TSTP Solution File: SYN477-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN477-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 23:55:46 EDT 2022
% Result : Unsatisfiable 0.97s 0.88s
% Output : Proof 1.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN477-1 : TPTP v8.1.0. Released v2.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 04:38:29 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.
% 0.97/0.88 % SZS status Unsatisfiable
% 0.97/0.88 % SZS output start Proof
% 0.97/0.88 tff(c2_1_type, type, (
% 0.97/0.88 c2_1: $i > $o)).
% 0.97/0.88 tff(a1204_type, type, (
% 0.97/0.88 a1204: $i)).
% 0.97/0.88 tff(hskp25_type, type, (
% 0.97/0.88 hskp25: $o)).
% 0.97/0.88 tff(c3_1_type, type, (
% 0.97/0.88 c3_1: $i > $o)).
% 0.97/0.88 tff(a1208_type, type, (
% 0.97/0.88 a1208: $i)).
% 0.97/0.88 tff(c0_1_type, type, (
% 0.97/0.88 c0_1: $i > $o)).
% 0.97/0.88 tff(c1_1_type, type, (
% 0.97/0.88 c1_1: $i > $o)).
% 0.97/0.88 tff(ndr1_0_type, type, (
% 0.97/0.88 ndr1_0: $o)).
% 0.97/0.88 tff(a1212_type, type, (
% 0.97/0.88 a1212: $i)).
% 0.97/0.88 tff(hskp5_type, type, (
% 0.97/0.88 hskp5: $o)).
% 0.97/0.88 tff(a1257_type, type, (
% 0.97/0.88 a1257: $i)).
% 0.97/0.88 tff(hskp21_type, type, (
% 0.97/0.88 hskp21: $o)).
% 0.97/0.88 tff(a1233_type, type, (
% 0.97/0.88 a1233: $i)).
% 0.97/0.88 tff(hskp15_type, type, (
% 0.97/0.88 hskp15: $o)).
% 0.97/0.88 tff(hskp6_type, type, (
% 0.97/0.88 hskp6: $o)).
% 0.97/0.88 tff(hskp0_type, type, (
% 0.97/0.88 hskp0: $o)).
% 0.97/0.88 tff(a1205_type, type, (
% 0.97/0.88 a1205: $i)).
% 0.97/0.88 tff(a1216_type, type, (
% 0.97/0.88 a1216: $i)).
% 0.97/0.88 tff(a1215_type, type, (
% 0.97/0.88 a1215: $i)).
% 0.97/0.88 tff(a1224_type, type, (
% 0.97/0.88 a1224: $i)).
% 0.97/0.88 tff(hskp11_type, type, (
% 0.97/0.88 hskp11: $o)).
% 0.97/0.88 tff(a1219_type, type, (
% 0.97/0.88 a1219: $i)).
% 0.97/0.88 tff(hskp9_type, type, (
% 0.97/0.88 hskp9: $o)).
% 0.97/0.88 tff(a1229_type, type, (
% 0.97/0.88 a1229: $i)).
% 0.97/0.88 tff(hskp13_type, type, (
% 0.97/0.88 hskp13: $o)).
% 0.97/0.88 tff(a1223_type, type, (
% 0.97/0.88 a1223: $i)).
% 0.97/0.88 tff(hskp10_type, type, (
% 0.97/0.88 hskp10: $o)).
% 0.97/0.88 tff(hskp7_type, type, (
% 0.97/0.88 hskp7: $o)).
% 0.97/0.88 tff(hskp2_type, type, (
% 0.97/0.88 hskp2: $o)).
% 0.97/0.88 tff(hskp24_type, type, (
% 0.97/0.88 hskp24: $o)).
% 0.97/0.88 tff(hskp28_type, type, (
% 0.97/0.88 hskp28: $o)).
% 0.97/0.88 tff(hskp26_type, type, (
% 0.97/0.88 hskp26: $o)).
% 0.97/0.88 tff(a1214_type, type, (
% 0.97/0.88 a1214: $i)).
% 0.97/0.88 tff(a1261_type, type, (
% 0.97/0.88 a1261: $i)).
% 0.97/0.88 tff(hskp23_type, type, (
% 0.97/0.88 hskp23: $o)).
% 0.97/0.88 tff(a1232_type, type, (
% 0.97/0.88 a1232: $i)).
% 0.97/0.88 tff(a1217_type, type, (
% 0.97/0.88 a1217: $i)).
% 0.97/0.88 tff(hskp8_type, type, (
% 0.97/0.88 hskp8: $o)).
% 0.97/0.88 tff(hskp19_type, type, (
% 0.97/0.88 hskp19: $o)).
% 0.97/0.88 tff(hskp14_type, type, (
% 0.97/0.88 hskp14: $o)).
% 0.97/0.88 tff(hskp4_type, type, (
% 0.97/0.88 hskp4: $o)).
% 0.97/0.88 tff(a1211_type, type, (
% 0.97/0.88 a1211: $i)).
% 0.97/0.88 tff(a1267_type, type, (
% 0.97/0.88 a1267: $i)).
% 0.97/0.88 tff(a1247_type, type, (
% 0.97/0.88 a1247: $i)).
% 0.97/0.88 tff(hskp1_type, type, (
% 0.97/0.88 hskp1: $o)).
% 0.97/0.88 tff(a1206_type, type, (
% 0.97/0.88 a1206: $i)).
% 0.97/0.88 tff(a1207_type, type, (
% 0.97/0.88 a1207: $i)).
% 0.97/0.88 tff(a1237_type, type, (
% 0.97/0.88 a1237: $i)).
% 0.97/0.88 tff(hskp17_type, type, (
% 0.97/0.88 hskp17: $o)).
% 0.97/0.88 tff(a1213_type, type, (
% 0.97/0.88 a1213: $i)).
% 0.97/0.88 tff(hskp27_type, type, (
% 0.97/0.88 hskp27: $o)).
% 0.97/0.88 tff(a1246_type, type, (
% 0.97/0.88 a1246: $i)).
% 0.97/0.88 tff(hskp18_type, type, (
% 0.97/0.88 hskp18: $o)).
% 0.97/0.88 tff(a1210_type, type, (
% 0.97/0.88 a1210: $i)).
% 0.97/0.88 tff(hskp3_type, type, (
% 0.97/0.88 hskp3: $o)).
% 0.97/0.88 tff(1,plain,
% 0.97/0.88 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 0.97/0.88 inference(bind,[status(th)],[])).
% 0.97/0.88 tff(2,plain,
% 0.97/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.97/0.88 inference(quant_intro,[status(thm)],[1])).
% 0.97/0.88 tff(3,plain,
% 0.97/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.97/0.88 inference(rewrite,[status(thm)],[])).
% 0.97/0.88 tff(4,plain,
% 0.97/0.88 (^[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)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_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)) | (~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)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_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))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_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))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 0.97/0.89 inference(bind,[status(th)],[])).
% 0.97/0.89 tff(5,plain,
% 0.97/0.89 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.97/0.89 inference(quant_intro,[status(thm)],[4])).
% 0.97/0.89 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 0.97/0.89 tff(7,plain,
% 0.97/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.97/0.89 tff(8,plain,
% 0.97/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.97/0.89 tff(9,plain,(
% 0.97/0.89 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.97/0.89 inference(skolemize,[status(sab)],[8])).
% 0.97/0.89 tff(10,plain,
% 0.97/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.97/0.89 tff(11,plain,
% 0.97/0.89 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.97/0.89 inference(bind,[status(th)],[])).
% 0.97/0.89 tff(12,plain,
% 0.97/0.89 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.97/0.89 inference(quant_intro,[status(thm)],[11])).
% 0.97/0.89 tff(13,plain,
% 0.97/0.89 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.97/0.89 inference(rewrite,[status(thm)],[])).
% 0.97/0.89 tff(14,plain,
% 0.97/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~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)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | 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)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | 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)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.97/0.89 inference(bind,[status(th)],[])).
% 0.97/0.89 tff(15,plain,
% 0.97/0.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.97/0.89 inference(quant_intro,[status(thm)],[14])).
% 0.97/0.89 tff(16,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 0.97/0.89 tff(17,plain,
% 0.97/0.89 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.97/0.89 tff(18,plain,
% 0.97/0.89 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.97/0.89 tff(19,plain,(
% 0.97/0.89 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.97/0.89 inference(skolemize,[status(sab)],[18])).
% 0.97/0.89 tff(20,plain,
% 0.97/0.89 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.97/0.89 tff(21,assumption,(~hskp5), introduced(assumption)).
% 0.97/0.89 tff(22,assumption,(~c0_1(a1205)), introduced(assumption)).
% 0.97/0.89 tff(23,assumption,(~c1_1(a1205)), introduced(assumption)).
% 0.97/0.89 tff(24,assumption,(~hskp6), introduced(assumption)).
% 0.97/0.89 tff(25,plain,
% 0.97/0.89 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.97/0.89 inference(bind,[status(th)],[])).
% 0.97/0.89 tff(26,plain,
% 0.97/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.97/0.89 inference(quant_intro,[status(thm)],[25])).
% 0.97/0.89 tff(27,plain,
% 0.97/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.97/0.89 inference(rewrite,[status(thm)],[])).
% 0.97/0.89 tff(28,plain,
% 0.97/0.89 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_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)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.97/0.89 inference(bind,[status(th)],[])).
% 0.97/0.89 tff(29,plain,
% 0.97/0.89 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.97/0.89 inference(quant_intro,[status(thm)],[28])).
% 0.97/0.89 tff(30,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 0.97/0.89 tff(31,plain,
% 0.97/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.97/0.89 tff(32,plain,
% 0.97/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.97/0.89 tff(33,plain,(
% 0.97/0.89 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.97/0.89 inference(skolemize,[status(sab)],[32])).
% 0.97/0.89 tff(34,plain,
% 0.97/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.97/0.89 tff(35,plain,
% 0.97/0.89 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.97/0.89 inference(bind,[status(th)],[])).
% 0.97/0.89 tff(36,plain,
% 0.97/0.89 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.97/0.89 inference(quant_intro,[status(thm)],[35])).
% 0.97/0.89 tff(37,plain,
% 0.97/0.89 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.97/0.89 inference(rewrite,[status(thm)],[])).
% 0.97/0.89 tff(38,plain,
% 0.97/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.97/0.89 inference(bind,[status(th)],[])).
