.68 tff(2816,plain,
% 2.07/1.68 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp19 | hskp18 | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0)),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2815, 2814])).
% 2.07/1.68 tff(2817,plain,
% 2.07/1.68 (hskp19 | hskp18 | c1_1(a496) | c3_1(a496)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2816, 112, 634, 2810])).
% 2.07/1.68 tff(2818,plain,
% 2.07/1.68 (hskp18),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2817, 2782, 632, 633])).
% 2.07/1.68 tff(2819,plain,
% 2.07/1.68 (((~hskp18) | (~c0_1(a533))) <=> ((~hskp18) | (~c0_1(a533)))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2820,plain,
% 2.07/1.68 (((~c0_1(a533)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a533)))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2821,axiom,((~c0_1(a533)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 2.07/1.68 tff(2822,plain,
% 2.07/1.68 ((~hskp18) | (~c0_1(a533))),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2821, 2820])).
% 2.07/1.68 tff(2823,plain,
% 2.07/1.68 ((~hskp18) | (~c0_1(a533))),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2822, 2819])).
% 2.07/1.68 tff(2824,plain,
% 2.07/1.68 (~c0_1(a533)),
% 2.07/1.68 inference(unit_resolution,[status(thm)],[2823, 2818])).
% 2.07/1.68 tff(2825,plain,
% 2.07/1.68 (((~hskp18) | c2_1(a533)) <=> ((~hskp18) | c2_1(a533))),
% 2.07/1.68 inference(rewrite,[status(thm)],[])).
% 2.07/1.68 tff(2826,axiom,((~hskp18) | c2_1(a533)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 2.07/1.68 tff(2827,plain,
% 2.07/1.68 ((~hskp18) | c2_1(a533)),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2826, 2825])).
% 2.07/1.68 tff(2828,plain,
% 2.07/1.68 ((~hskp18) | c2_1(a533)),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2827, 2825])).
% 2.07/1.68 tff(2829,plain,
% 2.07/1.68 ((~hskp18) | c2_1(a533)),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2828, 2825])).
% 2.07/1.68 tff(2830,plain,
% 2.07/1.68 ((~hskp18) | c2_1(a533)),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2829, 2825])).
% 2.07/1.68 tff(2831,plain,
% 2.07/1.68 ((~hskp18) | c2_1(a533)),
% 2.07/1.68 inference(modus_ponens,[status(thm)],[2830, 2825])).
% 2.07/1.68 tff(2832,plain,
% 2.07/1.68 ((~hskp18) | c2_1(a533)),
% 2.07/1.69 inference(modus_ponens,[status(thm)],[2831, 2825])).
% 2.07/1.69 tff(2833,plain,
% 2.07/1.69 ((~hskp18) | c2_1(a533)),
% 2.07/1.69 inference(modus_ponens,[status(thm)],[2832, 2825])).
% 2.07/1.69 tff(2834,plain,
% 2.07/1.69 ((~hskp18) | c2_1(a533)),
% 2.07/1.69 inference(modus_ponens,[status(thm)],[2833, 2825])).
% 2.07/1.69 tff(2835,plain,
% 2.07/1.69 (c2_1(a533)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[2834, 2818])).
% 2.07/1.69 tff(2836,plain,
% 2.07/1.69 (((~hskp18) | c1_1(a533)) <=> ((~hskp18) | c1_1(a533))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(2837,axiom,((~hskp18) | c1_1(a533)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 2.07/1.69 tff(2838,plain,
% 2.07/1.69 ((~hskp18) | c1_1(a533)),
% 2.07/1.69 inference(modus_ponens,[status(thm)],[2837, 2836])).
% 2.07/1.69 tff(2839,plain,
% 2.07/1.69 ((~hskp18) | c1_1(a533)),
% 2.07/1.69 inference(modus_ponens,[status(thm)],[2838, 2836])).
% 2.07/1.69 tff(2840,plain,
% 2.07/1.69 ((~hskp18) | c1_1(a533)),
% 2.07/1.69 inference(modus_ponens,[status(thm)],[2839, 2836])).
% 2.07/1.69 tff(2841,plain,
% 2.07/1.69 ((~hskp18) | c1_1(a533)),
% 2.07/1.69 inference(modus_ponens,[status(thm)],[2840, 2836])).
% 2.07/1.69 tff(2842,plain,
% 2.07/1.69 ((~hskp18) | c1_1(a533)),
% 2.07/1.69 inference(modus_ponens,[status(thm)],[2841, 2836])).
% 2.07/1.69 tff(2843,plain,
% 2.07/1.69 ((~hskp18) | c1_1(a533)),
% 2.07/1.69 inference(modus_ponens,[status(thm)],[2842, 2836])).
% 2.07/1.69 tff(2844,plain,
% 2.07/1.69 ((~hskp18) | c1_1(a533)),
% 2.07/1.69 inference(modus_ponens,[status(thm)],[2843, 2836])).
% 2.07/1.69 tff(2845,plain,
% 2.07/1.69 ((~hskp18) | c1_1(a533)),
% 2.07/1.69 inference(modus_ponens,[status(thm)],[2844, 2836])).
% 2.07/1.69 tff(2846,plain,
% 2.07/1.69 (c1_1(a533)),
% 2.07/1.69 inference(unit_resolution,[status(thm)],[2845, 2818])).
% 2.07/1.69 tff(2847,plain,
% 2.07/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a540) | c0_1(a533) | (~ndr1_0) | (~c1_1(a533)) | (~c2_1(a533)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a540) | c0_1(a533) | (~ndr1_0) | (~c1_1(a533)) | (~c2_1(a533)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(2848,plain,
% 2.07/1.69 (((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a533) | (~c1_1(a533)) | (~c2_1(a533)) | c0_1(a540) | c2_1(a540) | (~c1_1(a540))) <=> (c0_1(a540) | c0_1(a533) | (~ndr1_0) | (~c1_1(a533)) | (~c2_1(a533)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540))),
% 2.07/1.69 inference(rewrite,[status(thm)],[])).
% 2.07/1.69 tff(2849,plain,
% 2.07/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a533) | (~c1_1(a533)) | (~c2_1(a533)) | c0_1(a540) | c2_1(a540) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a540) | c0_1(a533) | (~ndr1_0) | (~c1_1(a533)) | (~c2_1(a533)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540)))),
% 2.07/1.69 inference(monotonicity,[status(thm)],[2848])).
% 2.07/1.69 tff(2850,plain,
% 2.07/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a533) | (~c1_1(a533)) | (~c2_1(a533)) | c0_1(a540) | c2_1(a540) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a540) | c0_1(a533) | (~ndr1_0) | (~c1_1(a533)) | (~c2_1(a533)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540))),
% 2.07/1.69 inference(transitivity,[status(thm)],[2849, 2847])).
% 2.07/1.69 tff(2851,plain,
% 2.07/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a533) | (~c1_1(a533)) | (~c2_1(a533)) | c0_1(a540) | c2_1(a540) | (~c1_1(a540)))),
% 2.07/1.69 inference(quant_inst,[status(thm)],[])).
% 2.07/1.69 tff(2852,plain,
% 2.11/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a540) | c0_1(a533) | (~ndr1_0) | (~c1_1(a533)) | (~c2_1(a533)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540)),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2851, 2850])).
% 2.11/1.69 tff(2853,plain,
% 2.11/1.69 ($false),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2852, 112, 2420, 2425, 2846, 2835, 2423, 2824, 1175, 2800])).
% 2.11/1.69 tff(2854,plain,(hskp19 | (~c1_1(a540)) | (~c3_1(a540)) | c0_1(a540) | hskp27 | c1_1(a496) | c3_1(a496) | c2_1(a496)), inference(lemma,lemma(discharge,[]))).
% 2.11/1.69 tff(2855,plain,
% 2.11/1.69 (hskp19),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2854, 632, 2775, 2773, 2781, 2774, 633, 634])).
% 2.11/1.69 tff(2856,plain,
% 2.11/1.69 (((~hskp19) | (~c2_1(a534))) <=> ((~hskp19) | (~c2_1(a534)))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2857,plain,
% 2.11/1.69 (((~c2_1(a534)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a534)))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2858,axiom,((~c2_1(a534)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 2.11/1.69 tff(2859,plain,
% 2.11/1.69 ((~hskp19) | (~c2_1(a534))),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2858, 2857])).
% 2.11/1.69 tff(2860,plain,
% 2.11/1.69 ((~hskp19) | (~c2_1(a534))),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2859, 2856])).
% 2.11/1.69 tff(2861,plain,
% 2.11/1.69 (~c2_1(a534)),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2860, 2855])).
% 2.11/1.69 tff(2862,plain,
% 2.11/1.69 (((~hskp19) | (~c3_1(a534))) <=> ((~hskp19) | (~c3_1(a534)))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2863,plain,
% 2.11/1.69 (((~c3_1(a534)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a534)))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2864,axiom,((~c3_1(a534)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 2.11/1.69 tff(2865,plain,
% 2.11/1.69 ((~hskp19) | (~c3_1(a534))),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2864, 2863])).
% 2.11/1.69 tff(2866,plain,
% 2.11/1.69 ((~hskp19) | (~c3_1(a534))),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2865, 2862])).
% 2.11/1.69 tff(2867,plain,
% 2.11/1.69 (~c3_1(a534)),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2866, 2855])).
% 2.11/1.69 tff(2868,plain,
% 2.11/1.69 (((~hskp19) | c1_1(a534)) <=> ((~hskp19) | c1_1(a534))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2869,axiom,((~hskp19) | c1_1(a534)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 2.11/1.69 tff(2870,plain,
% 2.11/1.69 ((~hskp19) | c1_1(a534)),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2869, 2868])).
% 2.11/1.69 tff(2871,plain,
% 2.11/1.69 ((~hskp19) | c1_1(a534)),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2870, 2868])).
% 2.11/1.69 tff(2872,plain,
% 2.11/1.69 ((~hskp19) | c1_1(a534)),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2871, 2868])).
% 2.11/1.69 tff(2873,plain,
% 2.11/1.69 ((~hskp19) | c1_1(a534)),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2872, 2868])).
% 2.11/1.69 tff(2874,plain,
% 2.11/1.69 ((~hskp19) | c1_1(a534)),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2873, 2868])).
% 2.11/1.69 tff(2875,plain,
% 2.11/1.69 ((~hskp19) | c1_1(a534)),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2874, 2868])).
% 2.11/1.69 tff(2876,plain,
% 2.11/1.69 ((~hskp19) | c1_1(a534)),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2875, 2868])).
% 2.11/1.69 tff(2877,plain,
% 2.11/1.69 ((~hskp19) | c1_1(a534)),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2876, 2868])).
% 2.11/1.69 tff(2878,plain,
% 2.11/1.69 (c1_1(a534)),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2877, 2855])).
% 2.11/1.69 tff(2879,assumption,(~c3_1(a534)), introduced(assumption)).
% 2.11/1.69 tff(2880,assumption,(~c2_1(a534)), introduced(assumption)).
% 2.11/1.69 tff(2881,assumption,(c1_1(a534)), introduced(assumption)).
% 2.11/1.69 tff(2882,plain,
% 2.11/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a534) | c3_1(a534) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a534)) | (~c0_1(a534)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a534) | c3_1(a534) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a534)) | (~c0_1(a534)))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2883,plain,
% 2.11/1.69 (((~ndr1_0) | c3_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c2_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c3_1(a496) | c0_1(a496) | c2_1(a496)) <=> (c2_1(a534) | c3_1(a534) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a534)) | (~c0_1(a534)))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2884,plain,
% 2.11/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c2_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a534) | c3_1(a534) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a534)) | (~c0_1(a534))))),
% 2.11/1.69 inference(monotonicity,[status(thm)],[2883])).
% 2.11/1.69 tff(2885,plain,
% 2.11/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c2_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a534) | c3_1(a534) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a534)) | (~c0_1(a534)))),
% 2.11/1.69 inference(transitivity,[status(thm)],[2884, 2882])).
% 2.11/1.69 tff(2886,plain,
% 2.11/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c2_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c3_1(a496) | c0_1(a496) | c2_1(a496))),
% 2.11/1.69 inference(quant_inst,[status(thm)],[])).
% 2.11/1.69 tff(2887,plain,
% 2.11/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a534) | c3_1(a534) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a534)) | (~c0_1(a534))),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2886, 2885])).
% 2.11/1.69 tff(2888,plain,
% 2.11/1.69 (c0_1(a496) | (~c0_1(a534))),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2887, 112, 2881, 2880, 2879, 634, 633, 996])).
% 2.11/1.69 tff(2889,plain,
% 2.11/1.69 (~c0_1(a534)),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2888, 635])).
% 2.11/1.69 tff(2890,plain,
% 2.11/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a540) | c2_1(a534) | c3_1(a534) | (~ndr1_0) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c2_1(a534) | c3_1(a534) | (~ndr1_0) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2891,plain,
% 2.11/1.69 (((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a534) | c0_1(a534) | c2_1(a534)) <=> (c0_1(a540) | c2_1(a534) | c3_1(a534) | (~ndr1_0) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2892,plain,
% 2.11/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a534) | c0_1(a534) | c2_1(a534))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a540) | c2_1(a534) | c3_1(a534) | (~ndr1_0) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 2.11/1.69 inference(monotonicity,[status(thm)],[2891])).
% 2.11/1.69 tff(2893,plain,
% 2.11/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a534) | c0_1(a534) | c2_1(a534))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c2_1(a534) | c3_1(a534) | (~ndr1_0) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.11/1.69 inference(transitivity,[status(thm)],[2892, 2890])).
% 2.11/1.69 tff(2894,plain,
% 2.11/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a540) | (~c1_1(a540)) | (~c2_1(a540)) | c3_1(a534) | c0_1(a534) | c2_1(a534))),
% 2.11/1.69 inference(quant_inst,[status(thm)],[])).
% 2.11/1.69 tff(2895,plain,
% 2.11/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a540) | c2_1(a534) | c3_1(a534) | (~ndr1_0) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2894, 2893])).
% 2.11/1.69 tff(2896,plain,
% 2.11/1.69 ($false),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2895, 112, 2774, 2775, 2773, 2880, 2879, 1246, 2777, 2889])).
% 2.11/1.69 tff(2897,plain,(c0_1(a496) | c2_1(a534) | c3_1(a534) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | (~c1_1(a534)) | c2_1(a496) | c3_1(a496) | c1_1(a528) | c3_1(a528) | c0_1(a528)), inference(lemma,lemma(discharge,[]))).
% 2.11/1.69 tff(2898,plain,
% 2.11/1.69 (c0_1(a496)),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2897, 2861, 2867, 2395, 2394, 2393, 2878, 634, 633, 2657, 1082, 2659])).
% 2.11/1.69 tff(2899,assumption,(~hskp9), introduced(assumption)).
% 2.11/1.69 tff(2900,plain,
% 2.11/1.69 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | c0_1(a534))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | c0_1(a534))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2901,plain,
% 2.11/1.69 ((hskp9 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c2_1(a534) | c0_1(a534) | (~c1_1(a534))) <=> (hskp9 | c2_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | c0_1(a534))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2902,plain,
% 2.11/1.69 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c2_1(a534) | c0_1(a534) | (~c1_1(a534)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | c0_1(a534)))),
% 2.11/1.69 inference(monotonicity,[status(thm)],[2901])).
% 2.11/1.69 tff(2903,plain,
% 2.11/1.69 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c2_1(a534) | c0_1(a534) | (~c1_1(a534)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | c0_1(a534))),
% 2.11/1.69 inference(transitivity,[status(thm)],[2902, 2900])).
% 2.11/1.69 tff(2904,plain,
% 2.11/1.69 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)) | c2_1(a534) | c0_1(a534) | (~c1_1(a534)))),
% 2.11/1.69 inference(quant_inst,[status(thm)],[])).
% 2.11/1.69 tff(2905,plain,
% 2.11/1.69 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | c0_1(a534)),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2904, 2903])).
% 2.11/1.69 tff(2906,plain,
% 2.11/1.69 (hskp9 | (~c0_1(a496)) | c0_1(a534)),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2905, 112, 2881, 2880, 632, 634, 2588])).
% 2.11/1.69 tff(2907,plain,
% 2.11/1.69 (c0_1(a534)),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2906, 2899, 2600])).
% 2.11/1.69 tff(2908,plain,
% 2.11/1.69 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c3_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | (~c0_1(a534)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | (~c0_1(a534)))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2909,plain,
% 2.11/1.69 ((hskp9 | (~ndr1_0) | c3_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496))) <=> (hskp9 | c3_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | (~c0_1(a534)))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2910,plain,
% 2.11/1.69 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c3_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | (~c0_1(a534))))),
% 2.11/1.69 inference(monotonicity,[status(thm)],[2909])).
% 2.11/1.69 tff(2911,plain,
% 2.11/1.69 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | (~c0_1(a534)))),
% 2.11/1.69 inference(transitivity,[status(thm)],[2910, 2908])).
% 2.11/1.69 tff(2912,plain,
% 2.11/1.69 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))),
% 2.11/1.69 inference(quant_inst,[status(thm)],[])).
% 2.11/1.69 tff(2913,plain,
% 2.11/1.69 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a534) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a534)) | (~c0_1(a534))),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2912, 2911])).
% 2.11/1.69 tff(2914,plain,
% 2.11/1.69 (hskp9 | (~c0_1(a496)) | (~c0_1(a534))),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2913, 112, 2881, 2879, 632, 634, 1282])).
% 2.11/1.69 tff(2915,plain,
% 2.11/1.69 ($false),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2914, 2907, 2899, 2600])).
% 2.11/1.69 tff(2916,plain,(hskp9 | (~c0_1(a496)) | (~c1_1(a534)) | c3_1(a534) | c1_1(a496) | c2_1(a496) | c2_1(a534)), inference(lemma,lemma(discharge,[]))).
% 2.11/1.69 tff(2917,plain,
% 2.11/1.69 (hskp9),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2916, 2898, 2878, 2867, 632, 634, 2861])).
% 2.11/1.69 tff(2918,plain,
% 2.11/1.69 (~c1_1(a507)),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[924, 2917])).
% 2.11/1.69 tff(2919,plain,
% 2.11/1.69 (~c0_1(a507)),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[930, 2917])).
% 2.11/1.69 tff(2920,plain,
% 2.11/1.69 (c3_1(a507)),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[941, 2917])).
% 2.11/1.69 tff(2921,plain,
% 2.11/1.69 (c2_1(a540)),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2435, 2920, 2775, 2774, 2773, 2919, 2918])).
% 2.11/1.69 tff(2922,plain,
% 2.11/1.69 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a540) | c2_1(a534) | (~ndr1_0) | (~c1_1(a534)) | (~c0_1(a534)) | (~c3_1(a540)) | (~c2_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a540) | c2_1(a534) | (~ndr1_0) | (~c1_1(a534)) | (~c0_1(a534)) | (~c3_1(a540)) | (~c2_1(a540)))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2923,plain,
% 2.11/1.69 ((hskp15 | (~ndr1_0) | c2_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540))) <=> (hskp15 | c0_1(a540) | c2_1(a534) | (~ndr1_0) | (~c1_1(a534)) | (~c0_1(a534)) | (~c3_1(a540)) | (~c2_1(a540)))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2924,plain,
% 2.11/1.69 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a540) | c2_1(a534) | (~ndr1_0) | (~c1_1(a534)) | (~c0_1(a534)) | (~c3_1(a540)) | (~c2_1(a540))))),
% 2.11/1.69 inference(monotonicity,[status(thm)],[2923])).
% 2.11/1.69 tff(2925,plain,
% 2.11/1.69 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a540) | c2_1(a534) | (~ndr1_0) | (~c1_1(a534)) | (~c0_1(a534)) | (~c3_1(a540)) | (~c2_1(a540)))),
% 2.11/1.69 inference(transitivity,[status(thm)],[2924, 2922])).
% 2.11/1.69 tff(2926,plain,
% 2.11/1.69 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a534) | (~c1_1(a534)) | (~c0_1(a534)) | c0_1(a540) | (~c2_1(a540)) | (~c3_1(a540)))),
% 2.11/1.69 inference(quant_inst,[status(thm)],[])).
% 2.11/1.69 tff(2927,plain,
% 2.11/1.69 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a540) | c2_1(a534) | (~ndr1_0) | (~c1_1(a534)) | (~c0_1(a534)) | (~c3_1(a540)) | (~c2_1(a540))),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2926, 2925])).
% 2.11/1.69 tff(2928,plain,
% 2.11/1.69 ((~c0_1(a534)) | (~c2_1(a540))),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2927, 112, 2658, 2775, 2878, 2773, 2861, 2446])).
% 2.11/1.69 tff(2929,plain,
% 2.11/1.69 (~c0_1(a534)),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2928, 2921])).
% 2.11/1.69 tff(2930,plain,
% 2.11/1.69 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2931,plain,
% 2.11/1.69 ((hskp1 | (~ndr1_0) | c3_1(a496) | c1_1(a496) | (~c0_1(a496)) | c1_1(a528) | c0_1(a528) | c3_1(a528)) <=> (hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2932,plain,
% 2.11/1.69 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a496) | c1_1(a496) | (~c0_1(a496)) | c1_1(a528) | c0_1(a528) | c3_1(a528))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496))))),
% 2.11/1.69 inference(monotonicity,[status(thm)],[2931])).
% 2.11/1.69 tff(2933,plain,
% 2.11/1.69 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a496) | c1_1(a496) | (~c0_1(a496)) | c1_1(a528) | c0_1(a528) | c3_1(a528))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)))),
% 2.11/1.69 inference(transitivity,[status(thm)],[2932, 2930])).
% 2.11/1.69 tff(2934,plain,
% 2.11/1.69 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a496) | c1_1(a496) | (~c0_1(a496)) | c1_1(a528) | c0_1(a528) | c3_1(a528))),
% 2.11/1.69 inference(quant_inst,[status(thm)],[])).
% 2.11/1.69 tff(2935,plain,
% 2.11/1.69 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a528) | c1_1(a528) | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496))),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2934, 2933])).
% 2.11/1.69 tff(2936,plain,
% 2.11/1.69 (hskp1 | c1_1(a496) | (~c0_1(a496))),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2935, 112, 2659, 2657, 1082, 633, 645])).
% 2.11/1.69 tff(2937,plain,
% 2.11/1.69 (hskp1),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2936, 2898, 632])).
% 2.11/1.69 tff(2938,plain,
% 2.11/1.69 (~c0_1(a495)),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[1025, 2937])).
% 2.11/1.69 tff(2939,plain,
% 2.11/1.69 (c1_1(a495)),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[1037, 2937])).
% 2.11/1.69 tff(2940,plain,
% 2.11/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a534) | c3_1(a534) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a534) | c3_1(a534) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2941,plain,
% 2.11/1.69 (((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a495) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a534) | c0_1(a534) | c2_1(a534)) <=> (c2_1(a534) | c3_1(a534) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.11/1.69 inference(rewrite,[status(thm)],[])).
% 2.11/1.69 tff(2942,plain,
% 2.11/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a495) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a534) | c0_1(a534) | c2_1(a534))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a534) | c3_1(a534) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 2.11/1.69 inference(monotonicity,[status(thm)],[2941])).
% 2.11/1.69 tff(2943,plain,
% 2.11/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a495) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a534) | c0_1(a534) | c2_1(a534))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a534) | c3_1(a534) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.11/1.69 inference(transitivity,[status(thm)],[2942, 2940])).
% 2.11/1.69 tff(2944,plain,
% 2.11/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a495) | (~c1_1(a495)) | (~c2_1(a495)) | c3_1(a534) | c0_1(a534) | c2_1(a534))),
% 2.11/1.69 inference(quant_inst,[status(thm)],[])).
% 2.11/1.69 tff(2945,plain,
% 2.11/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a534) | c3_1(a534) | c0_1(a495) | (~ndr1_0) | (~c1_1(a495)) | (~c2_1(a495)) | c0_1(a534) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540))),
% 2.11/1.69 inference(modus_ponens,[status(thm)],[2944, 2943])).
% 2.11/1.69 tff(2946,plain,
% 2.11/1.69 (~c2_1(a495)),
% 2.11/1.69 inference(unit_resolution,[status(thm)],[2945, 112, 2774, 2775, 2939, 2861, 2867, 2938, 1246, 2921, 2929])).
% 2.11/1.69 tff(2947,plain,
% 2.11/1.70 (~c3_1(a495)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[1019, 2937])).
% 2.11/1.70 tff(2948,plain,
% 2.11/1.70 ($false),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2523, 112, 2774, 2775, 2773, 2938, 2947, 1246, 2921, 2946])).
% 2.11/1.70 tff(2949,plain,(c1_1(a496) | c2_1(a496) | c0_1(a528) | c1_1(a528) | c3_1(a528) | c3_1(a496) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | hskp27), inference(lemma,lemma(discharge,[]))).
% 2.11/1.70 tff(2950,plain,
% 2.11/1.70 (c1_1(a496)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2949, 2781, 2659, 2657, 1082, 633, 2395, 2394, 2393, 634])).
% 2.11/1.70 tff(2951,plain,
% 2.11/1.70 (~hskp2),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[381, 2950])).
% 2.11/1.70 tff(2952,plain,
% 2.11/1.70 (~c1_1(a509)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2556, 2951])).
% 2.11/1.70 tff(2953,plain,
% 2.11/1.70 (hskp9),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2564, 2952])).
% 2.11/1.70 tff(2954,plain,
% 2.11/1.70 (~c1_1(a507)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[924, 2953])).
% 2.11/1.70 tff(2955,plain,
% 2.11/1.70 (~c0_1(a507)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[930, 2953])).
% 2.11/1.70 tff(2956,plain,
% 2.11/1.70 (c3_1(a507)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[941, 2953])).
% 2.11/1.70 tff(2957,plain,
% 2.11/1.70 (c2_1(a540)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2435, 2956, 2775, 2774, 2773, 2955, 2954])).
% 2.11/1.70 tff(2958,plain,
% 2.11/1.70 (hskp27 | hskp19 | (~c2_1(a540))),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2798, 112, 2774, 2775, 2792])).
% 2.11/1.70 tff(2959,plain,
% 2.11/1.70 (hskp19),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2958, 2957, 2781])).
% 2.11/1.70 tff(2960,plain,
% 2.11/1.70 (c1_1(a534)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2877, 2959])).
% 2.11/1.70 tff(2961,plain,
% 2.11/1.70 (~c0_1(a496)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2611, 2951, 2950])).
% 2.11/1.70 tff(2962,plain,
% 2.11/1.70 (~c2_1(a534)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2860, 2959])).
% 2.11/1.70 tff(2963,plain,
% 2.11/1.70 (~c3_1(a534)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2866, 2959])).
% 2.11/1.70 tff(2964,plain,
% 2.11/1.70 ($false),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2897, 2963, 2962, 2961, 2395, 2394, 2393, 2960, 634, 633, 2657, 1082, 2659])).
% 2.11/1.70 tff(2965,plain,(hskp27 | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | c2_1(a496) | c3_1(a496) | c1_1(a528) | c3_1(a528) | c0_1(a528)), inference(lemma,lemma(discharge,[]))).
% 2.11/1.70 tff(2966,plain,
% 2.11/1.70 (hskp27),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2965, 633, 2394, 2393, 634, 2395, 2657, 1082, 2659])).
% 2.11/1.70 tff(2967,plain,
% 2.11/1.70 (~c1_1(a568)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[251, 2966])).
% 2.11/1.70 tff(2968,plain,
% 2.11/1.70 (c3_1(a568)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[210, 2966])).
% 2.11/1.70 tff(2969,plain,
% 2.11/1.70 (c0_1(a568)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[221, 2966])).
% 2.11/1.70 tff(2970,plain,
% 2.11/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c0_1(a540) | (~c1_1(a496)) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c0_1(a540) | (~c1_1(a496)) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(2971,plain,
% 2.11/1.70 (((~ndr1_0) | c3_1(a496) | (~c1_1(a496)) | (~c0_1(a496)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540))) <=> (c1_1(a568) | c0_1(a540) | (~c1_1(a496)) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(2972,plain,
% 2.11/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a496) | (~c1_1(a496)) | (~c0_1(a496)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a568) | c0_1(a540) | (~c1_1(a496)) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568))))),
% 2.11/1.70 inference(monotonicity,[status(thm)],[2971])).
% 2.11/1.70 tff(2973,plain,
% 2.11/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a496) | (~c1_1(a496)) | (~c0_1(a496)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c0_1(a540) | (~c1_1(a496)) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568)))),
% 2.11/1.70 inference(transitivity,[status(thm)],[2972, 2970])).
% 2.11/1.70 tff(2974,plain,
% 2.11/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a496) | (~c1_1(a496)) | (~c0_1(a496)) | c1_1(a568) | (~c0_1(a568)) | (~c3_1(a568)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))),
% 2.11/1.70 inference(quant_inst,[status(thm)],[])).
% 2.11/1.70 tff(2975,plain,
% 2.11/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a568) | c0_1(a540) | (~c1_1(a496)) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c3_1(a540)) | (~c1_1(a540)) | (~c0_1(a568)) | (~c3_1(a568))),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[2974, 2973])).
% 2.11/1.70 tff(2976,plain,
% 2.11/1.70 ((~c1_1(a496)) | (~c0_1(a496))),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2975, 112, 2969, 2968, 2774, 2775, 2967, 2773, 633, 1398])).
% 2.11/1.70 tff(2977,plain,
% 2.11/1.70 (~c1_1(a496)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2976, 2780])).
% 2.11/1.70 tff(2978,plain,
% 2.11/1.70 (hskp1),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2936, 2977, 2780])).
% 2.11/1.70 tff(2979,plain,
% 2.11/1.70 (~c3_1(a495)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[1019, 2978])).
% 2.11/1.70 tff(2980,plain,
% 2.11/1.70 (~c0_1(a495)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[1025, 2978])).
% 2.11/1.70 tff(2981,plain,
% 2.11/1.70 (c1_1(a495)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[1037, 2978])).
% 2.11/1.70 tff(2982,plain,
% 2.11/1.70 (hskp8),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[1055, 112, 2969, 2968, 2981, 2967, 2980, 2979, 1049])).
% 2.11/1.70 tff(2983,plain,
% 2.11/1.70 (~c0_1(a505)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[1072, 2982])).
% 2.11/1.70 tff(2984,plain,
% 2.11/1.70 (c3_1(a505)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[1161, 2982])).
% 2.11/1.70 tff(2985,plain,
% 2.11/1.70 (c2_1(a505)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[1066, 2982])).
% 2.11/1.70 tff(2986,plain,
% 2.11/1.70 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c1_1(a509)) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c1_1(a509)) | (~c0_1(a509)))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(2987,plain,
% 2.11/1.70 ((hskp15 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505))) <=> (hskp15 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c1_1(a509)) | (~c0_1(a509)))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(2988,plain,
% 2.11/1.70 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c1_1(a509)) | (~c0_1(a509))))),
% 2.11/1.70 inference(monotonicity,[status(thm)],[2987])).
% 2.11/1.70 tff(2989,plain,
% 2.11/1.70 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c1_1(a509)) | (~c0_1(a509)))),
% 2.11/1.70 inference(transitivity,[status(thm)],[2988, 2986])).
% 2.11/1.70 tff(2990,plain,
% 2.11/1.70 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))),
% 2.11/1.70 inference(quant_inst,[status(thm)],[])).
% 2.11/1.70 tff(2991,plain,
% 2.11/1.70 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp15 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | (~c1_1(a509)) | (~c0_1(a509))),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[2990, 2989])).
% 2.11/1.70 tff(2992,plain,
% 2.11/1.70 (~c1_1(a509)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2991, 112, 2658, 2395, 2985, 2984, 2393, 2983, 2446])).
% 2.11/1.70 tff(2993,plain,
% 2.11/1.70 (hskp9),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2564, 2992])).
% 2.11/1.70 tff(2994,plain,
% 2.11/1.70 (~c1_1(a507)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[924, 2993])).
% 2.11/1.70 tff(2995,plain,
% 2.11/1.70 (~c0_1(a507)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[930, 2993])).
% 2.11/1.70 tff(2996,plain,
% 2.11/1.70 (c3_1(a507)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[941, 2993])).
% 2.11/1.70 tff(2997,plain,
% 2.11/1.70 (c2_1(a540)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2435, 2996, 2775, 2774, 2773, 2995, 2994])).
% 2.11/1.70 tff(2998,plain,
% 2.11/1.70 (c2_1(a528)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2702, 112, 2774, 2775, 2659, 2773, 1082, 1246, 2997])).
% 2.11/1.70 tff(2999,plain,
% 2.11/1.70 (c2_1(a495)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2523, 112, 2774, 2775, 2773, 2980, 2979, 1246, 2997])).
% 2.11/1.70 tff(3000,plain,
% 2.11/1.70 (~hskp4),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2728, 2981, 2657, 2659, 1082, 2979, 2999, 2774, 2773, 2997])).
% 2.11/1.70 tff(3001,plain,
% 2.11/1.70 (~hskp13),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2712, 3000, 2659, 2657, 2998])).
% 2.11/1.70 tff(3002,plain,
% 2.11/1.70 (hskp12),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[535, 3001, 2658])).
% 2.11/1.70 tff(3003,plain,
% 2.11/1.70 (c1_1(a514)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[563, 3002])).