% 0.97/0.89 tff(39,plain,
% 0.97/0.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.97/0.89 inference(quant_intro,[status(thm)],[38])).
% 0.97/0.89 tff(40,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 0.97/0.89 tff(41,plain,
% 0.97/0.89 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.97/0.89 tff(42,plain,
% 0.97/0.89 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.97/0.89 tff(43,plain,(
% 0.97/0.89 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.97/0.89 inference(skolemize,[status(sab)],[42])).
% 0.97/0.89 tff(44,plain,
% 0.97/0.89 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.97/0.89 tff(45,plain,
% 0.97/0.89 (^[U: $i] : refl((hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 0.97/0.89 inference(bind,[status(th)],[])).
% 0.97/0.89 tff(46,plain,
% 0.97/0.89 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.97/0.89 inference(quant_intro,[status(thm)],[45])).
% 0.97/0.89 tff(47,plain,
% 0.97/0.89 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.97/0.89 inference(rewrite,[status(thm)],[])).
% 0.97/0.89 tff(48,plain,
% 0.97/0.89 (^[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)) | hskp13) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp13))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp13) | hskp6) <=> ((hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp6))), rewrite(((hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp6) <=> (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp13) | hskp6) <=> (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 0.97/0.89 inference(bind,[status(th)],[])).
% 0.97/0.89 tff(49,plain,
% 0.97/0.89 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp13) | hskp6) <=> ![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.97/0.89 inference(quant_intro,[status(thm)],[48])).
% 0.97/0.89 tff(50,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp13) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 0.97/0.89 tff(51,plain,
% 0.97/0.89 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.97/0.89 tff(52,plain,
% 0.97/0.89 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.97/0.89 tff(53,plain,(
% 0.97/0.89 ![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.97/0.89 inference(skolemize,[status(sab)],[52])).
% 0.97/0.89 tff(54,plain,
% 0.97/0.89 (![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 0.97/0.89 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.97/0.89 tff(55,plain,
% 0.97/0.89 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.97/0.89 inference(bind,[status(th)],[])).
% 0.97/0.89 tff(56,plain,
% 0.97/0.89 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.97/0.89 inference(quant_intro,[status(thm)],[55])).
% 0.97/0.89 tff(57,plain,
% 0.97/0.89 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.97/0.89 inference(rewrite,[status(thm)],[])).
% 0.97/0.89 tff(58,plain,
% 0.97/0.89 (^[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))) | 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)) | (~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)) | (~c0_1(U)) | c2_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))) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_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))) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.97/0.89 inference(bind,[status(th)],[])).
% 0.97/0.89 tff(59,plain,
% 0.97/0.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.03/0.89 inference(quant_intro,[status(thm)],[58])).
% 1.03/0.89 tff(60,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 1.03/0.89 tff(61,plain,
% 1.03/0.89 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.03/0.89 tff(62,plain,
% 1.03/0.89 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[61, 57])).
% 1.03/0.89 tff(63,plain,(
% 1.03/0.89 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.03/0.89 inference(skolemize,[status(sab)],[62])).
% 1.03/0.89 tff(64,plain,
% 1.03/0.89 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[63, 56])).
% 1.03/0.89 tff(65,plain,
% 1.03/0.89 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 1.03/0.89 inference(bind,[status(th)],[])).
% 1.03/0.89 tff(66,plain,
% 1.03/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.03/0.89 inference(quant_intro,[status(thm)],[65])).
% 1.03/0.89 tff(67,plain,
% 1.03/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.03/0.89 inference(rewrite,[status(thm)],[])).
% 1.03/0.89 tff(68,plain,
% 1.03/0.89 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 1.03/0.89 inference(bind,[status(th)],[])).
% 1.03/0.89 tff(69,plain,
% 1.03/0.89 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.03/0.89 inference(quant_intro,[status(thm)],[68])).
% 1.03/0.89 tff(70,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 1.03/0.89 tff(71,plain,
% 1.03/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.03/0.89 tff(72,plain,
% 1.03/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[71, 67])).
% 1.03/0.89 tff(73,plain,(
% 1.03/0.89 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.03/0.89 inference(skolemize,[status(sab)],[72])).
% 1.03/0.89 tff(74,plain,
% 1.03/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[73, 66])).
% 1.03/0.89 tff(75,assumption,(~hskp15), introduced(assumption)).
% 1.03/0.89 tff(76,plain,
% 1.03/0.89 ((hskp15 | hskp6 | hskp5) <=> (hskp15 | hskp6 | hskp5)),
% 1.03/0.89 inference(rewrite,[status(thm)],[])).
% 1.03/0.89 tff(77,plain,
% 1.03/0.89 (((hskp15 | hskp6) | hskp5) <=> (hskp15 | hskp6 | hskp5)),
% 1.03/0.89 inference(rewrite,[status(thm)],[])).
% 1.03/0.89 tff(78,axiom,((hskp15 | hskp6) | hskp5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 1.03/0.89 tff(79,plain,
% 1.03/0.89 (hskp15 | hskp6 | hskp5),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[78, 77])).
% 1.03/0.89 tff(80,plain,
% 1.03/0.89 (hskp15 | hskp6 | hskp5),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[79, 76])).
% 1.03/0.89 tff(81,plain,
% 1.03/0.89 (hskp15 | hskp6 | hskp5),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[80, 76])).
% 1.03/0.89 tff(82,plain,
% 1.03/0.89 (hskp15 | hskp6 | hskp5),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[81, 76])).
% 1.03/0.89 tff(83,plain,
% 1.03/0.89 (hskp15 | hskp6 | hskp5),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[82, 76])).
% 1.03/0.89 tff(84,plain,
% 1.03/0.89 (hskp15 | hskp6 | hskp5),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[83, 76])).
% 1.03/0.89 tff(85,plain,
% 1.03/0.89 (hskp15 | hskp6 | hskp5),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[84, 76])).
% 1.03/0.89 tff(86,plain,
% 1.03/0.89 (hskp15 | hskp6 | hskp5),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[85, 76])).
% 1.03/0.89 tff(87,plain,
% 1.03/0.89 (hskp6),
% 1.03/0.89 inference(unit_resolution,[status(thm)],[86, 75, 21])).
% 1.03/0.89 tff(88,plain,
% 1.03/0.89 (((~hskp6) | (~c3_1(a1215))) <=> ((~hskp6) | (~c3_1(a1215)))),
% 1.03/0.89 inference(rewrite,[status(thm)],[])).
% 1.03/0.89 tff(89,plain,
% 1.03/0.89 (((~c3_1(a1215)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a1215)))),
% 1.03/0.89 inference(rewrite,[status(thm)],[])).
% 1.03/0.89 tff(90,axiom,((~c3_1(a1215)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 1.03/0.89 tff(91,plain,
% 1.03/0.89 ((~hskp6) | (~c3_1(a1215))),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.03/0.89 tff(92,plain,
% 1.03/0.89 ((~hskp6) | (~c3_1(a1215))),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[91, 88])).
% 1.03/0.89 tff(93,plain,
% 1.03/0.89 (~c3_1(a1215)),
% 1.03/0.89 inference(unit_resolution,[status(thm)],[92, 87])).
% 1.03/0.89 tff(94,plain,
% 1.03/0.89 (((~hskp6) | c1_1(a1215)) <=> ((~hskp6) | c1_1(a1215))),
% 1.03/0.89 inference(rewrite,[status(thm)],[])).
% 1.03/0.89 tff(95,axiom,((~hskp6) | c1_1(a1215)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.03/0.89 tff(96,plain,
% 1.03/0.89 ((~hskp6) | c1_1(a1215)),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.03/0.89 tff(97,plain,
% 1.03/0.89 ((~hskp6) | c1_1(a1215)),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[96, 94])).
% 1.03/0.89 tff(98,plain,
% 1.03/0.89 ((~hskp6) | c1_1(a1215)),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[97, 94])).
% 1.03/0.89 tff(99,plain,
% 1.03/0.89 ((~hskp6) | c1_1(a1215)),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[98, 94])).
% 1.03/0.89 tff(100,plain,
% 1.03/0.89 ((~hskp6) | c1_1(a1215)),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[99, 94])).
% 1.03/0.89 tff(101,plain,
% 1.03/0.89 ((~hskp6) | c1_1(a1215)),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[100, 94])).
% 1.03/0.89 tff(102,plain,
% 1.03/0.89 ((~hskp6) | c1_1(a1215)),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[101, 94])).
% 1.03/0.89 tff(103,plain,
% 1.03/0.89 ((~hskp6) | c1_1(a1215)),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[102, 94])).
% 1.03/0.89 tff(104,plain,
% 1.03/0.89 (c1_1(a1215)),
% 1.03/0.89 inference(unit_resolution,[status(thm)],[103, 87])).
% 1.03/0.89 tff(105,plain,
% 1.03/0.89 (((~hskp6) | c2_1(a1215)) <=> ((~hskp6) | c2_1(a1215))),
% 1.03/0.89 inference(rewrite,[status(thm)],[])).
% 1.03/0.89 tff(106,axiom,((~hskp6) | c2_1(a1215)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 1.03/0.89 tff(107,plain,
% 1.03/0.89 ((~hskp6) | c2_1(a1215)),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[106, 105])).
% 1.03/0.89 tff(108,plain,
% 1.03/0.89 ((~hskp6) | c2_1(a1215)),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[107, 105])).
% 1.03/0.89 tff(109,plain,
% 1.03/0.89 ((~hskp6) | c2_1(a1215)),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[108, 105])).
% 1.03/0.89 tff(110,plain,
% 1.03/0.89 ((~hskp6) | c2_1(a1215)),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[109, 105])).
% 1.03/0.89 tff(111,plain,
% 1.03/0.89 ((~hskp6) | c2_1(a1215)),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[110, 105])).
% 1.03/0.89 tff(112,plain,
% 1.03/0.89 ((~hskp6) | c2_1(a1215)),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[111, 105])).
% 1.03/0.89 tff(113,plain,
% 1.03/0.89 ((~hskp6) | c2_1(a1215)),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[112, 105])).
% 1.03/0.89 tff(114,plain,
% 1.03/0.89 ((~hskp6) | c2_1(a1215)),
% 1.03/0.89 inference(modus_ponens,[status(thm)],[113, 105])).
% 1.03/0.89 tff(115,plain,
% 1.03/0.89 (c2_1(a1215)),
% 1.03/0.89 inference(unit_resolution,[status(thm)],[114, 87])).
% 1.03/0.89 tff(116,assumption,(~c2_1(a1205)), introduced(assumption)).
% 1.03/0.89 tff(117,plain,
% 1.03/0.89 (((~hskp0) | c2_1(a1205)) <=> ((~hskp0) | c2_1(a1205))),
% 1.03/0.89 inference(rewrite,[status(thm)],[])).
% 1.03/0.89 tff(118,axiom,((~hskp0) | c2_1(a1205)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 1.03/0.90 tff(119,plain,
% 1.03/0.90 ((~hskp0) | c2_1(a1205)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[118, 117])).
% 1.03/0.90 tff(120,plain,
% 1.03/0.90 ((~hskp0) | c2_1(a1205)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[119, 117])).
% 1.03/0.90 tff(121,plain,
% 1.03/0.90 ((~hskp0) | c2_1(a1205)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[120, 117])).
% 1.03/0.90 tff(122,plain,
% 1.03/0.90 ((~hskp0) | c2_1(a1205)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[121, 117])).
% 1.03/0.90 tff(123,plain,
% 1.03/0.90 ((~hskp0) | c2_1(a1205)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[122, 117])).
% 1.03/0.90 tff(124,plain,
% 1.03/0.90 ((~hskp0) | c2_1(a1205)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[123, 117])).
% 1.03/0.90 tff(125,plain,
% 1.03/0.90 ((~hskp0) | c2_1(a1205)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[124, 117])).
% 1.03/0.90 tff(126,plain,
% 1.03/0.90 ((~hskp0) | c2_1(a1205)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[125, 117])).
% 1.03/0.90 tff(127,plain,
% 1.03/0.90 (~hskp0),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[126, 116])).
% 1.03/0.90 tff(128,plain,
% 1.03/0.90 (^[U: $i] : refl((hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(129,plain,
% 1.03/0.90 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[128])).
% 1.03/0.90 tff(130,plain,
% 1.03/0.90 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(131,plain,
% 1.03/0.90 (^[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)) | 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)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp21) <=> ((hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp21))), rewrite(((hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp21) <=> (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp21) <=> (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(132,plain,
% 1.03/0.90 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp21) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[131])).
% 1.03/0.90 tff(133,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 1.03/0.90 tff(134,plain,
% 1.03/0.90 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[133, 132])).
% 1.03/0.90 tff(135,plain,
% 1.03/0.90 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[134, 130])).
% 1.03/0.90 tff(136,plain,(
% 1.03/0.90 ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.03/0.90 inference(skolemize,[status(sab)],[135])).
% 1.03/0.90 tff(137,plain,
% 1.03/0.90 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[136, 129])).
% 1.03/0.90 tff(138,assumption,(~c3_1(a1215)), introduced(assumption)).
% 1.03/0.90 tff(139,assumption,(c2_1(a1215)), introduced(assumption)).
% 1.03/0.90 tff(140,assumption,(c1_1(a1215)), introduced(assumption)).
% 1.03/0.90 tff(141,assumption,(~ndr1_0), introduced(assumption)).
% 1.03/0.90 tff(142,plain,
% 1.03/0.90 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(143,plain,
% 1.03/0.90 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(144,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause6')).
% 1.03/0.90 tff(145,plain,
% 1.03/0.90 (ndr1_0 | (~hskp24)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[144, 143])).
% 1.03/0.90 tff(146,plain,
% 1.03/0.90 (ndr1_0 | (~hskp24)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[145, 142])).
% 1.03/0.90 tff(147,plain,
% 1.03/0.90 (~hskp24),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[146, 141])).
% 1.03/0.90 tff(148,plain,
% 1.03/0.90 (((~hskp28) | ndr1_0) <=> ((~hskp28) | ndr1_0)),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(149,axiom,((~hskp28) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 1.03/0.90 tff(150,plain,
% 1.03/0.90 ((~hskp28) | ndr1_0),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.03/0.90 tff(151,plain,
% 1.03/0.90 ((~hskp28) | ndr1_0),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[150, 148])).
% 1.03/0.90 tff(152,plain,
% 1.03/0.90 ((~hskp28) | ndr1_0),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[151, 148])).
% 1.03/0.90 tff(153,plain,
% 1.03/0.90 ((~hskp28) | ndr1_0),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[152, 148])).
% 1.03/0.90 tff(154,plain,
% 1.03/0.90 ((~hskp28) | ndr1_0),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[153, 148])).
% 1.03/0.90 tff(155,plain,
% 1.03/0.90 ((~hskp28) | ndr1_0),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[154, 148])).
% 1.03/0.90 tff(156,plain,
% 1.03/0.90 ((~hskp28) | ndr1_0),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[155, 148])).
% 1.03/0.90 tff(157,plain,
% 1.03/0.90 ((~hskp28) | ndr1_0),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[156, 148])).
% 1.03/0.90 tff(158,plain,
% 1.03/0.90 (~hskp28),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[157, 141])).
% 1.03/0.90 tff(159,plain,
% 1.03/0.90 ((ndr1_0 | (~hskp26)) <=> (ndr1_0 | (~hskp26))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(160,plain,
% 1.03/0.90 (((~hskp26) | ndr1_0) <=> (ndr1_0 | (~hskp26))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(161,axiom,((~hskp26) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause4')).
% 1.03/0.90 tff(162,plain,
% 1.03/0.90 (ndr1_0 | (~hskp26)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[161, 160])).
% 1.03/0.90 tff(163,plain,
% 1.03/0.90 (ndr1_0 | (~hskp26)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[162, 159])).
% 1.03/0.90 tff(164,plain,
% 1.03/0.90 (~hskp26),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[163, 141])).
% 1.03/0.90 tff(165,plain,
% 1.03/0.90 ((hskp28 | hskp26 | hskp24) <=> (hskp28 | hskp26 | hskp24)),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(166,plain,
% 1.03/0.90 (((hskp26 | hskp28) | hskp24) <=> (hskp28 | hskp26 | hskp24)),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(167,axiom,((hskp26 | hskp28) | hskp24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause31')).
% 1.03/0.90 tff(168,plain,
% 1.03/0.90 (hskp28 | hskp26 | hskp24),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.03/0.90 tff(169,plain,
% 1.03/0.90 (hskp28 | hskp26 | hskp24),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[168, 165])).
% 1.03/0.90 tff(170,plain,
% 1.03/0.90 (hskp28 | hskp26 | hskp24),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[169, 165])).
% 1.03/0.90 tff(171,plain,
% 1.03/0.90 (hskp28 | hskp26 | hskp24),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[170, 165])).
% 1.03/0.90 tff(172,plain,
% 1.03/0.90 (hskp28 | hskp26 | hskp24),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[171, 165])).
% 1.03/0.90 tff(173,plain,
% 1.03/0.90 (hskp28 | hskp26 | hskp24),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[172, 165])).
% 1.03/0.90 tff(174,plain,
% 1.03/0.90 (hskp28 | hskp26 | hskp24),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[173, 165])).
% 1.03/0.90 tff(175,plain,
% 1.03/0.90 (hskp28 | hskp26 | hskp24),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[174, 165])).
% 1.03/0.90 tff(176,plain,
% 1.03/0.90 ($false),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[175, 164, 158, 147])).
% 1.03/0.90 tff(177,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.03/0.90 tff(178,plain,
% 1.03/0.90 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp21 | hskp0 | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp21 | hskp0 | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(179,plain,
% 1.03/0.90 ((hskp21 | hskp0 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c1_1(a1215))) <=> (hskp21 | hskp0 | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(180,plain,
% 1.03/0.90 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c1_1(a1215)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp21 | hskp0 | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215))))),
% 1.03/0.90 inference(monotonicity,[status(thm)],[179])).
% 1.03/0.90 tff(181,plain,
% 1.03/0.90 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c1_1(a1215)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp21 | hskp0 | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)))),
% 1.03/0.90 inference(transitivity,[status(thm)],[180, 178])).
% 1.03/0.90 tff(182,plain,
% 1.03/0.90 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c1_1(a1215)))),
% 1.03/0.90 inference(quant_inst,[status(thm)],[])).
% 1.03/0.90 tff(183,plain,
% 1.03/0.90 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp21 | hskp0 | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[182, 181])).
% 1.03/0.90 tff(184,plain,
% 1.03/0.90 (hskp21 | hskp0),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[183, 177, 140, 139, 138, 137])).
% 1.03/0.90 tff(185,plain,
% 1.03/0.90 (hskp21),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[184, 127])).
% 1.03/0.90 tff(186,plain,
% 1.03/0.90 (((~hskp21) | (~c1_1(a1257))) <=> ((~hskp21) | (~c1_1(a1257)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(187,plain,
% 1.03/0.90 (((~c1_1(a1257)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a1257)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(188,axiom,((~c1_1(a1257)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 1.03/0.90 tff(189,plain,
% 1.03/0.90 ((~hskp21) | (~c1_1(a1257))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[188, 187])).
% 1.03/0.90 tff(190,plain,
% 1.03/0.90 ((~hskp21) | (~c1_1(a1257))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[189, 186])).
% 1.03/0.90 tff(191,plain,
% 1.03/0.90 (~c1_1(a1257)),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[190, 185])).
% 1.03/0.90 tff(192,plain,
% 1.03/0.90 (((~hskp21) | (~c0_1(a1257))) <=> ((~hskp21) | (~c0_1(a1257)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(193,plain,
% 1.03/0.90 (((~c0_1(a1257)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a1257)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(194,axiom,((~c0_1(a1257)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 1.03/0.90 tff(195,plain,
% 1.03/0.90 ((~hskp21) | (~c0_1(a1257))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[194, 193])).
% 1.03/0.90 tff(196,plain,
% 1.03/0.90 ((~hskp21) | (~c0_1(a1257))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[195, 192])).
% 1.03/0.90 tff(197,plain,
% 1.03/0.90 (~c0_1(a1257)),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[196, 185])).
% 1.03/0.90 tff(198,plain,
% 1.03/0.90 (((~hskp21) | c3_1(a1257)) <=> ((~hskp21) | c3_1(a1257))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(199,axiom,((~hskp21) | c3_1(a1257)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 1.03/0.90 tff(200,plain,
% 1.03/0.90 ((~hskp21) | c3_1(a1257)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[199, 198])).
% 1.03/0.90 tff(201,plain,
% 1.03/0.90 ((~hskp21) | c3_1(a1257)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[200, 198])).