% 2.11/1.70 tff(3004,plain,
% 2.11/1.70 (~c2_1(a514)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[541, 3002])).
% 2.11/1.70 tff(3005,plain,
% 2.11/1.70 (c3_1(a514)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[552, 3002])).
% 2.11/1.70 tff(3006,plain,
% 2.11/1.70 (c0_1(a514)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[1203, 3005, 2985, 2984, 2981, 3004, 2983, 2980, 3003])).
% 2.11/1.70 tff(3007,plain,
% 2.11/1.70 ($false),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2537, 112, 2658, 2775, 3003, 2773, 3004, 2446, 3006, 2997])).
% 2.11/1.70 tff(3008,plain,(c3_1(a496) | c0_1(a528) | c1_1(a528) | c3_1(a528) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | c2_1(a496)), inference(lemma,lemma(discharge,[]))).
% 2.11/1.70 tff(3009,plain,
% 2.11/1.70 ($false),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3008, 2733, 2732, 2657, 1082, 2395, 2394, 2393, 2659])).
% 2.11/1.70 tff(3010,plain,(c0_1(a528) | c1_1(a528) | c3_1(a528) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509)), inference(lemma,lemma(discharge,[]))).
% 2.11/1.70 tff(3011,plain,
% 2.11/1.70 (c0_1(a528)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3010, 2657, 1082, 2395, 2394, 2393])).
% 2.11/1.70 tff(3012,plain,
% 2.11/1.70 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | c2_1(a528))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | c2_1(a528))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(3013,plain,
% 2.11/1.70 ((hskp22 | (~ndr1_0) | c3_1(a528) | c2_1(a528) | (~c0_1(a528)) | c1_1(a528) | c3_1(a528) | (~c0_1(a528))) <=> (hskp22 | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | c2_1(a528))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(3014,plain,
% 2.11/1.70 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a528) | c2_1(a528) | (~c0_1(a528)) | c1_1(a528) | c3_1(a528) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | c2_1(a528)))),
% 2.11/1.70 inference(monotonicity,[status(thm)],[3013])).
% 2.11/1.70 tff(3015,plain,
% 2.11/1.70 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a528) | c2_1(a528) | (~c0_1(a528)) | c1_1(a528) | c3_1(a528) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | c2_1(a528))),
% 2.11/1.70 inference(transitivity,[status(thm)],[3014, 3012])).
% 2.11/1.70 tff(3016,plain,
% 2.11/1.70 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a528) | c2_1(a528) | (~c0_1(a528)) | c1_1(a528) | c3_1(a528) | (~c0_1(a528)))),
% 2.11/1.70 inference(quant_inst,[status(thm)],[])).
% 2.11/1.70 tff(3017,plain,
% 2.11/1.70 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a528) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | c2_1(a528)),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3016, 3015])).
% 2.11/1.70 tff(3018,plain,
% 2.11/1.70 (hskp22 | (~c0_1(a528)) | c2_1(a528)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3017, 112, 2657, 1082, 31])).
% 2.11/1.70 tff(3019,plain,
% 2.11/1.70 (c2_1(a528)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3018, 2407, 3011])).
% 2.11/1.70 tff(3020,plain,
% 2.11/1.70 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a528)) | (~c2_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp24 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a528)) | (~c2_1(a528)))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(3021,plain,
% 2.11/1.70 ((hskp24 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c0_1(a509)) | (~c3_1(a509))) <=> (hskp24 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a528)) | (~c2_1(a528)))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(3022,plain,
% 2.11/1.70 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c0_1(a509)) | (~c3_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a528)) | (~c2_1(a528))))),
% 2.11/1.70 inference(monotonicity,[status(thm)],[3021])).
% 2.11/1.70 tff(3023,plain,
% 2.11/1.70 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c0_1(a509)) | (~c3_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp24 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a528)) | (~c2_1(a528)))),
% 2.11/1.70 inference(transitivity,[status(thm)],[3022, 3020])).
% 2.11/1.70 tff(3024,plain,
% 2.11/1.70 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c0_1(a509)) | (~c3_1(a509)))),
% 2.11/1.70 inference(quant_inst,[status(thm)],[])).
% 2.11/1.70 tff(3025,plain,
% 2.11/1.70 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp24 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c0_1(a509)) | (~c0_1(a528)) | (~c2_1(a528))),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3024, 3023])).
% 2.11/1.70 tff(3026,plain,
% 2.11/1.70 (hskp24 | (~c0_1(a528)) | (~c2_1(a528))),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3025, 112, 2395, 2394, 1082, 2393, 1637])).
% 2.11/1.70 tff(3027,plain,
% 2.11/1.70 (hskp24),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3026, 3019, 3011])).
% 2.11/1.70 tff(3028,plain,
% 2.11/1.70 (~c3_1(a554)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[1666, 3027])).
% 2.11/1.70 tff(3029,plain,
% 2.11/1.70 (~c2_1(a554)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[1649, 3027])).
% 2.11/1.70 tff(3030,plain,
% 2.11/1.70 (c0_1(a554)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[1677, 3027])).
% 2.11/1.70 tff(3031,plain,
% 2.11/1.70 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a528) | c2_1(a554) | c3_1(a554) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | (~c0_1(a554)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a528) | c2_1(a554) | c3_1(a554) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | (~c0_1(a554)))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(3032,plain,
% 2.11/1.70 ((hskp22 | (~ndr1_0) | c3_1(a554) | c2_1(a554) | (~c0_1(a554)) | c1_1(a528) | c3_1(a528) | (~c0_1(a528))) <=> (hskp22 | c1_1(a528) | c2_1(a554) | c3_1(a554) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | (~c0_1(a554)))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(3033,plain,
% 2.11/1.70 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a554) | c2_1(a554) | (~c0_1(a554)) | c1_1(a528) | c3_1(a528) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a528) | c2_1(a554) | c3_1(a554) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | (~c0_1(a554))))),
% 2.11/1.70 inference(monotonicity,[status(thm)],[3032])).
% 2.11/1.70 tff(3034,plain,
% 2.11/1.70 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a554) | c2_1(a554) | (~c0_1(a554)) | c1_1(a528) | c3_1(a528) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a528) | c2_1(a554) | c3_1(a554) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | (~c0_1(a554)))),
% 2.11/1.70 inference(transitivity,[status(thm)],[3033, 3031])).
% 2.11/1.70 tff(3035,plain,
% 2.11/1.70 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a554) | c2_1(a554) | (~c0_1(a554)) | c1_1(a528) | c3_1(a528) | (~c0_1(a528)))),
% 2.11/1.70 inference(quant_inst,[status(thm)],[])).
% 2.11/1.70 tff(3036,plain,
% 2.11/1.70 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a528) | c2_1(a554) | c3_1(a554) | c3_1(a528) | (~ndr1_0) | (~c0_1(a528)) | (~c0_1(a554))),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3035, 3034])).
% 2.11/1.70 tff(3037,plain,
% 2.11/1.70 ($false),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3036, 112, 2407, 3030, 3011, 2657, 3029, 3028, 1082, 31])).
% 2.11/1.70 tff(3038,plain,(hskp22 | c1_1(a528) | c3_1(a528) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509)), inference(lemma,lemma(discharge,[]))).
% 2.11/1.70 tff(3039,plain,
% 2.11/1.70 (hskp22),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3038, 2657, 1082, 2646, 2644, 2645])).
% 2.11/1.70 tff(3040,plain,
% 2.11/1.70 (c3_1(a540)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[142, 3039])).
% 2.11/1.70 tff(3041,plain,
% 2.11/1.70 (~c0_1(a540)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[131, 3039])).
% 2.11/1.70 tff(3042,plain,
% 2.11/1.70 (c1_1(a540)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[153, 3039])).
% 2.11/1.70 tff(3043,plain,
% 2.11/1.70 (~hskp9),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2539, 2658, 3040, 3041, 2646, 2644, 3042, 2645])).
% 2.11/1.70 tff(3044,plain,
% 2.11/1.70 (hskp9 | c1_1(a509)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2363, 112, 2646, 2644, 2645, 2357])).
% 2.11/1.70 tff(3045,plain,
% 2.11/1.70 (c1_1(a509)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3044, 3043])).
% 2.11/1.70 tff(3046,plain,
% 2.11/1.70 (hskp2 | (~c1_1(a509))),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2345, 112, 2646, 2644, 2645, 601])).
% 2.11/1.70 tff(3047,plain,
% 2.11/1.70 (hskp2),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3046, 3045])).
% 2.11/1.70 tff(3048,plain,
% 2.11/1.70 (~c2_1(a496)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[368, 3047])).
% 2.11/1.70 tff(3049,plain,
% 2.11/1.70 (~c3_1(a496)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[362, 3047])).
% 2.11/1.70 tff(3050,plain,
% 2.11/1.70 (c1_1(a509)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3044, 2899])).
% 2.11/1.70 tff(3051,plain,
% 2.11/1.70 ((~c1_1(a509)) | (~c2_1(a540))),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2452, 112, 43, 2425, 2646, 2423, 2645, 2446])).
% 2.11/1.70 tff(3052,plain,
% 2.11/1.70 (~c2_1(a540)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3051, 3050])).
% 2.11/1.70 tff(3053,plain,
% 2.11/1.70 (^[U: $i] : refl((hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 2.11/1.70 inference(bind,[status(th)],[])).
% 2.11/1.70 tff(3054,plain,
% 2.11/1.70 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.11/1.70 inference(quant_intro,[status(thm)],[3053])).
% 2.11/1.70 tff(3055,plain,
% 2.11/1.70 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(3056,plain,
% 2.11/1.70 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp25))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp26) <=> ((hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp26))), rewrite(((hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp26) <=> (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp26) <=> (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 2.11/1.70 inference(bind,[status(th)],[])).
% 2.11/1.70 tff(3057,plain,
% 2.11/1.70 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp26) <=> ![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.11/1.70 inference(quant_intro,[status(thm)],[3056])).
% 2.11/1.70 tff(3058,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 2.11/1.70 tff(3059,plain,
% 2.11/1.70 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3058, 3057])).
% 2.11/1.70 tff(3060,plain,
% 2.11/1.70 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3059, 3055])).
% 2.11/1.70 tff(3061,plain,(
% 2.11/1.70 ![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.11/1.70 inference(skolemize,[status(sab)],[3060])).
% 2.11/1.70 tff(3062,plain,
% 2.11/1.70 (![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3061, 3054])).
% 2.11/1.70 tff(3063,plain,
% 2.11/1.70 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp26 | hskp25 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp26 | hskp25 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(3064,plain,
% 2.11/1.70 ((hskp26 | hskp25 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509))) <=> (hskp26 | hskp25 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(3065,plain,
% 2.11/1.70 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp26 | hskp25 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp26 | hskp25 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509))))),
% 2.11/1.70 inference(monotonicity,[status(thm)],[3064])).
% 2.11/1.70 tff(3066,plain,
% 2.11/1.70 (((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp26 | hskp25 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)))) <=> ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp26 | hskp25 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)))),
% 2.11/1.70 inference(transitivity,[status(thm)],[3065, 3063])).
% 2.11/1.70 tff(3067,plain,
% 2.11/1.70 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp26 | hskp25 | (~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)))),
% 2.11/1.70 inference(quant_inst,[status(thm)],[])).
% 2.11/1.70 tff(3068,plain,
% 2.11/1.70 ((~![U: $i] : (hskp26 | hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp26 | hskp25 | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509))),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3067, 3066])).
% 2.11/1.70 tff(3069,plain,
% 2.11/1.70 (hskp25 | (~c1_1(a509))),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3068, 112, 32, 2644, 2645, 3062])).
% 2.11/1.70 tff(3070,plain,
% 2.11/1.70 (hskp25),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3069, 3050])).
% 2.11/1.70 tff(3071,plain,
% 2.11/1.70 (((~hskp25) | (~c0_1(a558))) <=> ((~hskp25) | (~c0_1(a558)))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(3072,plain,
% 2.11/1.70 (((~c0_1(a558)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a558)))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(3073,axiom,((~c0_1(a558)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 2.11/1.70 tff(3074,plain,
% 2.11/1.70 ((~hskp25) | (~c0_1(a558))),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3073, 3072])).
% 2.11/1.70 tff(3075,plain,
% 2.11/1.70 ((~hskp25) | (~c0_1(a558))),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3074, 3071])).
% 2.11/1.70 tff(3076,plain,
% 2.11/1.70 (~c0_1(a558)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3075, 3070])).
% 2.11/1.70 tff(3077,plain,
% 2.11/1.70 (((~hskp25) | c2_1(a558)) <=> ((~hskp25) | c2_1(a558))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(3078,axiom,((~hskp25) | c2_1(a558)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 2.11/1.70 tff(3079,plain,
% 2.11/1.70 ((~hskp25) | c2_1(a558)),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3078, 3077])).
% 2.11/1.70 tff(3080,plain,
% 2.11/1.70 ((~hskp25) | c2_1(a558)),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3079, 3077])).
% 2.11/1.70 tff(3081,plain,
% 2.11/1.70 ((~hskp25) | c2_1(a558)),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3080, 3077])).
% 2.11/1.70 tff(3082,plain,
% 2.11/1.70 ((~hskp25) | c2_1(a558)),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3081, 3077])).
% 2.11/1.70 tff(3083,plain,
% 2.11/1.70 ((~hskp25) | c2_1(a558)),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3082, 3077])).
% 2.11/1.70 tff(3084,plain,
% 2.11/1.70 ((~hskp25) | c2_1(a558)),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3083, 3077])).
% 2.11/1.70 tff(3085,plain,
% 2.11/1.70 ((~hskp25) | c2_1(a558)),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3084, 3077])).
% 2.11/1.70 tff(3086,plain,
% 2.11/1.70 ((~hskp25) | c2_1(a558)),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3085, 3077])).
% 2.11/1.70 tff(3087,plain,
% 2.11/1.70 (c2_1(a558)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3086, 3070])).
% 2.11/1.70 tff(3088,plain,
% 2.11/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a558) | c0_1(a540) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | (~c1_1(a558)) | (~c2_1(a558)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a558) | c0_1(a540) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | (~c1_1(a558)) | (~c2_1(a558)))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(3089,plain,
% 2.11/1.70 (((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a558) | (~c1_1(a558)) | (~c2_1(a558)) | c0_1(a540) | c2_1(a540) | (~c1_1(a540))) <=> (c0_1(a558) | c0_1(a540) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | (~c1_1(a558)) | (~c2_1(a558)))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(3090,plain,
% 2.11/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a558) | (~c1_1(a558)) | (~c2_1(a558)) | c0_1(a540) | c2_1(a540) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a558) | c0_1(a540) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | (~c1_1(a558)) | (~c2_1(a558))))),
% 2.11/1.70 inference(monotonicity,[status(thm)],[3089])).
% 2.11/1.70 tff(3091,plain,
% 2.11/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a558) | (~c1_1(a558)) | (~c2_1(a558)) | c0_1(a540) | c2_1(a540) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a558) | c0_1(a540) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | (~c1_1(a558)) | (~c2_1(a558)))),
% 2.11/1.70 inference(transitivity,[status(thm)],[3090, 3088])).
% 2.11/1.70 tff(3092,plain,
% 2.11/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a540) | (~c3_1(a540)) | (~c1_1(a540)) | c0_1(a558) | (~c1_1(a558)) | (~c2_1(a558)) | c0_1(a540) | c2_1(a540) | (~c1_1(a540)))),
% 2.11/1.70 inference(quant_inst,[status(thm)],[])).
% 2.11/1.70 tff(3093,plain,
% 2.11/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a558) | c0_1(a540) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a540) | (~c1_1(a558)) | (~c2_1(a558))),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3092, 3091])).
% 2.11/1.70 tff(3094,plain,
% 2.11/1.70 (~c1_1(a558)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3093, 112, 3087, 2420, 2425, 3076, 2423, 1175, 3052])).
% 2.11/1.70 tff(3095,plain,
% 2.11/1.70 (hskp2),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3046, 3050])).
% 2.11/1.70 tff(3096,plain,
% 2.11/1.70 (~c1_1(a496)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[381, 3095])).
% 2.11/1.70 tff(3097,plain,
% 2.11/1.70 (~c0_1(a496)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2596, 112, 2899, 2420, 2423, 3096, 634, 2588, 3052])).
% 2.11/1.70 tff(3098,plain,
% 2.11/1.70 (hskp6 | c3_1(a496) | c0_1(a496) | (~c1_1(a509))),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[2553, 112, 2646, 2645, 634, 966])).
% 2.11/1.70 tff(3099,plain,
% 2.11/1.70 (hskp6),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3098, 3097, 633, 3050])).
% 2.11/1.70 tff(3100,plain,
% 2.11/1.70 (~c3_1(a501)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[651, 3099])).