% 1.03/0.90 tff(202,plain,
% 1.03/0.90 ((~hskp21) | c3_1(a1257)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[201, 198])).
% 1.03/0.90 tff(203,plain,
% 1.03/0.90 ((~hskp21) | c3_1(a1257)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[202, 198])).
% 1.03/0.90 tff(204,plain,
% 1.03/0.90 ((~hskp21) | c3_1(a1257)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[203, 198])).
% 1.03/0.90 tff(205,plain,
% 1.03/0.90 ((~hskp21) | c3_1(a1257)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[204, 198])).
% 1.03/0.90 tff(206,plain,
% 1.03/0.90 ((~hskp21) | c3_1(a1257)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[205, 198])).
% 1.03/0.90 tff(207,plain,
% 1.03/0.90 ((~hskp21) | c3_1(a1257)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[206, 198])).
% 1.03/0.90 tff(208,plain,
% 1.03/0.90 (c3_1(a1257)),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[207, 185])).
% 1.03/0.90 tff(209,plain,
% 1.03/0.90 (^[U: $i] : refl((hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(210,plain,
% 1.03/0.90 (![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[209])).
% 1.03/0.90 tff(211,plain,
% 1.03/0.90 (![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(212,plain,
% 1.03/0.90 (^[U: $i] : 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)) | hskp28) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp28))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(213,plain,
% 1.03/0.90 (![U: $i] : (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[212])).
% 1.03/0.90 tff(214,axiom,(![U: $i] : (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 1.03/0.90 tff(215,plain,
% 1.03/0.90 (![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[214, 213])).
% 1.03/0.90 tff(216,plain,
% 1.03/0.90 (![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[215, 211])).
% 1.03/0.90 tff(217,plain,(
% 1.03/0.90 ![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.03/0.90 inference(skolemize,[status(sab)],[216])).
% 1.03/0.90 tff(218,plain,
% 1.03/0.90 (![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[217, 210])).
% 1.03/0.90 tff(219,assumption,(~hskp28), introduced(assumption)).
% 1.03/0.90 tff(220,plain,
% 1.03/0.90 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c2_1(a1205) | c0_1(a1205) | (~ndr1_0) | c3_1(a1205))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c2_1(a1205) | c0_1(a1205) | (~ndr1_0) | c3_1(a1205))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(221,plain,
% 1.03/0.90 ((hskp28 | (~ndr1_0) | c3_1(a1205) | c2_1(a1205) | c0_1(a1205)) <=> (hskp28 | c2_1(a1205) | c0_1(a1205) | (~ndr1_0) | c3_1(a1205))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(222,plain,
% 1.03/0.90 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1205) | c2_1(a1205) | c0_1(a1205))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c2_1(a1205) | c0_1(a1205) | (~ndr1_0) | c3_1(a1205)))),
% 1.03/0.90 inference(monotonicity,[status(thm)],[221])).
% 1.03/0.90 tff(223,plain,
% 1.03/0.90 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1205) | c2_1(a1205) | c0_1(a1205))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c2_1(a1205) | c0_1(a1205) | (~ndr1_0) | c3_1(a1205))),
% 1.03/0.90 inference(transitivity,[status(thm)],[222, 220])).
% 1.03/0.90 tff(224,plain,
% 1.03/0.90 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1205) | c2_1(a1205) | c0_1(a1205))),
% 1.03/0.90 inference(quant_inst,[status(thm)],[])).
% 1.03/0.90 tff(225,plain,
% 1.03/0.90 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c2_1(a1205) | c0_1(a1205) | (~ndr1_0) | c3_1(a1205)),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[224, 223])).
% 1.03/0.90 tff(226,plain,
% 1.03/0.90 (hskp28 | c2_1(a1205) | c3_1(a1205)),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[225, 177, 22, 218])).
% 1.03/0.90 tff(227,plain,
% 1.03/0.90 (c3_1(a1205)),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[226, 219, 116])).
% 1.03/0.90 tff(228,plain,
% 1.03/0.90 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(229,plain,
% 1.03/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[228])).
% 1.03/0.90 tff(230,plain,
% 1.03/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(231,plain,
% 1.03/0.90 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(232,plain,
% 1.03/0.90 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[231])).
% 1.03/0.90 tff(233,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 1.03/0.90 tff(234,plain,
% 1.03/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[233, 232])).
% 1.03/0.90 tff(235,plain,
% 1.03/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[234, 230])).
% 1.03/0.90 tff(236,plain,(
% 1.03/0.90 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.03/0.90 inference(skolemize,[status(sab)],[235])).
% 1.03/0.90 tff(237,plain,
% 1.03/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[236, 229])).
% 1.03/0.90 tff(238,plain,
% 1.03/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1205) | c3_1(a1215) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1205) | c3_1(a1215) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(239,plain,
% 1.03/0.90 (((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1205) | c2_1(a1205) | (~c3_1(a1205)) | c2_1(a1205) | c1_1(a1205) | c0_1(a1205)) <=> (c2_1(a1205) | c3_1(a1215) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(240,plain,
% 1.03/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1205) | c2_1(a1205) | (~c3_1(a1205)) | c2_1(a1205) | c1_1(a1205) | c0_1(a1205))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1205) | c3_1(a1215) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | c0_1(a1215) | (~c1_1(a1215))))),
% 1.03/0.90 inference(monotonicity,[status(thm)],[239])).
% 1.03/0.90 tff(241,plain,
% 1.03/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1205) | c2_1(a1205) | (~c3_1(a1205)) | c2_1(a1205) | c1_1(a1205) | c0_1(a1205))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1205) | c3_1(a1215) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.03/0.90 inference(transitivity,[status(thm)],[240, 238])).
% 1.03/0.90 tff(242,plain,
% 1.03/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1205) | c2_1(a1205) | (~c3_1(a1205)) | c2_1(a1205) | c1_1(a1205) | c0_1(a1205))),
% 1.03/0.90 inference(quant_inst,[status(thm)],[])).
% 1.03/0.90 tff(243,plain,
% 1.03/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1205) | c3_1(a1215) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | c0_1(a1215) | (~c1_1(a1215))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[242, 241])).
% 1.03/0.90 tff(244,plain,
% 1.03/0.90 ((~c3_1(a1205)) | c0_1(a1215)),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[243, 177, 140, 116, 138, 22, 23, 237])).
% 1.03/0.90 tff(245,plain,
% 1.03/0.90 (c0_1(a1215)),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[244, 227])).
% 1.03/0.90 tff(246,plain,
% 1.03/0.90 (^[U: $i] : refl((hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(247,plain,
% 1.03/0.90 (![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[246])).
% 1.03/0.90 tff(248,plain,
% 1.03/0.90 (![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(249,plain,
% 1.03/0.90 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) | hskp23) <=> ((hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp23))), rewrite(((hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) | hskp23) <=> (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.03/0.90 inference(bind,[status(th)],[])).
% 1.03/0.90 tff(250,plain,
% 1.03/0.90 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) | hskp23) <=> ![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.90 inference(quant_intro,[status(thm)],[249])).
% 1.03/0.90 tff(251,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 1.03/0.90 tff(252,plain,
% 1.03/0.90 (![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[251, 250])).
% 1.03/0.90 tff(253,plain,
% 1.03/0.90 (![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[252, 248])).
% 1.03/0.90 tff(254,plain,(
% 1.03/0.90 ![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.90 inference(skolemize,[status(sab)],[253])).
% 1.03/0.90 tff(255,plain,
% 1.03/0.90 (![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[254, 247])).
% 1.03/0.90 tff(256,plain,
% 1.03/0.90 (((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)))) <=> ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp0 | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(257,plain,
% 1.03/0.90 ((hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215))) <=> (hskp23 | hskp0 | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(258,plain,
% 1.03/0.90 (((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)))) <=> ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215))))),
% 1.03/0.90 inference(monotonicity,[status(thm)],[257])).
% 1.03/0.90 tff(259,plain,
% 1.03/0.90 (((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)))) <=> ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp0 | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)))),
% 1.03/0.90 inference(transitivity,[status(thm)],[258, 256])).
% 1.03/0.90 tff(260,plain,
% 1.03/0.90 ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)))),
% 1.03/0.90 inference(quant_inst,[status(thm)],[])).
% 1.03/0.90 tff(261,plain,
% 1.03/0.90 ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp0 | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[260, 259])).
% 1.03/0.90 tff(262,plain,
% 1.03/0.90 (hskp23 | hskp0 | (~c0_1(a1215))),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[261, 177, 140, 139, 255])).
% 1.03/0.90 tff(263,plain,
% 1.03/0.90 (hskp23),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[262, 245, 127])).
% 1.03/0.90 tff(264,plain,
% 1.03/0.90 (((~hskp23) | (~c3_1(a1261))) <=> ((~hskp23) | (~c3_1(a1261)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(265,plain,
% 1.03/0.90 (((~c3_1(a1261)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a1261)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(266,axiom,((~c3_1(a1261)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 1.03/0.90 tff(267,plain,
% 1.03/0.90 ((~hskp23) | (~c3_1(a1261))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[266, 265])).
% 1.03/0.90 tff(268,plain,
% 1.03/0.90 ((~hskp23) | (~c3_1(a1261))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[267, 264])).
% 1.03/0.90 tff(269,plain,
% 1.03/0.90 (~c3_1(a1261)),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[268, 263])).
% 1.03/0.90 tff(270,plain,
% 1.03/0.90 (((~hskp23) | (~c2_1(a1261))) <=> ((~hskp23) | (~c2_1(a1261)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(271,plain,
% 1.03/0.90 (((~c2_1(a1261)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a1261)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(272,axiom,((~c2_1(a1261)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 1.03/0.90 tff(273,plain,
% 1.03/0.90 ((~hskp23) | (~c2_1(a1261))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[272, 271])).
% 1.03/0.90 tff(274,plain,
% 1.03/0.90 ((~hskp23) | (~c2_1(a1261))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[273, 270])).
% 1.03/0.90 tff(275,plain,
% 1.03/0.90 (~c2_1(a1261)),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[274, 263])).
% 1.03/0.90 tff(276,plain,
% 1.03/0.90 (((~hskp23) | (~c0_1(a1261))) <=> ((~hskp23) | (~c0_1(a1261)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(277,plain,
% 1.03/0.90 (((~c0_1(a1261)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a1261)))),
% 1.03/0.90 inference(rewrite,[status(thm)],[])).