% 2.11/1.70 tff(3101,plain,
% 2.11/1.70 (((~hskp25) | (~c3_1(a558))) <=> ((~hskp25) | (~c3_1(a558)))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(3102,plain,
% 2.11/1.70 (((~c3_1(a558)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a558)))),
% 2.11/1.70 inference(rewrite,[status(thm)],[])).
% 2.11/1.70 tff(3103,axiom,((~c3_1(a558)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 2.11/1.70 tff(3104,plain,
% 2.11/1.70 ((~hskp25) | (~c3_1(a558))),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3103, 3102])).
% 2.11/1.70 tff(3105,plain,
% 2.11/1.70 ((~hskp25) | (~c3_1(a558))),
% 2.11/1.70 inference(modus_ponens,[status(thm)],[3104, 3101])).
% 2.11/1.70 tff(3106,plain,
% 2.11/1.70 (~c3_1(a558)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[3105, 3070])).
% 2.11/1.70 tff(3107,plain,
% 2.11/1.70 (c2_1(a501)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[662, 3099])).
% 2.11/1.70 tff(3108,plain,
% 2.11/1.70 (c1_1(a501)),
% 2.11/1.70 inference(unit_resolution,[status(thm)],[673, 3099])).
% 2.11/1.70 tff(3109,plain,
% 2.11/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a558) | c3_1(a558) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)) | c1_1(a558))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a558) | c3_1(a558) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)) | c1_1(a558))),
% 2.11/1.71 inference(rewrite,[status(thm)],[])).
% 2.11/1.71 tff(3110,plain,
% 2.11/1.71 (((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a558) | c1_1(a558) | c0_1(a558)) <=> (c0_1(a558) | c3_1(a558) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)) | c1_1(a558))),
% 2.11/1.71 inference(rewrite,[status(thm)],[])).
% 2.11/1.71 tff(3111,plain,
% 2.11/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a558) | c1_1(a558) | c0_1(a558))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a558) | c3_1(a558) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)) | c1_1(a558)))),
% 2.11/1.71 inference(monotonicity,[status(thm)],[3110])).
% 2.11/1.71 tff(3112,plain,
% 2.11/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a558) | c1_1(a558) | c0_1(a558))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a558) | c3_1(a558) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)) | c1_1(a558))),
% 2.11/1.71 inference(transitivity,[status(thm)],[3111, 3109])).
% 2.11/1.71 tff(3113,plain,
% 2.11/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a558) | c1_1(a558) | c0_1(a558))),
% 2.11/1.71 inference(quant_inst,[status(thm)],[])).
% 2.11/1.71 tff(3114,plain,
% 2.11/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a558) | c3_1(a558) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)) | c1_1(a558)),
% 2.11/1.71 inference(modus_ponens,[status(thm)],[3113, 3112])).
% 2.11/1.71 tff(3115,plain,
% 2.11/1.71 ($false),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3114, 112, 3108, 3107, 3076, 3106, 3100, 634, 633, 784, 3097, 3094])).
% 2.11/1.71 tff(3116,plain,(hskp9 | c2_1(a496) | c3_1(a496) | (~c1_1(a540)) | c0_1(a540) | (~c3_1(a540)) | hskp15 | hskp26), inference(lemma,lemma(discharge,[]))).
% 2.11/1.71 tff(3117,plain,
% 2.11/1.71 ($false),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3116, 3049, 3048, 3043, 3042, 3041, 3040, 2658, 32])).
% 2.11/1.71 tff(3118,plain,(c1_1(a528) | hskp26 | c3_1(a528)), inference(lemma,lemma(discharge,[]))).
% 2.11/1.71 tff(3119,plain,
% 2.11/1.71 (c1_1(a528)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3118, 1082, 32])).
% 2.11/1.71 tff(3120,assumption,(~c1_1(a540)), introduced(assumption)).
% 2.11/1.71 tff(3121,assumption,(~c3_1(a540)), introduced(assumption)).
% 2.11/1.71 tff(3122,plain,
% 2.11/1.71 (~hskp22),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[153, 3120])).
% 2.11/1.71 tff(3123,plain,
% 2.11/1.71 (~c0_1(a496)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[2613, 3122, 2644, 2645, 634, 633, 2646])).
% 2.11/1.71 tff(3124,plain,
% 2.11/1.71 (hskp6),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3098, 2547, 633, 3123])).
% 2.11/1.71 tff(3125,plain,
% 2.11/1.71 (~c3_1(a501)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[651, 3124])).
% 2.11/1.71 tff(3126,plain,
% 2.11/1.71 (hskp25),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3069, 2547])).
% 2.11/1.71 tff(3127,plain,
% 2.11/1.71 (~c3_1(a558)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3105, 3126])).
% 2.11/1.71 tff(3128,plain,
% 2.11/1.71 (~c0_1(a558)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3075, 3126])).
% 2.11/1.71 tff(3129,plain,
% 2.11/1.71 (c2_1(a501)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[662, 3124])).
% 2.11/1.71 tff(3130,plain,
% 2.11/1.71 (c1_1(a501)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[673, 3124])).
% 2.11/1.71 tff(3131,plain,
% 2.11/1.71 (c1_1(a558)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3114, 112, 3130, 3129, 3128, 3127, 3125, 634, 633, 784, 3123])).
% 2.11/1.71 tff(3132,plain,
% 2.11/1.71 (c2_1(a558)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3086, 3126])).
% 2.11/1.71 tff(3133,plain,
% 2.11/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a540) | c3_1(a540) | c3_1(a558) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a558)) | (~c2_1(a558)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a540) | c3_1(a540) | c3_1(a558) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a558)) | (~c2_1(a558)))),
% 2.11/1.71 inference(rewrite,[status(thm)],[])).
% 2.11/1.71 tff(3134,plain,
% 2.11/1.71 (((~ndr1_0) | c3_1(a558) | (~c2_1(a558)) | (~c1_1(a558)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540)) <=> (c1_1(a540) | c3_1(a540) | c3_1(a558) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a558)) | (~c2_1(a558)))),
% 2.11/1.71 inference(rewrite,[status(thm)],[])).
% 2.11/1.71 tff(3135,plain,
% 2.11/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a558) | (~c2_1(a558)) | (~c1_1(a558)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a540) | c3_1(a540) | c3_1(a558) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a558)) | (~c2_1(a558))))),
% 2.11/1.71 inference(monotonicity,[status(thm)],[3134])).
% 2.11/1.71 tff(3136,plain,
% 2.11/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a558) | (~c2_1(a558)) | (~c1_1(a558)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a540) | c3_1(a540) | c3_1(a558) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a558)) | (~c2_1(a558)))),
% 2.11/1.71 inference(transitivity,[status(thm)],[3135, 3133])).
% 2.11/1.71 tff(3137,plain,
% 2.11/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a558) | (~c2_1(a558)) | (~c1_1(a558)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540))),
% 2.11/1.71 inference(quant_inst,[status(thm)],[])).
% 2.11/1.71 tff(3138,plain,
% 2.11/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a540) | c3_1(a540) | c3_1(a558) | c0_1(a540) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a558)) | (~c2_1(a558))),
% 2.11/1.71 inference(modus_ponens,[status(thm)],[3137, 3136])).
% 2.11/1.71 tff(3139,plain,
% 2.11/1.71 ($false),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3138, 112, 3132, 3120, 3121, 3127, 2423, 634, 633, 784, 3123, 3131])).
% 2.11/1.71 tff(3140,plain,((~c1_1(a509)) | c1_1(a540) | c3_1(a540) | c0_1(a540) | c2_1(a496) | c3_1(a496) | hskp26), inference(lemma,lemma(discharge,[]))).
% 2.11/1.71 tff(3141,plain,
% 2.11/1.71 (~c1_1(a509)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3140, 3121, 3120, 2423, 634, 633, 32])).
% 2.11/1.71 tff(3142,plain,
% 2.11/1.71 (hskp9),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3044, 3141])).
% 2.11/1.71 tff(3143,plain,
% 2.11/1.71 (~c1_1(a507)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[924, 3142])).
% 2.11/1.71 tff(3144,plain,
% 2.11/1.71 (~c0_1(a507)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[930, 3142])).
% 2.11/1.71 tff(3145,plain,
% 2.11/1.71 (c3_1(a507)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[941, 3142])).
% 2.11/1.71 tff(3146,plain,
% 2.11/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528)))),
% 2.11/1.71 inference(rewrite,[status(thm)],[])).
% 2.11/1.71 tff(3147,plain,
% 2.11/1.71 (((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540)) <=> (c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528)))),
% 2.11/1.71 inference(rewrite,[status(thm)],[])).
% 2.11/1.71 tff(3148,plain,
% 2.11/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528))))),
% 2.11/1.71 inference(monotonicity,[status(thm)],[3147])).
% 2.11/1.71 tff(3149,plain,
% 2.11/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528)))),
% 2.11/1.71 inference(transitivity,[status(thm)],[3148, 3146])).
% 2.11/1.71 tff(3150,plain,
% 2.11/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540))),
% 2.11/1.71 inference(quant_inst,[status(thm)],[])).
% 2.11/1.71 tff(3151,plain,
% 2.11/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528))),
% 2.11/1.71 inference(modus_ponens,[status(thm)],[3150, 3149])).
% 2.11/1.71 tff(3152,plain,
% 2.11/1.71 (~c2_1(a528)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3151, 112, 3120, 3121, 3119, 2423, 1082, 634, 633, 784, 3123])).
% 2.11/1.71 tff(3153,plain,
% 2.11/1.71 (~c0_1(a528)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[1003, 112, 3119, 1082, 634, 633, 996, 3123, 3152])).
% 2.11/1.71 tff(3154,plain,
% 2.11/1.71 (~hskp15),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[491, 3153])).
% 2.11/1.71 tff(3155,plain,
% 2.11/1.71 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c1_1(a540) | c3_1(a540) | c0_1(a540) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c1_1(a540) | c3_1(a540) | c0_1(a540) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 2.11/1.71 inference(rewrite,[status(thm)],[])).
% 2.11/1.71 tff(3156,plain,
% 2.11/1.71 ((hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a540) | c0_1(a540) | c3_1(a540)) <=> (hskp2 | c1_1(a540) | c3_1(a540) | c0_1(a540) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 2.11/1.71 inference(rewrite,[status(thm)],[])).
% 2.11/1.71 tff(3157,plain,
% 2.11/1.71 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a540) | c0_1(a540) | c3_1(a540))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c1_1(a540) | c3_1(a540) | c0_1(a540) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520))))),
% 2.11/1.71 inference(monotonicity,[status(thm)],[3156])).
% 2.11/1.71 tff(3158,plain,
% 2.11/1.71 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a540) | c0_1(a540) | c3_1(a540))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c1_1(a540) | c3_1(a540) | c0_1(a540) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520)))),
% 2.11/1.71 inference(transitivity,[status(thm)],[3157, 3155])).
% 2.11/1.71 tff(3159,plain,
% 2.11/1.71 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a520)) | (~c1_1(a520)) | (~c0_1(a520)) | c1_1(a540) | c0_1(a540) | c3_1(a540))),
% 2.11/1.71 inference(quant_inst,[status(thm)],[])).
% 2.11/1.71 tff(3160,plain,
% 2.11/1.71 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c1_1(a540) | c3_1(a540) | c0_1(a540) | (~ndr1_0) | (~c1_1(a520)) | (~c0_1(a520)) | (~c2_1(a520))),
% 2.11/1.71 inference(modus_ponens,[status(thm)],[3159, 3158])).
% 2.11/1.71 tff(3161,plain,
% 2.11/1.71 (~c1_1(a520)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3160, 112, 453, 3120, 3121, 2459, 2467, 2423, 320])).
% 2.11/1.71 tff(3162,plain,
% 2.11/1.71 (~c2_1(a554)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[1649, 2497])).
% 2.11/1.71 tff(3163,plain,
% 2.11/1.71 ($false),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[2413, 112, 3122, 2499, 2459, 3162, 2498, 2458, 31, 3161])).
% 2.11/1.71 tff(3164,plain,((~hskp13) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | hskp2 | c1_1(a540) | c3_1(a540) | c0_1(a540)), inference(lemma,lemma(discharge,[]))).
% 2.11/1.71 tff(3165,plain,
% 2.11/1.71 (~hskp13),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3164, 453, 2394, 2393, 3120, 3121, 2395, 2423])).
% 2.11/1.71 tff(3166,plain,
% 2.11/1.71 ($false),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[535, 3165, 2382, 43])).
% 2.11/1.71 tff(3167,plain,(hskp2 | hskp15 | (~c3_1(a509)) | c2_1(a509) | c1_1(a540) | c3_1(a540) | (~c0_1(a509)) | c0_1(a540) | (~c3_1(a507)) | c0_1(a507) | c1_1(a507)), inference(lemma,lemma(discharge,[]))).
% 2.11/1.71 tff(3168,plain,
% 2.11/1.71 (hskp2),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3167, 3154, 2644, 2645, 3120, 3121, 2646, 2423, 3145, 3144, 3143])).
% 2.11/1.71 tff(3169,plain,
% 2.11/1.71 (~c1_1(a496)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[381, 3168])).
% 2.11/1.71 tff(3170,plain,
% 2.11/1.71 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a528) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a528) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)))),
% 2.11/1.71 inference(rewrite,[status(thm)],[])).
% 2.11/1.71 tff(3171,plain,
% 2.11/1.71 ((hskp8 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c0_1(a528) | c3_1(a528) | (~c1_1(a528))) <=> (hskp8 | c0_1(a528) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)))),
% 2.11/1.71 inference(rewrite,[status(thm)],[])).
% 2.11/1.71 tff(3172,plain,
% 2.11/1.71 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c0_1(a528) | c3_1(a528) | (~c1_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a528) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528))))),
% 2.11/1.71 inference(monotonicity,[status(thm)],[3171])).
% 2.11/1.71 tff(3173,plain,
% 2.11/1.71 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c0_1(a528) | c3_1(a528) | (~c1_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a528) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)))),
% 2.11/1.71 inference(transitivity,[status(thm)],[3172, 3170])).
% 2.11/1.71 tff(3174,plain,
% 2.11/1.71 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c0_1(a528) | c3_1(a528) | (~c1_1(a528)))),
% 2.11/1.71 inference(quant_inst,[status(thm)],[])).
% 2.11/1.71 tff(3175,plain,
% 2.11/1.71 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a528) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528))),
% 2.11/1.71 inference(modus_ponens,[status(thm)],[3174, 3173])).
% 2.11/1.71 tff(3176,plain,
% 2.11/1.71 (hskp8),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3175, 112, 3153, 3119, 2646, 2644, 1082, 1049, 3141])).
% 2.11/1.71 tff(3177,plain,
% 2.11/1.71 (~c0_1(a505)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[1072, 3176])).
% 2.11/1.71 tff(3178,plain,
% 2.11/1.71 (c3_1(a505)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[1161, 3176])).
% 2.11/1.71 tff(3179,plain,
% 2.11/1.71 (c2_1(a505)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[1066, 3176])).
% 2.11/1.71 tff(3180,plain,
% 2.11/1.71 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | c1_1(a509) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | c1_1(a509) | (~c0_1(a509)))),
% 2.11/1.71 inference(rewrite,[status(thm)],[])).
% 2.11/1.71 tff(3181,plain,
% 2.11/1.71 ((hskp14 | (~ndr1_0) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505))) <=> (hskp14 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | c1_1(a509) | (~c0_1(a509)))),
% 2.11/1.71 inference(rewrite,[status(thm)],[])).
% 2.11/1.71 tff(3182,plain,
% 2.11/1.71 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | c1_1(a509) | (~c0_1(a509))))),
% 2.11/1.71 inference(monotonicity,[status(thm)],[3181])).
% 2.11/1.71 tff(3183,plain,
% 2.11/1.71 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | c1_1(a509) | (~c0_1(a509)))),
% 2.11/1.71 inference(transitivity,[status(thm)],[3182, 3180])).
% 2.11/1.71 tff(3184,plain,
% 2.11/1.71 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)) | c0_1(a505) | (~c2_1(a505)) | (~c3_1(a505)))),
% 2.11/1.71 inference(quant_inst,[status(thm)],[])).
% 2.11/1.71 tff(3185,plain,
% 2.11/1.71 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a509) | c0_1(a505) | (~ndr1_0) | (~c3_1(a505)) | (~c2_1(a505)) | c1_1(a509) | (~c0_1(a509))),
% 2.11/1.71 inference(modus_ponens,[status(thm)],[3184, 3183])).
% 2.11/1.71 tff(3186,plain,
% 2.11/1.71 (hskp14),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3185, 112, 2646, 3179, 3178, 2645, 3177, 1313, 3141])).
% 2.11/1.71 tff(3187,plain,
% 2.11/1.71 (~c3_1(a527)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[829, 3186])).