% 1.03/0.90 tff(278,axiom,((~c0_1(a1261)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 1.03/0.90 tff(279,plain,
% 1.03/0.90 ((~hskp23) | (~c0_1(a1261))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[278, 277])).
% 1.03/0.90 tff(280,plain,
% 1.03/0.90 ((~hskp23) | (~c0_1(a1261))),
% 1.03/0.90 inference(modus_ponens,[status(thm)],[279, 276])).
% 1.03/0.90 tff(281,plain,
% 1.03/0.90 (~c0_1(a1261)),
% 1.03/0.90 inference(unit_resolution,[status(thm)],[280, 263])).
% 1.03/0.90 tff(282,plain,
% 1.03/0.90 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c0_1(a1261) | c2_1(a1261) | c3_1(a1261) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c0_1(a1261) | c2_1(a1261) | c3_1(a1261) | (~ndr1_0))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(283,plain,
% 1.03/0.91 ((hskp28 | (~ndr1_0) | c3_1(a1261) | c2_1(a1261) | c0_1(a1261)) <=> (hskp28 | c0_1(a1261) | c2_1(a1261) | c3_1(a1261) | (~ndr1_0))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(284,plain,
% 1.03/0.91 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1261) | c2_1(a1261) | c0_1(a1261))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c0_1(a1261) | c2_1(a1261) | c3_1(a1261) | (~ndr1_0)))),
% 1.03/0.91 inference(monotonicity,[status(thm)],[283])).
% 1.03/0.91 tff(285,plain,
% 1.03/0.91 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1261) | c2_1(a1261) | c0_1(a1261))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c0_1(a1261) | c2_1(a1261) | c3_1(a1261) | (~ndr1_0))),
% 1.03/0.91 inference(transitivity,[status(thm)],[284, 282])).
% 1.03/0.91 tff(286,plain,
% 1.03/0.91 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1261) | c2_1(a1261) | c0_1(a1261))),
% 1.03/0.91 inference(quant_inst,[status(thm)],[])).
% 1.03/0.91 tff(287,plain,
% 1.03/0.91 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c0_1(a1261) | c2_1(a1261) | c3_1(a1261) | (~ndr1_0)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[286, 285])).
% 1.03/0.91 tff(288,plain,
% 1.03/0.91 ($false),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[287, 219, 177, 281, 275, 269, 218])).
% 1.03/0.91 tff(289,plain,(hskp28 | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1205) | c3_1(a1215) | c0_1(a1205) | c1_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 1.03/0.91 tff(290,plain,
% 1.03/0.91 (hskp28),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[289, 116, 139, 140, 138, 22, 23])).
% 1.03/0.91 tff(291,plain,
% 1.03/0.91 (((~hskp28) | c3_1(a1214)) <=> ((~hskp28) | c3_1(a1214))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(292,axiom,((~hskp28) | c3_1(a1214)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 1.03/0.91 tff(293,plain,
% 1.03/0.91 ((~hskp28) | c3_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[292, 291])).
% 1.03/0.91 tff(294,plain,
% 1.03/0.91 ((~hskp28) | c3_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[293, 291])).
% 1.03/0.91 tff(295,plain,
% 1.03/0.91 ((~hskp28) | c3_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[294, 291])).
% 1.03/0.91 tff(296,plain,
% 1.03/0.91 ((~hskp28) | c3_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[295, 291])).
% 1.03/0.91 tff(297,plain,
% 1.03/0.91 ((~hskp28) | c3_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[296, 291])).
% 1.03/0.91 tff(298,plain,
% 1.03/0.91 ((~hskp28) | c3_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[297, 291])).
% 1.03/0.91 tff(299,plain,
% 1.03/0.91 ((~hskp28) | c3_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[298, 291])).
% 1.03/0.91 tff(300,plain,
% 1.03/0.91 ((~hskp28) | c3_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[299, 291])).
% 1.03/0.91 tff(301,plain,
% 1.03/0.91 (c3_1(a1214)),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[300, 290])).
% 1.03/0.91 tff(302,plain,
% 1.03/0.91 (((~hskp28) | c1_1(a1214)) <=> ((~hskp28) | c1_1(a1214))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(303,axiom,((~hskp28) | c1_1(a1214)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 1.03/0.91 tff(304,plain,
% 1.03/0.91 ((~hskp28) | c1_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[303, 302])).
% 1.03/0.91 tff(305,plain,
% 1.03/0.91 ((~hskp28) | c1_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[304, 302])).
% 1.03/0.91 tff(306,plain,
% 1.03/0.91 ((~hskp28) | c1_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[305, 302])).
% 1.03/0.91 tff(307,plain,
% 1.03/0.91 ((~hskp28) | c1_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[306, 302])).
% 1.03/0.91 tff(308,plain,
% 1.03/0.91 ((~hskp28) | c1_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[307, 302])).
% 1.03/0.91 tff(309,plain,
% 1.03/0.91 ((~hskp28) | c1_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[308, 302])).
% 1.03/0.91 tff(310,plain,
% 1.03/0.91 ((~hskp28) | c1_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[309, 302])).
% 1.03/0.91 tff(311,plain,
% 1.03/0.91 ((~hskp28) | c1_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[310, 302])).
% 1.03/0.91 tff(312,plain,
% 1.03/0.91 (c1_1(a1214)),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[311, 290])).
% 1.03/0.91 tff(313,plain,
% 1.03/0.91 (((~hskp28) | c0_1(a1214)) <=> ((~hskp28) | c0_1(a1214))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(314,axiom,((~hskp28) | c0_1(a1214)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 1.03/0.91 tff(315,plain,
% 1.03/0.91 ((~hskp28) | c0_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[314, 313])).
% 1.03/0.91 tff(316,plain,
% 1.03/0.91 ((~hskp28) | c0_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[315, 313])).
% 1.03/0.91 tff(317,plain,
% 1.03/0.91 ((~hskp28) | c0_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[316, 313])).
% 1.03/0.91 tff(318,plain,
% 1.03/0.91 ((~hskp28) | c0_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[317, 313])).
% 1.03/0.91 tff(319,plain,
% 1.03/0.91 ((~hskp28) | c0_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[318, 313])).
% 1.03/0.91 tff(320,plain,
% 1.03/0.91 ((~hskp28) | c0_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[319, 313])).
% 1.03/0.91 tff(321,plain,
% 1.03/0.91 ((~hskp28) | c0_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[320, 313])).
% 1.03/0.91 tff(322,plain,
% 1.03/0.91 ((~hskp28) | c0_1(a1214)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[321, 313])).
% 1.03/0.91 tff(323,plain,
% 1.03/0.91 (c0_1(a1214)),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[322, 290])).
% 1.03/0.91 tff(324,plain,
% 1.03/0.91 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(325,plain,
% 1.03/0.91 ((hskp5 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257))) <=> (hskp5 | c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(326,plain,
% 1.03/0.91 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 1.03/0.91 inference(monotonicity,[status(thm)],[325])).
% 1.03/0.91 tff(327,plain,
% 1.03/0.91 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.03/0.91 inference(transitivity,[status(thm)],[326, 324])).
% 1.03/0.91 tff(328,plain,
% 1.03/0.91 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))),
% 1.03/0.91 inference(quant_inst,[status(thm)],[])).
% 1.03/0.91 tff(329,plain,
% 1.03/0.91 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[328, 327])).
% 1.03/0.91 tff(330,plain,
% 1.03/0.91 ($false),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[329, 177, 21, 323, 312, 301, 208, 197, 191, 20])).
% 1.03/0.91 tff(331,plain,(c2_1(a1205) | hskp5 | (~c2_1(a1215)) | (~c1_1(a1215)) | c3_1(a1215) | c0_1(a1205) | c1_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 1.03/0.91 tff(332,plain,
% 1.03/0.91 (c2_1(a1205)),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[331, 115, 21, 104, 93, 22, 23])).
% 1.03/0.91 tff(333,assumption,(~hskp11), introduced(assumption)).
% 1.03/0.91 tff(334,plain,
% 1.03/0.91 (^[U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.03/0.91 inference(bind,[status(th)],[])).
% 1.03/0.91 tff(335,plain,
% 1.03/0.91 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.03/0.91 inference(quant_intro,[status(thm)],[334])).
% 1.03/0.91 tff(336,plain,
% 1.03/0.91 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(337,plain,
% 1.03/0.91 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.03/0.91 inference(bind,[status(th)],[])).
% 1.03/0.91 tff(338,plain,
% 1.03/0.91 (![U: $i] : (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11) <=> ![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.03/0.91 inference(quant_intro,[status(thm)],[337])).
% 1.03/0.91 tff(339,axiom,(![U: $i] : (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 1.03/0.91 tff(340,plain,
% 1.03/0.91 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[339, 338])).
% 1.03/0.91 tff(341,plain,
% 1.03/0.91 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[340, 336])).
% 1.03/0.91 tff(342,plain,(
% 1.03/0.91 ![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.03/0.91 inference(skolemize,[status(sab)],[341])).
% 1.03/0.91 tff(343,plain,
% 1.03/0.91 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[342, 335])).
% 1.03/0.91 tff(344,plain,
% 1.03/0.91 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c2_1(a1215)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c2_1(a1215)))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(345,plain,
% 1.03/0.91 ((hskp11 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c2_1(a1215))) <=> (hskp11 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c2_1(a1215)))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(346,plain,
% 1.03/0.91 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c2_1(a1215)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c2_1(a1215))))),
% 1.03/0.91 inference(monotonicity,[status(thm)],[345])).
% 1.03/0.91 tff(347,plain,
% 1.03/0.91 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c2_1(a1215)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c2_1(a1215)))),
% 1.03/0.91 inference(transitivity,[status(thm)],[346, 344])).
% 1.03/0.91 tff(348,plain,
% 1.03/0.91 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c2_1(a1215)))),
% 1.03/0.91 inference(quant_inst,[status(thm)],[])).
% 1.03/0.91 tff(349,plain,
% 1.03/0.91 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c2_1(a1215))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[348, 347])).
% 1.03/0.91 tff(350,plain,
% 1.03/0.91 (hskp11 | c0_1(a1215)),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[349, 177, 139, 138, 343])).
% 1.03/0.91 tff(351,plain,
% 1.03/0.91 (c0_1(a1215)),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[350, 333])).
% 1.03/0.91 tff(352,assumption,(hskp4), introduced(assumption)).