% 2.11/1.71 tff(3188,plain,
% 2.11/1.71 (~c1_1(a527)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[835, 3186])).
% 2.11/1.71 tff(3189,plain,
% 2.11/1.71 (c2_1(a527)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[864, 3186])).
% 2.11/1.71 tff(3190,plain,
% 2.11/1.71 (hskp0 | c1_1(a496)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[871, 112, 3189, 3188, 3187, 634, 854, 3123])).
% 2.11/1.71 tff(3191,plain,
% 2.11/1.71 (hskp0),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3190, 3169])).
% 2.11/1.71 tff(3192,plain,
% 2.11/1.71 (~c2_1(a494)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[1702, 3191])).
% 2.11/1.71 tff(3193,plain,
% 2.11/1.71 (~c0_1(a494)),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[878, 3191])).
% 2.11/1.71 tff(3194,plain,
% 2.11/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))),
% 2.11/1.71 inference(rewrite,[status(thm)],[])).
% 2.11/1.71 tff(3195,plain,
% 2.11/1.71 (((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540)) <=> (c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))),
% 2.11/1.71 inference(rewrite,[status(thm)],[])).
% 2.11/1.71 tff(3196,plain,
% 2.11/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501))))),
% 2.11/1.71 inference(monotonicity,[status(thm)],[3195])).
% 2.11/1.71 tff(3197,plain,
% 2.11/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501)))),
% 2.11/1.71 inference(transitivity,[status(thm)],[3196, 3194])).
% 2.11/1.71 tff(3198,plain,
% 2.11/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a501) | (~c2_1(a501)) | (~c1_1(a501)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a540) | c1_1(a540) | c0_1(a540))),
% 2.11/1.71 inference(quant_inst,[status(thm)],[])).
% 2.11/1.71 tff(3199,plain,
% 2.11/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a540) | c3_1(a540) | c0_1(a540) | c3_1(a501) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a501)) | (~c2_1(a501))),
% 2.11/1.71 inference(modus_ponens,[status(thm)],[3198, 3197])).
% 2.11/1.71 tff(3200,plain,
% 2.11/1.71 ($false),
% 2.11/1.71 inference(unit_resolution,[status(thm)],[3199, 112, 3120, 3121, 674, 663, 2423, 652, 634, 633, 784, 635])).
% 2.11/1.71 tff(3201,plain,((~hskp6) | c1_1(a540) | c3_1(a540) | c0_1(a540) | c2_1(a496) | c3_1(a496) | c0_1(a496)), inference(lemma,lemma(discharge,[]))).
% 2.11/1.71 tff(3202,plain,
% 2.11/1.72 (~hskp6),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[3201, 3121, 3120, 2423, 634, 633, 3123])).
% 2.11/1.72 tff(3203,plain,
% 2.11/1.72 (~hskp12),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[975, 3202, 634, 633, 3123, 3144, 3145, 3143])).
% 2.11/1.72 tff(3204,plain,
% 2.11/1.72 (hskp13),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[535, 3203, 3154])).
% 2.11/1.72 tff(3205,plain,
% 2.11/1.72 (~c3_1(a520)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[1458, 3204])).
% 2.11/1.72 tff(3206,plain,
% 2.11/1.72 (c3_1(a494)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[893, 3191])).
% 2.11/1.72 tff(3207,plain,
% 2.11/1.72 (c0_1(a520)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[1480, 3204])).
% 2.11/1.72 tff(3208,plain,
% 2.11/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a528) | c3_1(a528) | c3_1(a520) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c1_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a528) | c3_1(a528) | c3_1(a520) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c1_1(a528)))),
% 2.11/1.72 inference(rewrite,[status(thm)],[])).
% 2.11/1.72 tff(3209,plain,
% 2.11/1.72 (((~ndr1_0) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)) | c0_1(a528) | c3_1(a528) | (~c1_1(a528)) | c0_1(a494) | (~c3_1(a494)) | c2_1(a494)) <=> (c0_1(a528) | c3_1(a528) | c3_1(a520) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c1_1(a528)))),
% 2.11/1.72 inference(rewrite,[status(thm)],[])).
% 2.11/1.72 tff(3210,plain,
% 2.11/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)) | c0_1(a528) | c3_1(a528) | (~c1_1(a528)) | c0_1(a494) | (~c3_1(a494)) | c2_1(a494))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | (c0_1(a528) | c3_1(a528) | c3_1(a520) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c1_1(a528))))),
% 2.11/1.72 inference(monotonicity,[status(thm)],[3209])).
% 2.11/1.72 tff(3211,plain,
% 2.11/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)) | c0_1(a528) | c3_1(a528) | (~c1_1(a528)) | c0_1(a494) | (~c3_1(a494)) | c2_1(a494))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a528) | c3_1(a528) | c3_1(a520) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c1_1(a528)))),
% 2.11/1.72 inference(transitivity,[status(thm)],[3210, 3208])).
% 2.11/1.72 tff(3212,plain,
% 2.11/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | ((~ndr1_0) | c3_1(a520) | (~c1_1(a520)) | (~c0_1(a520)) | c0_1(a528) | c3_1(a528) | (~c1_1(a528)) | c0_1(a494) | (~c3_1(a494)) | c2_1(a494))),
% 2.11/1.72 inference(quant_inst,[status(thm)],[])).
% 2.11/1.72 tff(3213,plain,
% 2.11/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)) | c2_1(W))) | c0_1(a528) | c3_1(a528) | c3_1(a520) | c0_1(a494) | c2_1(a494) | (~ndr1_0) | (~c3_1(a494)) | (~c1_1(a520)) | (~c0_1(a520)) | (~c1_1(a528))),
% 2.11/1.72 inference(modus_ponens,[status(thm)],[3212, 3211])).
% 2.11/1.72 tff(3214,plain,
% 2.11/1.72 (~c1_1(a520)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[3213, 112, 3153, 3119, 3207, 3206, 1082, 3205, 3193, 3192, 21])).
% 2.11/1.72 tff(3215,plain,
% 2.11/1.72 (c2_1(a520)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[1469, 3204])).
% 2.11/1.72 tff(3216,plain,
% 2.11/1.72 (hskp24),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[2402, 112, 3207, 3215, 2646, 2644, 3205, 2645, 1637])).
% 2.11/1.72 tff(3217,plain,
% 2.11/1.72 (~c3_1(a554)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[1666, 3216])).
% 2.11/1.72 tff(3218,plain,
% 2.11/1.72 (~c2_1(a554)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[1649, 3216])).
% 2.11/1.72 tff(3219,plain,
% 2.11/1.72 (c0_1(a554)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[1677, 3216])).
% 2.11/1.72 tff(3220,plain,
% 2.11/1.72 ($false),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[2413, 112, 3122, 3219, 3207, 3218, 3217, 3205, 31, 3214])).
% 2.11/1.72 tff(3221,plain,(c3_1(a540) | c3_1(a528) | c2_1(a496) | c3_1(a496) | c1_1(a540) | c0_1(a540) | hskp26), inference(lemma,lemma(discharge,[]))).
% 2.11/1.72 tff(3222,plain,
% 2.11/1.72 (c3_1(a540)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[3221, 3120, 634, 633, 1082, 2423, 32])).
% 2.11/1.72 tff(3223,plain,
% 2.11/1.72 (~c0_1(a496)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[2613, 3122, 2394, 2393, 634, 633, 2395])).
% 2.11/1.72 tff(3224,plain,
% 2.11/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a540) | c0_1(a540) | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a509)) | (~c1_1(a509)) | (~c3_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a540) | c0_1(a540) | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a509)) | (~c1_1(a509)) | (~c3_1(a540)))),
% 2.11/1.72 inference(rewrite,[status(thm)],[])).
% 2.11/1.72 tff(3225,plain,
% 2.11/1.72 (((~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)) | c2_1(a496) | c0_1(a496) | (~c1_1(a496)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540))) <=> (c1_1(a540) | c0_1(a540) | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a509)) | (~c1_1(a509)) | (~c3_1(a540)))),
% 2.11/1.72 inference(rewrite,[status(thm)],[])).
% 2.11/1.72 tff(3226,plain,
% 2.11/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)) | c2_1(a496) | c0_1(a496) | (~c1_1(a496)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a540) | c0_1(a540) | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a509)) | (~c1_1(a509)) | (~c3_1(a540))))),
% 2.11/1.72 inference(monotonicity,[status(thm)],[3225])).
% 2.11/1.72 tff(3227,plain,
% 2.11/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)) | c2_1(a496) | c0_1(a496) | (~c1_1(a496)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a540) | c0_1(a540) | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a509)) | (~c1_1(a509)) | (~c3_1(a540)))),
% 2.11/1.72 inference(transitivity,[status(thm)],[3226, 3224])).
% 2.11/1.72 tff(3228,plain,
% 2.11/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)) | c2_1(a496) | c0_1(a496) | (~c1_1(a496)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540)))),
% 2.11/1.72 inference(quant_inst,[status(thm)],[])).
% 2.11/1.72 tff(3229,plain,
% 2.11/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a540) | c0_1(a540) | c2_1(a509) | (~c1_1(a496)) | c2_1(a496) | (~ndr1_0) | c0_1(a496) | (~c3_1(a509)) | (~c1_1(a509)) | (~c3_1(a540))),
% 2.11/1.72 inference(modus_ponens,[status(thm)],[3228, 3227])).
% 2.11/1.72 tff(3230,plain,
% 2.11/1.72 ((~c1_1(a496)) | (~c1_1(a509)) | (~c3_1(a540))),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[3229, 112, 3120, 2394, 2423, 2393, 634, 618, 3223])).
% 2.11/1.72 tff(3231,plain,
% 2.11/1.72 (~c1_1(a496)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[3230, 2547, 2425])).
% 2.11/1.72 tff(3232,plain,
% 2.11/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a528) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a528) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528)))),
% 2.11/1.72 inference(rewrite,[status(thm)],[])).
% 2.11/1.72 tff(3233,plain,
% 2.11/1.72 (((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496)) <=> (c3_1(a528) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528)))),
% 2.11/1.72 inference(rewrite,[status(thm)],[])).
% 2.11/1.72 tff(3234,plain,
% 2.11/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a528) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528))))),
% 2.11/1.72 inference(monotonicity,[status(thm)],[3233])).
% 2.11/1.72 tff(3235,plain,
% 2.11/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a528) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528)))),
% 2.11/1.72 inference(transitivity,[status(thm)],[3234, 3232])).
% 2.11/1.72 tff(3236,plain,
% 2.11/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a496) | c0_1(a496) | c3_1(a496) | c3_1(a496) | c1_1(a496) | c0_1(a496))),
% 2.11/1.72 inference(quant_inst,[status(thm)],[])).
% 2.11/1.72 tff(3237,plain,
% 2.11/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | c3_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a528) | c1_1(a496) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c2_1(a528))),
% 2.11/1.72 inference(modus_ponens,[status(thm)],[3236, 3235])).
% 2.11/1.72 tff(3238,plain,
% 2.11/1.72 (c1_1(a496) | c0_1(a496) | (~c2_1(a528))),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[3237, 112, 1091, 1082, 634, 633, 784])).
% 2.11/1.72 tff(3239,plain,
% 2.11/1.72 (~c2_1(a528)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[3238, 3231, 3223])).
% 2.11/1.72 tff(3240,plain,
% 2.11/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 2.11/1.72 inference(rewrite,[status(thm)],[])).
% 2.11/1.72 tff(3241,plain,
% 2.11/1.72 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c3_1(a496) | c0_1(a496) | c2_1(a496)) <=> (c3_1(a528) | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 2.11/1.72 inference(rewrite,[status(thm)],[])).
% 2.11/1.72 tff(3242,plain,
% 2.11/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a528) | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528))))),
% 2.11/1.72 inference(monotonicity,[status(thm)],[3241])).
% 2.11/1.72 tff(3243,plain,
% 2.11/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 2.11/1.72 inference(transitivity,[status(thm)],[3242, 3240])).
% 2.11/1.72 tff(3244,plain,
% 2.11/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c3_1(a496) | c0_1(a496) | c2_1(a496))),
% 2.11/1.72 inference(quant_inst,[status(thm)],[])).
% 2.11/1.72 tff(3245,plain,
% 2.11/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a528) | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528))),
% 2.11/1.72 inference(modus_ponens,[status(thm)],[3244, 3243])).
% 2.11/1.72 tff(3246,plain,
% 2.11/1.72 (c0_1(a496) | (~c1_1(a509)) | (~c0_1(a528))),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[3245, 112, 1091, 2395, 1082, 2393, 634, 633, 996])).
% 2.11/1.72 tff(3247,plain,
% 2.11/1.72 (~c0_1(a528)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[3246, 2547, 3223])).
% 2.11/1.72 tff(3248,plain,
% 2.11/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a540) | c0_1(a528) | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c1_1(a528)) | c2_1(a528) | (~c3_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a540) | c0_1(a528) | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c1_1(a528)) | c2_1(a528) | (~c3_1(a540)))),
% 2.11/1.72 inference(rewrite,[status(thm)],[])).
% 2.11/1.72 tff(3249,plain,
% 2.11/1.72 (((~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)) | c2_1(a528) | c0_1(a528) | (~c1_1(a528)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540))) <=> (c1_1(a540) | c0_1(a528) | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c1_1(a528)) | c2_1(a528) | (~c3_1(a540)))),
% 2.11/1.72 inference(rewrite,[status(thm)],[])).
% 2.11/1.72 tff(3250,plain,
% 2.11/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)) | c2_1(a528) | c0_1(a528) | (~c1_1(a528)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a540) | c0_1(a528) | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c1_1(a528)) | c2_1(a528) | (~c3_1(a540))))),
% 2.11/1.72 inference(monotonicity,[status(thm)],[3249])).
% 2.11/1.72 tff(3251,plain,
% 2.11/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)) | c2_1(a528) | c0_1(a528) | (~c1_1(a528)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a540) | c0_1(a528) | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c1_1(a528)) | c2_1(a528) | (~c3_1(a540)))),
% 2.11/1.72 inference(transitivity,[status(thm)],[3250, 3248])).
% 2.11/1.72 tff(3252,plain,
% 2.11/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a509) | (~c3_1(a509)) | (~c1_1(a509)) | c2_1(a528) | c0_1(a528) | (~c1_1(a528)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540)))),
% 2.11/1.72 inference(quant_inst,[status(thm)],[])).
% 2.11/1.72 tff(3253,plain,
% 2.11/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a540) | c0_1(a528) | c0_1(a540) | c2_1(a509) | (~ndr1_0) | (~c3_1(a509)) | (~c1_1(a509)) | (~c1_1(a528)) | c2_1(a528) | (~c3_1(a540))),
% 2.11/1.72 inference(modus_ponens,[status(thm)],[3252, 3251])).
% 2.11/1.72 tff(3254,plain,
% 2.11/1.72 ($false),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[3253, 112, 3120, 2425, 3247, 1091, 2394, 2423, 2393, 618, 2547, 3239])).
% 2.11/1.72 tff(3255,plain,((~c1_1(a509)) | c1_1(a540) | (~c3_1(a540)) | (~c1_1(a528)) | (~c3_1(a509)) | c0_1(a540) | c2_1(a509) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~c0_1(a509))), inference(lemma,lemma(discharge,[]))).
% 2.11/1.72 tff(3256,plain,
% 2.11/1.72 (~c1_1(a509)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[3255, 3120, 3222, 3119, 2644, 2423, 2645, 1082, 634, 633, 2646])).
% 2.11/1.72 tff(3257,plain,
% 2.11/1.72 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a540) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a540) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)))),
% 2.11/1.72 inference(rewrite,[status(thm)],[])).
% 2.11/1.72 tff(3258,plain,
% 2.11/1.72 ((hskp28 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540))) <=> (hskp28 | c1_1(a540) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)))),
% 2.11/1.72 inference(rewrite,[status(thm)],[])).
% 2.11/1.72 tff(3259,plain,
% 2.11/1.72 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a540) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540))))),
% 2.11/1.72 inference(monotonicity,[status(thm)],[3258])).
% 2.11/1.72 tff(3260,plain,
% 2.11/1.72 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a540) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540)))),
% 2.11/1.72 inference(transitivity,[status(thm)],[3259, 3257])).
% 2.11/1.72 tff(3261,plain,
% 2.11/1.72 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a509) | (~c3_1(a509)) | (~c0_1(a509)) | c1_1(a540) | c0_1(a540) | (~c3_1(a540)))),
% 2.11/1.72 inference(quant_inst,[status(thm)],[])).
% 2.11/1.72 tff(3262,plain,
% 2.11/1.72 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a540) | c0_1(a540) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a540))),
% 2.11/1.72 inference(modus_ponens,[status(thm)],[3261, 3260])).