% 1.03/0.91 tff(353,plain,
% 1.03/0.91 (((~hskp4) | (~c2_1(a1211))) <=> ((~hskp4) | (~c2_1(a1211)))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(354,plain,
% 1.03/0.91 (((~c2_1(a1211)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a1211)))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(355,axiom,((~c2_1(a1211)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.03/0.91 tff(356,plain,
% 1.03/0.91 ((~hskp4) | (~c2_1(a1211))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[355, 354])).
% 1.03/0.91 tff(357,plain,
% 1.03/0.91 ((~hskp4) | (~c2_1(a1211))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[356, 353])).
% 1.03/0.91 tff(358,plain,
% 1.03/0.91 (~c2_1(a1211)),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[357, 352])).
% 1.03/0.91 tff(359,plain,
% 1.03/0.91 (((~hskp4) | (~c0_1(a1211))) <=> ((~hskp4) | (~c0_1(a1211)))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(360,plain,
% 1.03/0.91 (((~c0_1(a1211)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a1211)))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(361,axiom,((~c0_1(a1211)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 1.03/0.91 tff(362,plain,
% 1.03/0.91 ((~hskp4) | (~c0_1(a1211))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[361, 360])).
% 1.03/0.91 tff(363,plain,
% 1.03/0.91 ((~hskp4) | (~c0_1(a1211))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[362, 359])).
% 1.03/0.91 tff(364,plain,
% 1.03/0.91 (~c0_1(a1211)),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[363, 352])).
% 1.03/0.91 tff(365,plain,
% 1.03/0.91 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | c3_1(a1211))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | c3_1(a1211))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(366,plain,
% 1.03/0.91 ((hskp28 | (~ndr1_0) | c3_1(a1211) | c2_1(a1211) | c0_1(a1211)) <=> (hskp28 | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | c3_1(a1211))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(367,plain,
% 1.03/0.91 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1211) | c2_1(a1211) | c0_1(a1211))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | c3_1(a1211)))),
% 1.03/0.91 inference(monotonicity,[status(thm)],[366])).
% 1.03/0.91 tff(368,plain,
% 1.03/0.91 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1211) | c2_1(a1211) | c0_1(a1211))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | c3_1(a1211))),
% 1.03/0.91 inference(transitivity,[status(thm)],[367, 365])).
% 1.03/0.91 tff(369,plain,
% 1.03/0.91 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1211) | c2_1(a1211) | c0_1(a1211))),
% 1.03/0.91 inference(quant_inst,[status(thm)],[])).
% 1.03/0.91 tff(370,plain,
% 1.03/0.91 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | c3_1(a1211)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[369, 368])).
% 1.03/0.91 tff(371,plain,
% 1.03/0.91 (c3_1(a1211)),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[370, 219, 177, 364, 358, 218])).
% 1.03/0.91 tff(372,assumption,(c0_1(a1215)), introduced(assumption)).
% 1.03/0.91 tff(373,plain,
% 1.03/0.91 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.03/0.91 inference(bind,[status(th)],[])).
% 1.03/0.91 tff(374,plain,
% 1.03/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.03/0.91 inference(quant_intro,[status(thm)],[373])).
% 1.03/0.91 tff(375,plain,
% 1.03/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(376,plain,
% 1.03/0.91 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.03/0.91 inference(bind,[status(th)],[])).
% 1.03/0.91 tff(377,plain,
% 1.03/0.91 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.03/0.91 inference(quant_intro,[status(thm)],[376])).
% 1.03/0.91 tff(378,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 1.03/0.91 tff(379,plain,
% 1.03/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[378, 377])).
% 1.03/0.91 tff(380,plain,
% 1.03/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[379, 375])).
% 1.03/0.91 tff(381,plain,(
% 1.03/0.91 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.03/0.91 inference(skolemize,[status(sab)],[380])).
% 1.03/0.91 tff(382,plain,
% 1.03/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[381, 374])).
% 1.03/0.91 tff(383,plain,
% 1.03/0.91 (((~hskp4) | c1_1(a1211)) <=> ((~hskp4) | c1_1(a1211))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(384,axiom,((~hskp4) | c1_1(a1211)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 1.03/0.91 tff(385,plain,
% 1.03/0.91 ((~hskp4) | c1_1(a1211)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[384, 383])).
% 1.03/0.91 tff(386,plain,
% 1.03/0.91 ((~hskp4) | c1_1(a1211)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[385, 383])).
% 1.03/0.91 tff(387,plain,
% 1.03/0.91 ((~hskp4) | c1_1(a1211)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[386, 383])).
% 1.03/0.91 tff(388,plain,
% 1.03/0.91 ((~hskp4) | c1_1(a1211)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[387, 383])).
% 1.03/0.91 tff(389,plain,
% 1.03/0.91 ((~hskp4) | c1_1(a1211)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[388, 383])).
% 1.03/0.91 tff(390,plain,
% 1.03/0.91 ((~hskp4) | c1_1(a1211)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[389, 383])).
% 1.03/0.91 tff(391,plain,
% 1.03/0.91 ((~hskp4) | c1_1(a1211)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[390, 383])).
% 1.03/0.91 tff(392,plain,
% 1.03/0.91 ((~hskp4) | c1_1(a1211)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[391, 383])).
% 1.03/0.91 tff(393,plain,
% 1.03/0.91 (c1_1(a1211)),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[392, 352])).
% 1.03/0.91 tff(394,plain,
% 1.03/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c3_1(a1211)) | (~c1_1(a1211)) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c3_1(a1211)) | (~c1_1(a1211)) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(395,plain,
% 1.03/0.91 (((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1211) | (~c3_1(a1211)) | (~c1_1(a1211)) | c2_1(a1211) | c0_1(a1211) | (~c3_1(a1211))) <=> (c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c3_1(a1211)) | (~c1_1(a1211)) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(396,plain,
% 1.03/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1211) | (~c3_1(a1211)) | (~c1_1(a1211)) | c2_1(a1211) | c0_1(a1211) | (~c3_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c3_1(a1211)) | (~c1_1(a1211)) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215))))),
% 1.03/0.91 inference(monotonicity,[status(thm)],[395])).
% 1.03/0.91 tff(397,plain,
% 1.03/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1211) | (~c3_1(a1211)) | (~c1_1(a1211)) | c2_1(a1211) | c0_1(a1211) | (~c3_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c3_1(a1211)) | (~c1_1(a1211)) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)))),
% 1.03/0.91 inference(transitivity,[status(thm)],[396, 394])).
% 1.03/0.91 tff(398,plain,
% 1.03/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1211) | (~c3_1(a1211)) | (~c1_1(a1211)) | c2_1(a1211) | c0_1(a1211) | (~c3_1(a1211)))),
% 1.03/0.91 inference(quant_inst,[status(thm)],[])).
% 1.03/0.91 tff(399,plain,
% 1.03/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c3_1(a1211)) | (~c1_1(a1211)) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[398, 397])).
% 1.03/0.91 tff(400,plain,
% 1.03/0.91 ($false),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[399, 177, 140, 139, 393, 364, 358, 382, 372, 371])).
% 1.03/0.91 tff(401,plain,((~hskp4) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1215)) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.03/0.91 tff(402,plain,
% 1.03/0.91 (~hskp4),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[401, 351, 139, 140, 219])).
% 1.03/0.91 tff(403,plain,
% 1.03/0.91 (^[U: $i] : refl((hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 1.03/0.91 inference(bind,[status(th)],[])).
% 1.03/0.91 tff(404,plain,
% 1.03/0.91 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.03/0.91 inference(quant_intro,[status(thm)],[403])).
% 1.03/0.91 tff(405,plain,
% 1.03/0.91 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(406,plain,
% 1.03/0.91 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp15) | hskp4) <=> ((hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp4))), rewrite(((hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp4) <=> (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp15) | hskp4) <=> (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 1.03/0.91 inference(bind,[status(th)],[])).
% 1.03/0.91 tff(407,plain,
% 1.03/0.91 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp15) | hskp4) <=> ![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.03/0.91 inference(quant_intro,[status(thm)],[406])).
% 1.03/0.91 tff(408,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp15) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 1.03/0.91 tff(409,plain,
% 1.03/0.91 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[408, 407])).
% 1.03/0.91 tff(410,plain,
% 1.03/0.91 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[409, 405])).
% 1.03/0.91 tff(411,plain,(
% 1.03/0.91 ![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.03/0.91 inference(skolemize,[status(sab)],[410])).
% 1.03/0.91 tff(412,plain,
% 1.03/0.91 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[411, 404])).
% 1.03/0.91 tff(413,assumption,(hskp14), introduced(assumption)).
% 1.03/0.91 tff(414,plain,
% 1.03/0.91 (((~hskp14) | (~c2_1(a1232))) <=> ((~hskp14) | (~c2_1(a1232)))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(415,plain,
% 1.03/0.91 (((~c2_1(a1232)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a1232)))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(416,axiom,((~c2_1(a1232)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 1.03/0.91 tff(417,plain,
% 1.03/0.91 ((~hskp14) | (~c2_1(a1232))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[416, 415])).
% 1.03/0.91 tff(418,plain,
% 1.03/0.91 ((~hskp14) | (~c2_1(a1232))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[417, 414])).
% 1.03/0.91 tff(419,plain,
% 1.03/0.91 (~c2_1(a1232)),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[418, 413])).
% 1.03/0.91 tff(420,plain,
% 1.03/0.91 (((~hskp14) | c3_1(a1232)) <=> ((~hskp14) | c3_1(a1232))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(421,axiom,((~hskp14) | c3_1(a1232)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 1.03/0.91 tff(422,plain,
% 1.03/0.91 ((~hskp14) | c3_1(a1232)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[421, 420])).
% 1.03/0.91 tff(423,plain,
% 1.03/0.91 ((~hskp14) | c3_1(a1232)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[422, 420])).
% 1.03/0.91 tff(424,plain,
% 1.03/0.91 ((~hskp14) | c3_1(a1232)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[423, 420])).
% 1.03/0.91 tff(425,plain,
% 1.03/0.91 ((~hskp14) | c3_1(a1232)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[424, 420])).
% 1.03/0.91 tff(426,plain,
% 1.03/0.91 ((~hskp14) | c3_1(a1232)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[425, 420])).
% 1.03/0.91 tff(427,plain,
% 1.03/0.91 ((~hskp14) | c3_1(a1232)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[426, 420])).