% 2.11/1.72 tff(3263,plain,
% 2.11/1.72 (hskp28),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[3262, 112, 3120, 3222, 2646, 2644, 2423, 262, 3256])).
% 2.11/1.72 tff(3264,plain,
% 2.11/1.72 (c3_1(a500)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[429, 3263])).
% 2.11/1.72 tff(3265,plain,
% 2.11/1.72 (c2_1(a500)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[440, 3263])).
% 2.11/1.72 tff(3266,plain,
% 2.11/1.72 (c0_1(a500)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[451, 3263])).
% 2.11/1.72 tff(3267,plain,
% 2.11/1.72 (hskp9),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[2564, 2456])).
% 2.11/1.72 tff(3268,plain,
% 2.11/1.72 (~c1_1(a507)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[924, 3267])).
% 2.11/1.72 tff(3269,plain,
% 2.11/1.72 (~c0_1(a507)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[930, 3267])).
% 2.11/1.72 tff(3270,plain,
% 2.11/1.72 (c3_1(a507)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[941, 3267])).
% 2.11/1.72 tff(3271,plain,
% 2.11/1.72 (~hskp15),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[491, 2659])).
% 2.11/1.72 tff(3272,plain,
% 2.11/1.72 (hskp2),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[2415, 3271, 2395, 2394, 2393, 495, 494, 493, 2407, 3270, 3269, 3268])).
% 2.11/1.72 tff(3273,plain,
% 2.11/1.72 (~c1_1(a496)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[381, 3272])).
% 2.11/1.72 tff(3274,plain,
% 2.11/1.72 (hskp8),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[3175, 112, 2659, 1091, 2395, 2394, 1082, 1049, 2456])).
% 2.11/1.72 tff(3275,plain,
% 2.11/1.72 (~c0_1(a505)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[1072, 3274])).
% 2.11/1.72 tff(3276,plain,
% 2.11/1.72 (c3_1(a505)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[1161, 3274])).
% 2.11/1.72 tff(3277,plain,
% 2.11/1.72 (c2_1(a505)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[1066, 3274])).
% 2.11/1.72 tff(3278,plain,
% 2.11/1.72 (hskp14),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[3185, 112, 2395, 3277, 3276, 2393, 3275, 1313, 2456])).
% 2.11/1.72 tff(3279,plain,
% 2.11/1.72 (~c3_1(a527)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[829, 3278])).
% 2.11/1.72 tff(3280,plain,
% 2.11/1.72 (~c1_1(a527)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[835, 3278])).
% 2.11/1.72 tff(3281,plain,
% 2.11/1.72 (c2_1(a527)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[864, 3278])).
% 2.11/1.72 tff(3282,plain,
% 2.11/1.72 (hskp0 | c1_1(a496)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[871, 112, 3281, 3280, 3279, 634, 854, 2747])).
% 2.11/1.72 tff(3283,plain,
% 2.11/1.72 (hskp0),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[3282, 3273])).
% 2.11/1.72 tff(3284,plain,
% 2.11/1.72 (~c2_1(a494)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[1702, 3283])).
% 2.11/1.72 tff(3285,plain,
% 2.11/1.72 (~c0_1(a494)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[878, 3283])).
% 2.11/1.72 tff(3286,plain,
% 2.11/1.72 (~hskp6),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[2560, 3273, 634, 633, 2747])).
% 2.11/1.72 tff(3287,plain,
% 2.11/1.72 (~hskp12),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[975, 3286, 634, 633, 2747, 3269, 3270, 3268])).
% 2.11/1.72 tff(3288,plain,
% 2.11/1.72 (hskp13),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[535, 3287, 3271])).
% 2.11/1.72 tff(3289,plain,
% 2.11/1.72 (~c3_1(a520)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[1458, 3288])).
% 2.11/1.72 tff(3290,plain,
% 2.11/1.72 (c3_1(a494)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[893, 3283])).
% 2.11/1.72 tff(3291,plain,
% 2.11/1.72 (c0_1(a520)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[1480, 3288])).
% 2.11/1.72 tff(3292,plain,
% 2.11/1.72 (~c1_1(a520)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[3213, 112, 2659, 1091, 3291, 3290, 1082, 3289, 3285, 3284, 21])).
% 2.11/1.72 tff(3293,plain,
% 2.11/1.72 (c2_1(a520)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[1469, 3288])).
% 2.11/1.72 tff(3294,plain,
% 2.11/1.72 (hskp24),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[2402, 112, 3291, 3293, 2395, 2394, 3289, 2393, 1637])).
% 2.11/1.72 tff(3295,plain,
% 2.11/1.72 (~c3_1(a554)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[1666, 3294])).
% 2.11/1.72 tff(3296,plain,
% 2.11/1.72 (~c2_1(a554)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[1649, 3294])).
% 2.11/1.72 tff(3297,plain,
% 2.11/1.72 (c0_1(a554)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[1677, 3294])).
% 2.11/1.72 tff(3298,plain,
% 2.11/1.72 ($false),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[2413, 112, 2407, 3297, 3291, 3296, 3295, 3289, 31, 3292])).
% 2.11/1.72 tff(3299,plain,(c0_1(a528) | hskp22 | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | (~c1_1(a528)) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~c0_1(a500)) | (~c2_1(a500)) | (~c3_1(a500)) | c1_1(a509)), inference(lemma,lemma(discharge,[]))).
% 2.11/1.72 tff(3300,plain,
% 2.11/1.72 (c0_1(a528)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[3299, 3122, 2646, 2644, 2645, 3119, 1082, 634, 633, 3266, 3265, 3264, 3256])).
% 2.11/1.72 tff(3301,assumption,(hskp21), introduced(assumption)).
% 2.11/1.72 tff(3302,plain,
% 2.11/1.72 (~c3_1(a538)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[2070, 3301])).
% 2.11/1.72 tff(3303,plain,
% 2.11/1.72 (~c1_1(a538)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[2076, 3301])).
% 2.11/1.72 tff(3304,plain,
% 2.11/1.72 (c0_1(a538)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[2087, 3301])).
% 2.11/1.72 tff(3305,plain,
% 2.11/1.72 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a538) | c3_1(a538) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a538)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a538) | c3_1(a538) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a538)))),
% 2.11/1.72 inference(rewrite,[status(thm)],[])).
% 2.11/1.72 tff(3306,plain,
% 2.11/1.72 ((hskp22 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | (~c0_1(a496)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538))) <=> (hskp22 | c1_1(a538) | c3_1(a538) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a538)))),
% 2.11/1.72 inference(rewrite,[status(thm)],[])).
% 2.11/1.72 tff(3307,plain,
% 2.11/1.72 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | (~c0_1(a496)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a538) | c3_1(a538) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a538))))),
% 2.11/1.72 inference(monotonicity,[status(thm)],[3306])).
% 2.11/1.72 tff(3308,plain,
% 2.11/1.72 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | (~c0_1(a496)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a538) | c3_1(a538) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a538)))),
% 2.11/1.72 inference(transitivity,[status(thm)],[3307, 3305])).
% 2.11/1.72 tff(3309,plain,
% 2.11/1.72 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a496) | c2_1(a496) | (~c0_1(a496)) | c1_1(a538) | c3_1(a538) | (~c0_1(a538)))),
% 2.11/1.72 inference(quant_inst,[status(thm)],[])).
% 2.11/1.72 tff(3310,plain,
% 2.11/1.72 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a538) | c3_1(a538) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c0_1(a538))),
% 2.11/1.72 inference(modus_ponens,[status(thm)],[3309, 3308])).
% 2.11/1.72 tff(3311,plain,
% 2.11/1.72 (~c0_1(a496)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[3310, 112, 2407, 3304, 3303, 3302, 634, 633, 31])).
% 2.11/1.72 tff(3312,plain,
% 2.11/1.72 (hskp23),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[2094, 112, 3304, 1092, 1091, 3303, 3302, 1082, 2010])).
% 2.11/1.72 tff(3313,plain,
% 2.11/1.72 (~c2_1(a541)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[2100, 3312])).
% 2.11/1.72 tff(3314,plain,
% 2.11/1.72 (c1_1(a541)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[2111, 3312])).
% 2.11/1.72 tff(3315,plain,
% 2.11/1.72 (c0_1(a541)),
% 2.11/1.72 inference(unit_resolution,[status(thm)],[2122, 3312])).
% 2.11/1.72 tff(3316,plain,
% 2.11/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a541) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a541) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 2.11/1.72 inference(rewrite,[status(thm)],[])).
% 2.11/1.72 tff(3317,plain,
% 2.11/1.72 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c3_1(a496) | c0_1(a496) | c2_1(a496)) <=> (c2_1(a541) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 2.11/1.73 inference(rewrite,[status(thm)],[])).
% 2.11/1.73 tff(3318,plain,
% 2.11/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a541) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541))))),
% 2.11/1.73 inference(monotonicity,[status(thm)],[3317])).
% 2.11/1.73 tff(3319,plain,
% 2.11/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c3_1(a496) | c0_1(a496) | c2_1(a496))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a541) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 2.11/1.73 inference(transitivity,[status(thm)],[3318, 3316])).
% 2.11/1.73 tff(3320,plain,
% 2.11/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)) | c3_1(a496) | c0_1(a496) | c2_1(a496))),
% 2.11/1.73 inference(quant_inst,[status(thm)],[])).
% 2.11/1.73 tff(3321,plain,
% 2.11/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a541) | c3_1(a528) | c2_1(a496) | c3_1(a496) | (~ndr1_0) | c0_1(a496) | (~c1_1(a528)) | (~c0_1(a528)) | (~c1_1(a541)) | (~c0_1(a541))),
% 2.11/1.73 inference(modus_ponens,[status(thm)],[3320, 3319])).
% 2.11/1.73 tff(3322,plain,
% 2.11/1.73 ($false),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3321, 112, 3315, 3314, 1092, 1091, 3313, 1082, 634, 633, 996, 3311])).
% 2.11/1.73 tff(3323,plain,((~hskp21) | (~c0_1(a528)) | (~c1_1(a528)) | c3_1(a528) | c2_1(a496) | c3_1(a496) | hskp22), inference(lemma,lemma(discharge,[]))).
% 2.11/1.73 tff(3324,plain,
% 2.11/1.73 (~hskp21),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3323, 3300, 3119, 1082, 634, 633, 3122])).
% 2.11/1.73 tff(3325,plain,
% 2.11/1.73 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c2_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c2_1(a528)))),
% 2.11/1.73 inference(rewrite,[status(thm)],[])).
% 2.11/1.73 tff(3326,plain,
% 2.11/1.73 ((hskp21 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509))) <=> (hskp21 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c2_1(a528)))),
% 2.11/1.73 inference(rewrite,[status(thm)],[])).
% 2.11/1.73 tff(3327,plain,
% 2.11/1.73 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c2_1(a528))))),
% 2.11/1.73 inference(monotonicity,[status(thm)],[3326])).
% 2.11/1.73 tff(3328,plain,
% 2.11/1.73 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c2_1(a528)))),
% 2.11/1.73 inference(transitivity,[status(thm)],[3327, 3325])).
% 2.11/1.73 tff(3329,plain,
% 2.11/1.73 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a528) | (~c2_1(a528)) | (~c1_1(a528)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)))),
% 2.11/1.73 inference(quant_inst,[status(thm)],[])).
% 2.11/1.73 tff(3330,plain,
% 2.11/1.73 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a528) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c2_1(a528))),
% 2.11/1.73 inference(modus_ponens,[status(thm)],[3329, 3328])).
% 2.11/1.73 tff(3331,plain,
% 2.11/1.73 (hskp21 | c1_1(a509) | (~c1_1(a528)) | (~c2_1(a528))),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3330, 112, 2646, 1082, 2645, 2279])).
% 2.11/1.73 tff(3332,plain,
% 2.11/1.73 (~c2_1(a528)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3331, 3324, 3119, 3256])).
% 2.11/1.73 tff(3333,plain,
% 2.11/1.73 ($false),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[1003, 112, 3300, 3119, 1082, 634, 633, 996, 3123, 3332])).
% 2.11/1.73 tff(3334,plain,(c1_1(a540) | c3_1(a528) | c2_1(a496) | c3_1(a496) | c0_1(a540) | hskp26), inference(lemma,lemma(discharge,[]))).
% 2.11/1.73 tff(3335,plain,
% 2.11/1.73 (c1_1(a540)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3334, 2423, 634, 633, 1082, 32])).
% 2.11/1.73 tff(3336,plain,
% 2.11/1.73 (~hskp22),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[142, 3121])).
% 2.11/1.73 tff(3337,plain,
% 2.11/1.73 (~c0_1(a496)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[2613, 3336, 2394, 2393, 634, 633, 2395])).
% 2.11/1.73 tff(3338,plain,
% 2.11/1.73 (~c1_1(a509)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[2562, 3337, 633, 634, 2395, 2393, 2394])).
% 2.11/1.73 tff(3339,plain,
% 2.11/1.73 (hskp28),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[2374, 112, 2395, 2394, 3270, 3269, 3268, 262, 2456])).
% 2.11/1.73 tff(3340,plain,
% 2.11/1.73 (c3_1(a500)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[429, 3339])).
% 2.11/1.73 tff(3341,plain,
% 2.11/1.73 (c0_1(a500)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[451, 3339])).
% 2.11/1.73 tff(3342,plain,
% 2.11/1.73 (c2_1(a500)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[440, 3339])).
% 2.11/1.73 tff(3343,plain,
% 2.11/1.73 ($false),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3299, 3342, 3341, 2395, 2394, 2393, 1091, 1082, 634, 633, 2407, 2659, 3340, 2456])).
% 2.11/1.73 tff(3344,plain,(c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c2_1(a509) | (~c1_1(a528)) | c3_1(a528) | c2_1(a496) | c3_1(a496) | hskp22 | c0_1(a528)), inference(lemma,lemma(discharge,[]))).
% 2.11/1.73 tff(3345,plain,
% 2.11/1.73 (c0_1(a528)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3344, 3338, 2394, 2393, 1091, 1082, 634, 633, 3336, 2395])).
% 2.11/1.73 tff(3346,plain,
% 2.11/1.73 (~hskp21),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3323, 3345, 1091, 1082, 634, 633, 3336])).
% 2.11/1.73 tff(3347,plain,
% 2.11/1.73 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c3_1(a540) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a540)) | (~c2_1(a540)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a540) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.11/1.73 inference(rewrite,[status(thm)],[])).
% 2.11/1.73 tff(3348,plain,
% 2.11/1.73 ((hskp21 | (~ndr1_0) | c3_1(a540) | (~c2_1(a540)) | (~c1_1(a540)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509))) <=> (hskp21 | c3_1(a540) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.11/1.73 inference(rewrite,[status(thm)],[])).
% 2.11/1.73 tff(3349,plain,
% 2.11/1.73 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a540) | (~c2_1(a540)) | (~c1_1(a540)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c3_1(a540) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a540)) | (~c2_1(a540))))),
% 2.11/1.73 inference(monotonicity,[status(thm)],[3348])).
% 2.11/1.73 tff(3350,plain,
% 2.11/1.73 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a540) | (~c2_1(a540)) | (~c1_1(a540)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a540) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a540)) | (~c2_1(a540)))),
% 2.11/1.73 inference(transitivity,[status(thm)],[3349, 3347])).
% 2.11/1.73 tff(3351,plain,
% 2.11/1.73 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a540) | (~c2_1(a540)) | (~c1_1(a540)) | c2_1(a509) | c1_1(a509) | (~c0_1(a509)))),
% 2.11/1.73 inference(quant_inst,[status(thm)],[])).
% 2.11/1.73 tff(3352,plain,
% 2.11/1.73 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a540) | c2_1(a509) | (~ndr1_0) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a540)) | (~c2_1(a540))),
% 2.11/1.73 inference(modus_ponens,[status(thm)],[3351, 3350])).
% 2.11/1.73 tff(3353,plain,
% 2.11/1.73 (hskp21 | c1_1(a509) | (~c2_1(a540))),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3352, 112, 2420, 3121, 2395, 2393, 2279])).
% 2.11/1.73 tff(3354,plain,
% 2.11/1.73 (~c2_1(a540)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3353, 3346, 3338])).
% 2.11/1.73 tff(3355,plain,
% 2.11/1.73 (hskp21 | c1_1(a509) | (~c1_1(a528)) | (~c2_1(a528))),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3330, 112, 2395, 1082, 2393, 2279])).
% 2.11/1.73 tff(3356,plain,
% 2.11/1.73 (~c2_1(a528)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3355, 3346, 1091, 3338])).
% 2.11/1.73 tff(3357,plain,
% 2.11/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a540) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c2_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a540) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c2_1(a540))),
% 2.11/1.73 inference(rewrite,[status(thm)],[])).