% 1.03/0.91 tff(428,plain,
% 1.03/0.91 ((~hskp14) | c3_1(a1232)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[427, 420])).
% 1.03/0.91 tff(429,plain,
% 1.03/0.91 ((~hskp14) | c3_1(a1232)),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[428, 420])).
% 1.03/0.91 tff(430,plain,
% 1.03/0.91 (c3_1(a1232)),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[429, 413])).
% 1.03/0.91 tff(431,assumption,(~hskp4), introduced(assumption)).
% 1.03/0.91 tff(432,plain,
% 1.03/0.91 (((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | c2_1(a1232) | (~ndr1_0) | c1_1(a1232) | (~c3_1(a1232)))) <=> ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp15 | hskp4 | c2_1(a1232) | (~ndr1_0) | c1_1(a1232) | (~c3_1(a1232)))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(433,plain,
% 1.03/0.91 ((hskp15 | hskp4 | (~ndr1_0) | c2_1(a1232) | c1_1(a1232) | (~c3_1(a1232))) <=> (hskp15 | hskp4 | c2_1(a1232) | (~ndr1_0) | c1_1(a1232) | (~c3_1(a1232)))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(434,plain,
% 1.03/0.91 (((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | (~ndr1_0) | c2_1(a1232) | c1_1(a1232) | (~c3_1(a1232)))) <=> ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | c2_1(a1232) | (~ndr1_0) | c1_1(a1232) | (~c3_1(a1232))))),
% 1.03/0.91 inference(monotonicity,[status(thm)],[433])).
% 1.03/0.91 tff(435,plain,
% 1.03/0.91 (((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | (~ndr1_0) | c2_1(a1232) | c1_1(a1232) | (~c3_1(a1232)))) <=> ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp15 | hskp4 | c2_1(a1232) | (~ndr1_0) | c1_1(a1232) | (~c3_1(a1232)))),
% 1.03/0.91 inference(transitivity,[status(thm)],[434, 432])).
% 1.03/0.91 tff(436,plain,
% 1.03/0.91 ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | (~ndr1_0) | c2_1(a1232) | c1_1(a1232) | (~c3_1(a1232)))),
% 1.03/0.91 inference(quant_inst,[status(thm)],[])).
% 1.03/0.91 tff(437,plain,
% 1.03/0.91 ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp15 | hskp4 | c2_1(a1232) | (~ndr1_0) | c1_1(a1232) | (~c3_1(a1232))),
% 1.03/0.91 inference(modus_ponens,[status(thm)],[436, 435])).
% 1.03/0.91 tff(438,plain,
% 1.03/0.91 (c1_1(a1232)),
% 1.03/0.91 inference(unit_resolution,[status(thm)],[437, 177, 75, 431, 430, 419, 412])).
% 1.03/0.91 tff(439,plain,
% 1.03/0.91 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.03/0.91 inference(bind,[status(th)],[])).
% 1.03/0.91 tff(440,plain,
% 1.03/0.91 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.03/0.91 inference(quant_intro,[status(thm)],[439])).
% 1.03/0.91 tff(441,plain,
% 1.03/0.91 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.03/0.91 inference(rewrite,[status(thm)],[])).
% 1.03/0.91 tff(442,plain,
% 1.03/0.91 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.03/0.92 inference(bind,[status(th)],[])).
% 1.03/0.92 tff(443,plain,
% 1.03/0.92 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.03/0.92 inference(quant_intro,[status(thm)],[442])).
% 1.03/0.92 tff(444,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 1.03/0.92 tff(445,plain,
% 1.03/0.92 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[444, 443])).
% 1.03/0.92 tff(446,plain,
% 1.03/0.92 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[445, 441])).
% 1.03/0.92 tff(447,plain,(
% 1.03/0.92 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.03/0.92 inference(skolemize,[status(sab)],[446])).
% 1.03/0.92 tff(448,plain,
% 1.03/0.92 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[447, 440])).
% 1.03/0.92 tff(449,plain,
% 1.03/0.92 (((~hskp14) | (~c0_1(a1232))) <=> ((~hskp14) | (~c0_1(a1232)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(450,plain,
% 1.03/0.92 (((~c0_1(a1232)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a1232)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(451,axiom,((~c0_1(a1232)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 1.03/0.92 tff(452,plain,
% 1.03/0.92 ((~hskp14) | (~c0_1(a1232))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[451, 450])).
% 1.03/0.92 tff(453,plain,
% 1.03/0.92 ((~hskp14) | (~c0_1(a1232))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[452, 449])).
% 1.03/0.92 tff(454,plain,
% 1.03/0.92 (~c0_1(a1232)),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[453, 413])).
% 1.03/0.92 tff(455,plain,
% 1.03/0.92 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c0_1(a1232) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1232)) | (~c1_1(a1232)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c0_1(a1232) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(456,plain,
% 1.03/0.92 ((hskp11 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c1_1(a1215)) | c0_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232))) <=> (hskp11 | c0_1(a1232) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(457,plain,
% 1.03/0.92 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c1_1(a1215)) | c0_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c0_1(a1232) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1232)) | (~c1_1(a1232))))),
% 1.03/0.92 inference(monotonicity,[status(thm)],[456])).
% 1.03/0.92 tff(458,plain,
% 1.03/0.92 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c1_1(a1215)) | c0_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c0_1(a1232) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 1.03/0.92 inference(transitivity,[status(thm)],[457, 455])).
% 1.03/0.92 tff(459,plain,
% 1.03/0.92 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c1_1(a1215)) | c0_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 1.03/0.92 inference(quant_inst,[status(thm)],[])).
% 1.03/0.92 tff(460,plain,
% 1.03/0.92 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c0_1(a1232) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1232)) | (~c1_1(a1232))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[459, 458])).
% 1.03/0.92 tff(461,plain,
% 1.03/0.92 ($false),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[460, 177, 333, 430, 140, 139, 454, 138, 448, 438])).
% 1.03/0.92 tff(462,plain,((~hskp14) | hskp11 | (~c1_1(a1215)) | (~c2_1(a1215)) | c3_1(a1215) | hskp15 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.03/0.92 tff(463,plain,
% 1.03/0.92 (~hskp14),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[462, 402, 140, 139, 138, 75, 333])).
% 1.03/0.92 tff(464,plain,
% 1.03/0.92 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 1.03/0.92 inference(bind,[status(th)],[])).
% 1.03/0.92 tff(465,plain,
% 1.03/0.92 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.03/0.92 inference(quant_intro,[status(thm)],[464])).
% 1.03/0.92 tff(466,plain,
% 1.03/0.92 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(467,plain,
% 1.03/0.92 (^[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(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)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | 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)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | 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)) | (~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)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_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)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 1.03/0.92 inference(bind,[status(th)],[])).
% 1.03/0.92 tff(468,plain,
% 1.03/0.92 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.03/0.92 inference(quant_intro,[status(thm)],[467])).
% 1.03/0.92 tff(469,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 1.03/0.92 tff(470,plain,
% 1.03/0.92 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[469, 468])).
% 1.03/0.92 tff(471,plain,
% 1.03/0.92 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[470, 466])).
% 1.03/0.92 tff(472,plain,(
% 1.03/0.92 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.03/0.92 inference(skolemize,[status(sab)],[471])).
% 1.03/0.92 tff(473,plain,
% 1.03/0.92 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[472, 465])).
% 1.03/0.92 tff(474,assumption,(hskp24), introduced(assumption)).
% 1.03/0.92 tff(475,plain,
% 1.03/0.92 (((~hskp24) | (~c2_1(a1267))) <=> ((~hskp24) | (~c2_1(a1267)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(476,plain,
% 1.03/0.92 (((~c2_1(a1267)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a1267)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(477,axiom,((~c2_1(a1267)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 1.03/0.92 tff(478,plain,
% 1.03/0.92 ((~hskp24) | (~c2_1(a1267))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[477, 476])).
% 1.03/0.92 tff(479,plain,
% 1.03/0.92 ((~hskp24) | (~c2_1(a1267))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[478, 475])).
% 1.03/0.92 tff(480,plain,
% 1.03/0.92 (~c2_1(a1267)),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[479, 474])).
% 1.03/0.92 tff(481,plain,
% 1.03/0.92 (((~hskp24) | (~c1_1(a1267))) <=> ((~hskp24) | (~c1_1(a1267)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(482,plain,
% 1.03/0.92 (((~c1_1(a1267)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a1267)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(483,axiom,((~c1_1(a1267)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 1.03/0.92 tff(484,plain,
% 1.03/0.92 ((~hskp24) | (~c1_1(a1267))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[483, 482])).
% 1.03/0.92 tff(485,plain,
% 1.03/0.92 ((~hskp24) | (~c1_1(a1267))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[484, 481])).
% 1.03/0.92 tff(486,plain,
% 1.03/0.92 (~c1_1(a1267)),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[485, 474])).
% 1.03/0.92 tff(487,plain,
% 1.03/0.92 (((~hskp24) | c0_1(a1267)) <=> ((~hskp24) | c0_1(a1267))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(488,axiom,((~hskp24) | c0_1(a1267)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 1.03/0.92 tff(489,plain,
% 1.03/0.92 ((~hskp24) | c0_1(a1267)),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[488, 487])).
% 1.03/0.92 tff(490,plain,
% 1.03/0.92 ((~hskp24) | c0_1(a1267)),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[489, 487])).
% 1.03/0.92 tff(491,plain,
% 1.03/0.92 ((~hskp24) | c0_1(a1267)),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[490, 487])).
% 1.03/0.92 tff(492,plain,
% 1.03/0.92 ((~hskp24) | c0_1(a1267)),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[491, 487])).
% 1.03/0.92 tff(493,plain,
% 1.03/0.92 ((~hskp24) | c0_1(a1267)),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[492, 487])).
% 1.03/0.92 tff(494,plain,
% 1.03/0.92 ((~hskp24) | c0_1(a1267)),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[493, 487])).
% 1.03/0.92 tff(495,plain,
% 1.03/0.92 ((~hskp24) | c0_1(a1267)),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[494, 487])).
% 1.03/0.92 tff(496,plain,
% 1.03/0.92 ((~hskp24) | c0_1(a1267)),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[495, 487])).
% 1.03/0.92 tff(497,plain,
% 1.03/0.92 (c0_1(a1267)),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[496, 474])).
% 1.03/0.92 tff(498,assumption,(~hskp14), introduced(assumption)).