% 2.11/1.73 tff(3358,plain,
% 2.11/1.73 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a540) | c0_1(a540) | c2_1(a540)) <=> (c3_1(a540) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c2_1(a540))),
% 2.11/1.73 inference(rewrite,[status(thm)],[])).
% 2.11/1.73 tff(3359,plain,
% 2.11/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a540) | c0_1(a540) | c2_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a540) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c2_1(a540)))),
% 2.11/1.73 inference(monotonicity,[status(thm)],[3358])).
% 2.11/1.73 tff(3360,plain,
% 2.11/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a540) | c0_1(a540) | c2_1(a540))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a540) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c2_1(a540))),
% 2.11/1.73 inference(transitivity,[status(thm)],[3359, 3357])).
% 2.11/1.73 tff(3361,plain,
% 2.11/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c3_1(a540) | c0_1(a540) | c2_1(a540))),
% 2.11/1.73 inference(quant_inst,[status(thm)],[])).
% 2.11/1.73 tff(3362,plain,
% 2.11/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a540) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a528) | c2_1(a540)),
% 2.11/1.73 inference(modus_ponens,[status(thm)],[3361, 3360])).
% 2.11/1.73 tff(3363,plain,
% 2.11/1.73 ($false),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3362, 112, 3121, 3345, 1091, 2423, 1082, 996, 3356, 3354])).
% 2.11/1.73 tff(3364,plain,(c3_1(a540) | (~c1_1(a528)) | c0_1(a540) | c3_1(a528) | (~c1_1(a540)) | (~c0_1(a509)) | c2_1(a509) | c2_1(a496) | c3_1(a496) | (~c3_1(a509))), inference(lemma,lemma(discharge,[]))).
% 2.11/1.73 tff(3365,plain,
% 2.11/1.73 (c3_1(a540)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3364, 2423, 3119, 1082, 3335, 2646, 2645, 634, 633, 2644])).
% 2.11/1.73 tff(3366,plain,
% 2.11/1.73 (c0_1(a496)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[2577, 3335, 3365, 2423, 634, 633, 2646, 2644, 2645])).
% 2.11/1.73 tff(3367,plain,
% 2.11/1.73 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 2.11/1.73 inference(bind,[status(th)],[])).
% 2.11/1.73 tff(3368,plain,
% 2.11/1.73 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.11/1.73 inference(quant_intro,[status(thm)],[3367])).
% 2.11/1.73 tff(3369,plain,
% 2.11/1.73 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.11/1.73 inference(rewrite,[status(thm)],[])).
% 2.11/1.73 tff(3370,plain,
% 2.11/1.73 (^[V: $i, U: $i] : 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)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | 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(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | 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(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp3) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp3))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 2.11/1.73 inference(bind,[status(th)],[])).
% 2.11/1.73 tff(3371,plain,
% 2.11/1.73 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.11/1.73 inference(quant_intro,[status(thm)],[3370])).
% 2.11/1.73 tff(3372,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 2.11/1.73 tff(3373,plain,
% 2.11/1.73 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.11/1.73 inference(modus_ponens,[status(thm)],[3372, 3371])).
% 2.11/1.73 tff(3374,plain,
% 2.11/1.73 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.11/1.73 inference(modus_ponens,[status(thm)],[3373, 3369])).
% 2.11/1.73 tff(3375,plain,(
% 2.11/1.73 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.11/1.73 inference(skolemize,[status(sab)],[3374])).
% 2.11/1.73 tff(3376,plain,
% 2.11/1.73 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.11/1.73 inference(modus_ponens,[status(thm)],[3375, 3368])).
% 2.11/1.73 tff(3377,plain,
% 2.11/1.73 (hskp15),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[2539, 3267, 2420, 2423, 2395, 2394, 2425, 2393])).
% 2.11/1.73 tff(3378,plain,
% 2.11/1.73 (c0_1(a528)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[491, 3377])).
% 2.11/1.73 tff(3379,plain,
% 2.11/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 2.11/1.73 inference(rewrite,[status(thm)],[])).
% 2.11/1.73 tff(3380,plain,
% 2.11/1.73 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540))) <=> (c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 2.11/1.73 inference(rewrite,[status(thm)],[])).
% 2.11/1.73 tff(3381,plain,
% 2.11/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540))))),
% 2.11/1.73 inference(monotonicity,[status(thm)],[3380])).
% 2.11/1.73 tff(3382,plain,
% 2.11/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 2.11/1.73 inference(transitivity,[status(thm)],[3381, 3379])).
% 2.11/1.73 tff(3383,plain,
% 2.11/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a509) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))),
% 2.11/1.73 inference(quant_inst,[status(thm)],[])).
% 2.11/1.73 tff(3384,plain,
% 2.11/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a540) | c3_1(a528) | (~ndr1_0) | (~c3_1(a509)) | c1_1(a509) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540))),
% 2.11/1.73 inference(modus_ponens,[status(thm)],[3383, 3382])).
% 2.11/1.73 tff(3385,plain,
% 2.11/1.73 ($false),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3384, 112, 2420, 2425, 3378, 1091, 2395, 2394, 2423, 1082, 1398, 2456])).
% 2.11/1.73 tff(3386,plain,(c1_1(a509) | (~c1_1(a540)) | (~c3_1(a540)) | (~c1_1(a528)) | (~c0_1(a509)) | (~c3_1(a509)) | c0_1(a540) | c3_1(a528) | c2_1(a509)), inference(lemma,lemma(discharge,[]))).
% 2.11/1.73 tff(3387,plain,
% 2.11/1.73 (c1_1(a509)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3386, 3335, 3365, 3119, 2646, 2644, 2423, 1082, 2645])).
% 2.11/1.73 tff(3388,plain,
% 2.11/1.73 (hskp2),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3046, 3387])).
% 2.11/1.73 tff(3389,plain,
% 2.11/1.73 (~c1_1(a496)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[381, 3388])).
% 2.11/1.73 tff(3390,plain,
% 2.11/1.73 (~hskp9),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[2539, 43, 2420, 2423, 2646, 2644, 2425, 2645])).
% 2.11/1.73 tff(3391,plain,
% 2.11/1.73 ($false),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3116, 3390, 43, 634, 633, 2423, 2420, 2425, 32])).
% 2.11/1.73 tff(3392,plain,(hskp15 | c2_1(a496) | c3_1(a496) | c0_1(a540) | (~c1_1(a540)) | (~c3_1(a540)) | hskp26), inference(lemma,lemma(discharge,[]))).
% 2.11/1.73 tff(3393,plain,
% 2.11/1.73 (hskp15),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3392, 2423, 633, 634, 3335, 3365, 32])).
% 2.11/1.73 tff(3394,plain,
% 2.11/1.73 (c0_1(a528)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[491, 3393])).
% 2.11/1.73 tff(3395,plain,
% 2.11/1.73 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c3_1(a528) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a528) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 2.11/1.73 inference(rewrite,[status(thm)],[])).
% 2.11/1.73 tff(3396,plain,
% 2.11/1.73 ((hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496))) <=> (hskp9 | c3_1(a528) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 2.11/1.73 inference(rewrite,[status(thm)],[])).
% 2.11/1.73 tff(3397,plain,
% 2.11/1.73 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c3_1(a528) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528))))),
% 2.11/1.73 inference(monotonicity,[status(thm)],[3396])).
% 2.11/1.73 tff(3398,plain,
% 2.11/1.73 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a528) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 2.11/1.73 inference(transitivity,[status(thm)],[3397, 3395])).
% 2.11/1.73 tff(3399,plain,
% 2.11/1.73 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))),
% 2.11/1.73 inference(quant_inst,[status(thm)],[])).
% 2.11/1.73 tff(3400,plain,
% 2.11/1.73 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a528) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528))),
% 2.11/1.73 inference(modus_ponens,[status(thm)],[3399, 3398])).
% 2.11/1.73 tff(3401,plain,
% 2.11/1.73 (hskp9 | c1_1(a496) | (~c0_1(a496)) | (~c0_1(a528))),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3400, 112, 3119, 1082, 634, 1282])).
% 2.11/1.73 tff(3402,plain,
% 2.11/1.73 (hskp9),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[3401, 3394, 3389, 3366])).
% 2.11/1.73 tff(3403,plain,
% 2.11/1.73 (c3_1(a507)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[941, 3402])).
% 2.11/1.73 tff(3404,plain,
% 2.11/1.73 (~c0_1(a507)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[930, 3402])).
% 2.11/1.73 tff(3405,plain,
% 2.11/1.73 (~c1_1(a507)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[924, 3402])).
% 2.11/1.73 tff(3406,plain,
% 2.11/1.73 (c2_1(a540)),
% 2.11/1.73 inference(unit_resolution,[status(thm)],[2435, 3405, 3335, 3365, 2423, 3404, 3403])).
% 2.11/1.73 tff(3407,plain,
% 2.11/1.73 (^[V: $i, U: $i] : refl((hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 2.11/1.73 inference(bind,[status(th)],[])).
% 2.11/1.73 tff(3408,plain,
% 2.11/1.73 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.11/1.73 inference(quant_intro,[status(thm)],[3407])).
% 2.11/1.73 tff(3409,plain,
% 2.11/1.73 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.11/1.73 inference(rewrite,[status(thm)],[])).
% 2.11/1.73 tff(3410,plain,
% 2.11/1.73 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp31) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp31))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp31) <=> (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp31) <=> (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 2.11/1.73 inference(bind,[status(th)],[])).
% 2.11/1.73 tff(3411,plain,
% 2.11/1.73 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp31) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.11/1.73 inference(quant_intro,[status(thm)],[3410])).
% 2.11/1.73 tff(3412,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 2.11/1.73 tff(3413,plain,
% 2.11/1.73 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.11/1.73 inference(modus_ponens,[status(thm)],[3412, 3411])).
% 2.11/1.73 tff(3414,plain,
% 2.11/1.73 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.11/1.73 inference(modus_ponens,[status(thm)],[3413, 3409])).
% 2.11/1.73 tff(3415,plain,(
% 2.11/1.73 ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.11/1.73 inference(skolemize,[status(sab)],[3414])).
% 2.11/1.73 tff(3416,plain,
% 2.11/1.73 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.11/1.73 inference(modus_ponens,[status(thm)],[3415, 3408])).
% 2.11/1.73 tff(3417,plain,
% 2.11/1.73 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 2.11/1.73 inference(rewrite,[status(thm)],[])).
% 2.11/1.73 tff(3418,plain,
% 2.11/1.73 ((hskp23 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a496) | c3_1(a496) | (~c0_1(a496))) <=> (hskp23 | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 2.11/1.73 inference(rewrite,[status(thm)],[])).
% 2.11/1.73 tff(3419,plain,
% 2.11/1.73 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a496) | c3_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528))))),
% 2.11/1.73 inference(monotonicity,[status(thm)],[3418])).
% 2.11/1.73 tff(3420,plain,
% 2.11/1.73 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a496) | c3_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 2.11/1.73 inference(transitivity,[status(thm)],[3419, 3417])).
% 2.11/1.73 tff(3421,plain,
% 2.11/1.73 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a496) | c3_1(a496) | (~c0_1(a496)))),
% 2.11/1.74 inference(quant_inst,[status(thm)],[])).
% 2.11/1.74 tff(3422,plain,
% 2.11/1.74 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp23 | c3_1(a528) | c1_1(a496) | c3_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c1_1(a528)) | (~c0_1(a528))),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3421, 3420])).
% 2.11/1.74 tff(3423,plain,
% 2.11/1.74 (hskp23 | (~c0_1(a528))),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[3422, 112, 3119, 1082, 3389, 633, 2010, 3366])).
% 2.11/1.74 tff(3424,plain,
% 2.11/1.74 (hskp23),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[3423, 3394])).
% 2.11/1.74 tff(3425,plain,
% 2.11/1.74 (~c2_1(a541)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[2100, 3424])).
% 2.11/1.74 tff(3426,plain,
% 2.11/1.74 (c1_1(a541)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[2111, 3424])).
% 2.11/1.74 tff(3427,plain,
% 2.11/1.74 (c0_1(a541)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[2122, 3424])).
% 2.11/1.74 tff(3428,plain,
% 2.11/1.74 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp31 | c2_1(a541) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp31 | c2_1(a541) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3429,plain,
% 2.11/1.74 ((hskp31 | (~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541))) <=> (hskp31 | c2_1(a541) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3430,plain,
% 2.11/1.74 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp31 | c2_1(a541) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c1_1(a541)) | (~c0_1(a541))))),
% 2.11/1.74 inference(monotonicity,[status(thm)],[3429])).
% 2.11/1.74 tff(3431,plain,
% 2.11/1.74 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp31 | c2_1(a541) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c1_1(a541)) | (~c0_1(a541)))),
% 2.11/1.74 inference(transitivity,[status(thm)],[3430, 3428])).
% 2.11/1.74 tff(3432,plain,
% 2.11/1.74 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp31 | (~ndr1_0) | (~c2_1(a540)) | (~c3_1(a540)) | (~c1_1(a540)) | c2_1(a541) | (~c1_1(a541)) | (~c0_1(a541)))),
% 2.11/1.74 inference(quant_inst,[status(thm)],[])).
% 2.11/1.74 tff(3433,plain,
% 2.11/1.74 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp31 | c2_1(a541) | (~ndr1_0) | (~c3_1(a540)) | (~c1_1(a540)) | (~c2_1(a540)) | (~c1_1(a541)) | (~c0_1(a541))),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3432, 3431])).
% 2.11/1.74 tff(3434,plain,
% 2.11/1.74 (hskp31),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[3433, 112, 3427, 3426, 3335, 3365, 3425, 3416, 3406])).
% 2.11/1.74 tff(3435,plain,
% 2.11/1.74 (c2_1(a522)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[739, 3434])).
% 2.11/1.74 tff(3436,plain,
% 2.11/1.74 (c1_1(a522)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[750, 3434])).
% 2.11/1.74 tff(3437,plain,
% 2.11/1.74 (c0_1(a522)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[761, 3434])).
% 2.11/1.74 tff(3438,plain,
% 2.11/1.74 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3439,plain,
% 2.11/1.74 ((hskp3 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496))) <=> (hskp3 | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3440,plain,
% 2.11/1.74 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522))))),
% 2.11/1.74 inference(monotonicity,[status(thm)],[3439])).
% 2.11/1.74 tff(3441,plain,
% 2.11/1.74 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)))),
% 2.11/1.74 inference(transitivity,[status(thm)],[3440, 3438])).
% 2.11/1.74 tff(3442,plain,
% 2.11/1.74 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))),
% 2.11/1.74 inference(quant_inst,[status(thm)],[])).
% 2.11/1.74 tff(3443,plain,
% 2.11/1.74 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522))),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3442, 3441])).
% 2.11/1.74 tff(3444,plain,
% 2.11/1.74 (hskp3),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[3443, 112, 3437, 3436, 3435, 3389, 634, 3376, 3366])).
% 2.11/1.74 tff(3445,plain,
% 2.11/1.74 (((~hskp3) | (~c1_1(a497))) <=> ((~hskp3) | (~c1_1(a497)))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3446,plain,
% 2.11/1.74 (((~c1_1(a497)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a497)))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3447,axiom,((~c1_1(a497)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 2.11/1.74 tff(3448,plain,
% 2.11/1.74 ((~hskp3) | (~c1_1(a497))),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3447, 3446])).
% 2.11/1.74 tff(3449,plain,
% 2.11/1.74 ((~hskp3) | (~c1_1(a497))),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3448, 3445])).
% 2.11/1.74 tff(3450,plain,
% 2.11/1.74 (~c1_1(a497)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[3449, 3444])).
% 2.11/1.74 tff(3451,plain,
% 2.11/1.74 (((~hskp3) | (~c0_1(a497))) <=> ((~hskp3) | (~c0_1(a497)))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3452,plain,
% 2.11/1.74 (((~c0_1(a497)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a497)))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3453,axiom,((~c0_1(a497)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 2.11/1.74 tff(3454,plain,
% 2.11/1.74 ((~hskp3) | (~c0_1(a497))),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3453, 3452])).
% 2.11/1.74 tff(3455,plain,
% 2.11/1.74 ((~hskp3) | (~c0_1(a497))),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3454, 3451])).
% 2.11/1.74 tff(3456,plain,
% 2.11/1.74 (~c0_1(a497)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[3455, 3444])).
% 2.11/1.74 tff(3457,plain,
% 2.11/1.74 (((~hskp3) | c2_1(a497)) <=> ((~hskp3) | c2_1(a497))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3458,axiom,((~hskp3) | c2_1(a497)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 2.11/1.74 tff(3459,plain,
% 2.11/1.74 ((~hskp3) | c2_1(a497)),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3458, 3457])).
% 2.11/1.74 tff(3460,plain,
% 2.11/1.74 ((~hskp3) | c2_1(a497)),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3459, 3457])).
% 2.11/1.74 tff(3461,plain,
% 2.11/1.74 ((~hskp3) | c2_1(a497)),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3460, 3457])).
% 2.11/1.74 tff(3462,plain,
% 2.11/1.74 ((~hskp3) | c2_1(a497)),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3461, 3457])).
% 2.11/1.74 tff(3463,plain,
% 2.11/1.74 ((~hskp3) | c2_1(a497)),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3462, 3457])).
% 2.11/1.74 tff(3464,plain,
% 2.11/1.74 ((~hskp3) | c2_1(a497)),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3463, 3457])).
% 2.11/1.74 tff(3465,plain,
% 2.11/1.74 ((~hskp3) | c2_1(a497)),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3464, 3457])).
% 2.11/1.74 tff(3466,plain,
% 2.11/1.74 ((~hskp3) | c2_1(a497)),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3465, 3457])).
% 2.11/1.74 tff(3467,plain,
% 2.11/1.74 (c2_1(a497)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[3466, 3444])).
% 2.11/1.74 tff(3468,plain,
% 2.11/1.74 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a497) | c1_1(a497) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | (~c2_1(a497)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a497) | c1_1(a497) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | (~c2_1(a497)))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3469,plain,
% 2.11/1.74 ((hskp5 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c1_1(a497) | c0_1(a497) | (~c2_1(a497))) <=> (hskp5 | c0_1(a497) | c1_1(a497) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | (~c2_1(a497)))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3470,plain,
% 2.11/1.74 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c1_1(a497) | c0_1(a497) | (~c2_1(a497)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a497) | c1_1(a497) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | (~c2_1(a497))))),
% 2.11/1.74 inference(monotonicity,[status(thm)],[3469])).
% 2.11/1.74 tff(3471,plain,
% 2.11/1.74 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c1_1(a497) | c0_1(a497) | (~c2_1(a497)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a497) | c1_1(a497) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | (~c2_1(a497)))),
% 2.11/1.74 inference(transitivity,[status(thm)],[3470, 3468])).
% 2.11/1.74 tff(3472,plain,
% 2.11/1.74 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | c1_1(a497) | c0_1(a497) | (~c2_1(a497)))),
% 2.11/1.74 inference(quant_inst,[status(thm)],[])).
% 2.11/1.74 tff(3473,plain,
% 2.11/1.74 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a497) | c1_1(a497) | (~ndr1_0) | (~c2_1(a522)) | (~c1_1(a522)) | (~c0_1(a522)) | (~c2_1(a497))),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3472, 3471])).
% 2.11/1.74 tff(3474,plain,
% 2.11/1.74 (hskp5),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[3473, 112, 3437, 3436, 3435, 3467, 3456, 3450, 2656])).
% 2.11/1.74 tff(3475,plain,
% 2.11/1.74 (~c1_1(a499)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[1925, 3474])).
% 2.11/1.74 tff(3476,plain,
% 2.11/1.74 (c0_1(a499)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[1908, 3474])).
% 2.11/1.74 tff(3477,plain,
% 2.11/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a540) | c3_1(a528) | c1_1(a499) | (~ndr1_0) | (~c3_1(a499)) | (~c0_1(a499)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a540) | c3_1(a528) | c1_1(a499) | (~ndr1_0) | (~c3_1(a499)) | (~c0_1(a499)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3478,plain,
% 2.11/1.74 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a499) | (~c0_1(a499)) | (~c3_1(a499)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540))) <=> (c0_1(a540) | c3_1(a528) | c1_1(a499) | (~ndr1_0) | (~c3_1(a499)) | (~c0_1(a499)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3479,plain,
% 2.11/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a499) | (~c0_1(a499)) | (~c3_1(a499)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a540) | c3_1(a528) | c1_1(a499) | (~ndr1_0) | (~c3_1(a499)) | (~c0_1(a499)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540))))),
% 2.11/1.74 inference(monotonicity,[status(thm)],[3478])).
% 2.11/1.74 tff(3480,plain,
% 2.11/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a499) | (~c0_1(a499)) | (~c3_1(a499)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a540) | c3_1(a528) | c1_1(a499) | (~ndr1_0) | (~c3_1(a499)) | (~c0_1(a499)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540)))),
% 2.11/1.74 inference(transitivity,[status(thm)],[3479, 3477])).
% 2.11/1.74 tff(3481,plain,
% 2.11/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c1_1(a499) | (~c0_1(a499)) | (~c3_1(a499)) | c0_1(a540) | (~c3_1(a540)) | (~c1_1(a540)))),
% 2.11/1.74 inference(quant_inst,[status(thm)],[])).
% 2.11/1.74 tff(3482,plain,
% 2.11/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a540) | c3_1(a528) | c1_1(a499) | (~ndr1_0) | (~c3_1(a499)) | (~c0_1(a499)) | (~c1_1(a528)) | (~c0_1(a528)) | (~c3_1(a540)) | (~c1_1(a540))),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3481, 3480])).
% 2.11/1.74 tff(3483,plain,
% 2.11/1.74 (~c3_1(a499)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[3482, 112, 3335, 3365, 3394, 3119, 3476, 2423, 1082, 3475, 1398])).
% 2.11/1.74 tff(3484,plain,
% 2.11/1.74 (c2_1(a499)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[1919, 3474])).
% 2.11/1.74 tff(3485,plain,
% 2.11/1.74 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a507) | c1_1(a507) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a507) | c1_1(a507) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a507)))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3486,plain,
% 2.11/1.74 ((hskp7 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507))) <=> (hskp7 | c0_1(a507) | c1_1(a507) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a507)))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3487,plain,
% 2.11/1.74 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a507) | c1_1(a507) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a507))))),
% 2.11/1.74 inference(monotonicity,[status(thm)],[3486])).
% 2.11/1.74 tff(3488,plain,
% 2.11/1.74 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a507) | c1_1(a507) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a507)))),
% 2.11/1.74 inference(transitivity,[status(thm)],[3487, 3485])).
% 2.11/1.74 tff(3489,plain,
% 2.11/1.74 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c1_1(a507) | c0_1(a507) | (~c3_1(a507)))),
% 2.11/1.74 inference(quant_inst,[status(thm)],[])).
% 2.11/1.74 tff(3490,plain,
% 2.11/1.74 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a507) | c1_1(a507) | c1_1(a499) | (~ndr1_0) | (~c2_1(a499)) | (~c0_1(a499)) | (~c3_1(a507))),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3489, 3488])).
% 2.11/1.74 tff(3491,plain,
% 2.11/1.74 (hskp7),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[3490, 112, 3403, 3476, 3484, 3404, 3405, 3475, 240])).
% 2.11/1.74 tff(3492,plain,
% 2.11/1.74 (~c3_1(a502)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[332, 3491])).
% 2.11/1.74 tff(3493,plain,
% 2.11/1.74 (~c1_1(a502)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[338, 3491])).
% 2.11/1.74 tff(3494,plain,
% 2.11/1.74 (~c0_1(a502)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[709, 3491])).
% 2.11/1.74 tff(3495,plain,
% 2.11/1.74 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | c1_1(a499) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a499)) | (~c0_1(a499)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp20 | c1_1(a499) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a499)) | (~c0_1(a499)))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3496,plain,
% 2.11/1.74 ((hskp20 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496))) <=> (hskp20 | c1_1(a499) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a499)) | (~c0_1(a499)))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3497,plain,
% 2.11/1.74 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | c1_1(a499) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a499)) | (~c0_1(a499))))),
% 2.11/1.74 inference(monotonicity,[status(thm)],[3496])).
% 2.11/1.74 tff(3498,plain,
% 2.11/1.74 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp20 | c1_1(a499) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a499)) | (~c0_1(a499)))),
% 2.11/1.74 inference(transitivity,[status(thm)],[3497, 3495])).
% 2.11/1.74 tff(3499,plain,
% 2.11/1.74 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a499) | (~c2_1(a499)) | (~c0_1(a499)) | c2_1(a496) | c1_1(a496) | (~c0_1(a496)))),
% 2.11/1.74 inference(quant_inst,[status(thm)],[])).
% 2.11/1.74 tff(3500,plain,
% 2.11/1.74 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp20 | c1_1(a499) | c1_1(a496) | c2_1(a496) | (~ndr1_0) | (~c0_1(a496)) | (~c2_1(a499)) | (~c0_1(a499))),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3499, 3498])).
% 2.11/1.74 tff(3501,plain,
% 2.11/1.74 (hskp20),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[3500, 112, 3476, 3484, 3475, 3389, 634, 1594, 3366])).
% 2.11/1.74 tff(3502,plain,
% 2.11/1.74 (~hskp1),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[1556, 3492, 3119, 1082, 3394, 3493, 3501, 3494])).
% 2.11/1.74 tff(3503,plain,
% 2.11/1.74 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a499) | (~ndr1_0) | c3_1(a499) | (~c0_1(a499)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a499) | (~ndr1_0) | c3_1(a499) | (~c0_1(a499)))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3504,plain,
% 2.11/1.74 ((hskp1 | (~ndr1_0) | c3_1(a499) | c1_1(a499) | (~c0_1(a499)) | c1_1(a502) | c0_1(a502) | c3_1(a502)) <=> (hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a499) | (~ndr1_0) | c3_1(a499) | (~c0_1(a499)))),
% 2.11/1.74 inference(rewrite,[status(thm)],[])).
% 2.11/1.74 tff(3505,plain,
% 2.11/1.74 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a499) | c1_1(a499) | (~c0_1(a499)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a499) | (~ndr1_0) | c3_1(a499) | (~c0_1(a499))))),
% 2.11/1.74 inference(monotonicity,[status(thm)],[3504])).
% 2.11/1.74 tff(3506,plain,
% 2.11/1.74 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a499) | c1_1(a499) | (~c0_1(a499)) | c1_1(a502) | c0_1(a502) | c3_1(a502))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a499) | (~ndr1_0) | c3_1(a499) | (~c0_1(a499)))),
% 2.11/1.74 inference(transitivity,[status(thm)],[3505, 3503])).
% 2.11/1.74 tff(3507,plain,
% 2.11/1.74 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a499) | c1_1(a499) | (~c0_1(a499)) | c1_1(a502) | c0_1(a502) | c3_1(a502))),
% 2.11/1.74 inference(quant_inst,[status(thm)],[])).
% 2.11/1.74 tff(3508,plain,
% 2.11/1.74 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp1 | c0_1(a502) | c1_1(a502) | c3_1(a502) | c1_1(a499) | (~ndr1_0) | c3_1(a499) | (~c0_1(a499))),
% 2.11/1.74 inference(modus_ponens,[status(thm)],[3507, 3506])).
% 2.11/1.74 tff(3509,plain,
% 2.11/1.74 ($false),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[3508, 112, 3502, 3476, 3494, 3493, 3492, 3475, 645, 3483])).
% 2.11/1.74 tff(3510,plain,(c0_1(a540) | c3_1(a528) | c2_1(a496) | c3_1(a496) | hskp26), inference(lemma,lemma(discharge,[]))).
% 2.11/1.74 tff(3511,plain,
% 2.11/1.74 (c0_1(a540)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[3510, 633, 634, 1082, 32])).
% 2.11/1.74 tff(3512,plain,
% 2.11/1.74 (~hskp22),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[131, 3511])).
% 2.11/1.74 tff(3513,plain,
% 2.11/1.74 (~c0_1(a496)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[2613, 3512, 2644, 2645, 634, 633, 2646])).
% 2.11/1.74 tff(3514,plain,
% 2.11/1.74 (~c1_1(a509)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[2562, 3513, 633, 634, 2646, 2645, 2644])).
% 2.11/1.74 tff(3515,plain,
% 2.11/1.74 (c0_1(a528)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[3344, 3514, 2644, 2645, 3119, 1082, 634, 633, 3512, 2646])).
% 2.11/1.74 tff(3516,plain,
% 2.11/1.74 (~hskp21),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[3323, 3515, 3119, 1082, 634, 633, 3512])).
% 2.11/1.74 tff(3517,plain,
% 2.11/1.74 (~c2_1(a528)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[3331, 3516, 3119, 3514])).
% 2.11/1.74 tff(3518,plain,
% 2.11/1.74 ($false),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[1003, 112, 3515, 3119, 1082, 634, 633, 996, 3513, 3517])).
% 2.11/1.74 tff(3519,plain,(c3_1(a496) | c3_1(a528) | c2_1(a496) | hskp26), inference(lemma,lemma(discharge,[]))).
% 2.11/1.74 tff(3520,plain,
% 2.11/1.74 (hskp26),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[3519, 2642, 633, 634])).
% 2.11/1.74 tff(3521,plain,
% 2.11/1.74 (~c3_1(a559)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[2191, 3520])).
% 2.11/1.74 tff(3522,plain,
% 2.11/1.74 (~c2_1(a559)),
% 2.11/1.74 inference(unit_resolution,[status(thm)],[2197, 3520])).
% 2.11/1.75 tff(3523,plain,
% 2.11/1.75 (~c0_1(a559)),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[2203, 3520])).
% 2.11/1.75 tff(3524,assumption,(~c2_1(a528)), introduced(assumption)).
% 2.11/1.75 tff(3525,plain,
% 2.11/1.75 ($false),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[2309, 112, 1092, 1091, 2222, 2221, 2220, 1082, 996, 3524])).
% 2.11/1.75 tff(3526,plain,(c2_1(a528) | (~c0_1(a528)) | (~c1_1(a528)) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528)), inference(lemma,lemma(discharge,[]))).
% 2.11/1.75 tff(3527,plain,
% 2.11/1.75 (c2_1(a528)),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[3526, 2641, 2640, 3523, 3522, 3521, 2642])).
% 2.11/1.75 tff(3528,plain,
% 2.11/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 2.11/1.75 inference(rewrite,[status(thm)],[])).
% 2.11/1.75 tff(3529,plain,
% 2.11/1.75 (((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c3_1(a559) | c0_1(a559) | c2_1(a559)) <=> (c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 2.11/1.75 inference(rewrite,[status(thm)],[])).
% 2.11/1.75 tff(3530,plain,
% 2.11/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c3_1(a559) | c0_1(a559) | c2_1(a559))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528))))),
% 2.11/1.75 inference(monotonicity,[status(thm)],[3529])).
% 2.11/1.75 tff(3531,plain,
% 2.11/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c3_1(a559) | c0_1(a559) | c2_1(a559))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528)))),
% 2.11/1.75 inference(transitivity,[status(thm)],[3530, 3528])).
% 2.11/1.75 tff(3532,plain,
% 2.11/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a528) | (~c1_1(a528)) | (~c0_1(a528)) | c2_1(a509) | (~c1_1(a509)) | (~c0_1(a509)) | c3_1(a559) | c0_1(a559) | c2_1(a559))),
% 2.11/1.75 inference(quant_inst,[status(thm)],[])).
% 2.11/1.75 tff(3533,plain,
% 2.11/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a559) | c2_1(a559) | c3_1(a559) | c3_1(a528) | c2_1(a509) | (~ndr1_0) | (~c1_1(a509)) | (~c0_1(a509)) | (~c1_1(a528)) | (~c0_1(a528))),
% 2.11/1.75 inference(modus_ponens,[status(thm)],[3532, 3531])).
% 2.11/1.75 tff(3534,plain,
% 2.11/1.75 (~c1_1(a509)),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[3533, 112, 2641, 2640, 2339, 3523, 3522, 3521, 2642, 2317, 996])).
% 2.11/1.75 tff(3535,plain,
% 2.11/1.75 (hskp21 | (~c2_1(a528))),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[3330, 112, 2640, 2339, 2642, 2317, 2279, 3534])).
% 2.11/1.75 tff(3536,plain,
% 2.11/1.75 (hskp21),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[3535, 3527])).
% 2.11/1.75 tff(3537,plain,
% 2.11/1.75 (hskp22),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[3323, 3536, 634, 2642, 2641, 2640, 633])).
% 2.11/1.75 tff(3538,plain,
% 2.11/1.75 (~c0_1(a540)),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[131, 3537])).
% 2.11/1.75 tff(3539,plain,
% 2.11/1.75 (c1_1(a540)),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[153, 3537])).
% 2.11/1.75 tff(3540,plain,
% 2.11/1.75 (c3_1(a540)),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[142, 3537])).
% 2.11/1.75 tff(3541,plain,
% 2.11/1.75 ($false),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[3386, 3540, 3539, 2317, 2339, 2640, 2328, 3534, 2642, 3538])).
% 2.11/1.75 tff(3542,plain,(c3_1(a496) | c2_1(a496)), inference(lemma,lemma(discharge,[]))).
% 2.11/1.75 tff(3543,plain,
% 2.11/1.75 ($false),
% 2.11/1.75 inference(unit_resolution,[status(thm)],[3542, 2543, 2542])).
% 2.11/1.75 % SZS output end Proof
%------------------------------------------------------------------------------