% 1.03/0.92 tff(499,plain,
% 1.03/0.92 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(500,plain,
% 1.03/0.92 ((hskp14 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c0_1(a1215)) | c1_1(a1267) | c2_1(a1267) | (~c0_1(a1267))) <=> (hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(501,plain,
% 1.03/0.92 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c0_1(a1215)) | c1_1(a1267) | c2_1(a1267) | (~c0_1(a1267)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267))))),
% 1.03/0.92 inference(monotonicity,[status(thm)],[500])).
% 1.03/0.92 tff(502,plain,
% 1.03/0.92 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c0_1(a1215)) | c1_1(a1267) | c2_1(a1267) | (~c0_1(a1267)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)))),
% 1.03/0.92 inference(transitivity,[status(thm)],[501, 499])).
% 1.03/0.92 tff(503,plain,
% 1.03/0.92 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1215) | (~c2_1(a1215)) | (~c0_1(a1215)) | c1_1(a1267) | c2_1(a1267) | (~c0_1(a1267)))),
% 1.03/0.92 inference(quant_inst,[status(thm)],[])).
% 1.03/0.92 tff(504,plain,
% 1.03/0.92 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[503, 502])).
% 1.03/0.92 tff(505,plain,
% 1.03/0.92 ($false),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[504, 177, 498, 497, 139, 486, 480, 138, 473, 372])).
% 1.03/0.92 tff(506,plain,((~hskp24) | hskp14 | (~c2_1(a1215)) | c3_1(a1215) | (~c0_1(a1215))), inference(lemma,lemma(discharge,[]))).
% 1.03/0.92 tff(507,plain,
% 1.03/0.92 (~hskp24),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[506, 463, 139, 138, 351])).
% 1.03/0.92 tff(508,plain,
% 1.03/0.92 ((hskp24 | hskp19 | hskp14) <=> (hskp24 | hskp19 | hskp14)),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(509,plain,
% 1.03/0.92 (((hskp24 | hskp19) | hskp14) <=> (hskp24 | hskp19 | hskp14)),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(510,plain,
% 1.03/0.92 ((hskp24 | hskp19) <=> (hskp24 | hskp19)),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(511,plain,
% 1.03/0.92 (((hskp24 | hskp19) | hskp14) <=> ((hskp24 | hskp19) | hskp14)),
% 1.03/0.92 inference(monotonicity,[status(thm)],[510])).
% 1.03/0.92 tff(512,plain,
% 1.03/0.92 (((hskp24 | hskp19) | hskp14) <=> (hskp24 | hskp19 | hskp14)),
% 1.03/0.92 inference(transitivity,[status(thm)],[511, 509])).
% 1.03/0.92 tff(513,axiom,((hskp24 | hskp19) | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 1.03/0.92 tff(514,plain,
% 1.03/0.92 (hskp24 | hskp19 | hskp14),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[513, 512])).
% 1.03/0.92 tff(515,plain,
% 1.03/0.92 (hskp24 | hskp19 | hskp14),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[514, 508])).
% 1.03/0.92 tff(516,plain,
% 1.03/0.92 (hskp24 | hskp19 | hskp14),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[515, 508])).
% 1.03/0.92 tff(517,plain,
% 1.03/0.92 (hskp24 | hskp19 | hskp14),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[516, 508])).
% 1.03/0.92 tff(518,plain,
% 1.03/0.92 (hskp24 | hskp19 | hskp14),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[517, 508])).
% 1.03/0.92 tff(519,plain,
% 1.03/0.92 (hskp24 | hskp19 | hskp14),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[518, 508])).
% 1.03/0.92 tff(520,plain,
% 1.03/0.92 (hskp24 | hskp19 | hskp14),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[519, 508])).
% 1.03/0.92 tff(521,plain,
% 1.03/0.92 (hskp24 | hskp19 | hskp14),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[520, 508])).
% 1.03/0.92 tff(522,plain,
% 1.03/0.92 (hskp19),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[521, 507, 463])).
% 1.03/0.92 tff(523,plain,
% 1.03/0.92 (^[U: $i] : refl((hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.03/0.92 inference(bind,[status(th)],[])).
% 1.03/0.92 tff(524,plain,
% 1.03/0.92 (![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.92 inference(quant_intro,[status(thm)],[523])).
% 1.03/0.92 tff(525,plain,
% 1.03/0.92 (![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(526,plain,
% 1.03/0.92 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp11) | hskp8) <=> ((hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp8))), rewrite(((hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp8) <=> (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp11) | hskp8) <=> (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.03/0.92 inference(bind,[status(th)],[])).
% 1.03/0.92 tff(527,plain,
% 1.03/0.92 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp11) | hskp8) <=> ![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.92 inference(quant_intro,[status(thm)],[526])).
% 1.03/0.92 tff(528,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp11) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 1.03/0.92 tff(529,plain,
% 1.03/0.92 (![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[528, 527])).
% 1.03/0.92 tff(530,plain,
% 1.03/0.92 (![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[529, 525])).
% 1.03/0.92 tff(531,plain,(
% 1.03/0.92 ![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.92 inference(skolemize,[status(sab)],[530])).
% 1.03/0.92 tff(532,plain,
% 1.03/0.92 (![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[531, 524])).
% 1.03/0.92 tff(533,assumption,(hskp19), introduced(assumption)).
% 1.03/0.92 tff(534,plain,
% 1.03/0.92 (((~hskp19) | (~c2_1(a1247))) <=> ((~hskp19) | (~c2_1(a1247)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(535,plain,
% 1.03/0.92 (((~c2_1(a1247)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a1247)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(536,axiom,((~c2_1(a1247)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 1.03/0.92 tff(537,plain,
% 1.03/0.92 ((~hskp19) | (~c2_1(a1247))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[536, 535])).
% 1.03/0.92 tff(538,plain,
% 1.03/0.92 ((~hskp19) | (~c2_1(a1247))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[537, 534])).
% 1.03/0.92 tff(539,plain,
% 1.03/0.92 (~c2_1(a1247)),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[538, 533])).
% 1.03/0.92 tff(540,plain,
% 1.03/0.92 (((~hskp19) | c1_1(a1247)) <=> ((~hskp19) | c1_1(a1247))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(541,axiom,((~hskp19) | c1_1(a1247)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 1.03/0.92 tff(542,plain,
% 1.03/0.92 ((~hskp19) | c1_1(a1247)),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[541, 540])).
% 1.03/0.92 tff(543,plain,
% 1.03/0.92 ((~hskp19) | c1_1(a1247)),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[542, 540])).
% 1.03/0.92 tff(544,plain,
% 1.03/0.92 ((~hskp19) | c1_1(a1247)),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[543, 540])).
% 1.03/0.92 tff(545,plain,
% 1.03/0.92 ((~hskp19) | c1_1(a1247)),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[544, 540])).
% 1.03/0.92 tff(546,plain,
% 1.03/0.92 ((~hskp19) | c1_1(a1247)),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[545, 540])).
% 1.03/0.92 tff(547,plain,
% 1.03/0.92 ((~hskp19) | c1_1(a1247)),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[546, 540])).
% 1.03/0.92 tff(548,plain,
% 1.03/0.92 ((~hskp19) | c1_1(a1247)),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[547, 540])).
% 1.03/0.92 tff(549,plain,
% 1.03/0.92 ((~hskp19) | c1_1(a1247)),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[548, 540])).
% 1.03/0.92 tff(550,plain,
% 1.03/0.92 (c1_1(a1247)),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[549, 533])).
% 1.03/0.92 tff(551,assumption,(~hskp8), introduced(assumption)).
% 1.03/0.92 tff(552,plain,
% 1.03/0.92 (((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | c2_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)))) <=> ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp8 | c2_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(553,plain,
% 1.03/0.92 ((hskp11 | hskp8 | (~ndr1_0) | c2_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247))) <=> (hskp11 | hskp8 | c2_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(554,plain,
% 1.03/0.92 (((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | (~ndr1_0) | c2_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)))) <=> ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | c2_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247))))),
% 1.03/0.92 inference(monotonicity,[status(thm)],[553])).
% 1.03/0.92 tff(555,plain,
% 1.03/0.92 (((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | (~ndr1_0) | c2_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)))) <=> ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp8 | c2_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)))),
% 1.03/0.92 inference(transitivity,[status(thm)],[554, 552])).
% 1.03/0.92 tff(556,plain,
% 1.03/0.92 ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | (~ndr1_0) | c2_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)))),
% 1.03/0.92 inference(quant_inst,[status(thm)],[])).
% 1.03/0.92 tff(557,plain,
% 1.03/0.92 ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp8 | c2_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[556, 555])).
% 1.03/0.92 tff(558,plain,
% 1.03/0.92 (~c0_1(a1247)),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[557, 177, 333, 551, 550, 539, 532])).
% 1.03/0.92 tff(559,plain,
% 1.03/0.92 (((~hskp19) | (~c3_1(a1247))) <=> ((~hskp19) | (~c3_1(a1247)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(560,plain,
% 1.03/0.92 (((~c3_1(a1247)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a1247)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(561,axiom,((~c3_1(a1247)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 1.03/0.92 tff(562,plain,
% 1.03/0.92 ((~hskp19) | (~c3_1(a1247))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[561, 560])).
% 1.03/0.92 tff(563,plain,
% 1.03/0.92 ((~hskp19) | (~c3_1(a1247))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[562, 559])).
% 1.03/0.92 tff(564,plain,
% 1.03/0.92 (~c3_1(a1247)),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[563, 533])).
% 1.03/0.92 tff(565,plain,
% 1.03/0.92 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c0_1(a1247))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c0_1(a1247))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(566,plain,
% 1.03/0.92 ((hskp28 | (~ndr1_0) | c3_1(a1247) | c2_1(a1247) | c0_1(a1247)) <=> (hskp28 | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c0_1(a1247))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(567,plain,
% 1.03/0.92 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1247) | c2_1(a1247) | c0_1(a1247))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c0_1(a1247)))),
% 1.03/0.92 inference(monotonicity,[status(thm)],[566])).
% 1.03/0.92 tff(568,plain,
% 1.03/0.92 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1247) | c2_1(a1247) | c0_1(a1247))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c0_1(a1247))),
% 1.03/0.92 inference(transitivity,[status(thm)],[567, 565])).
% 1.03/0.92 tff(569,plain,
% 1.03/0.92 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1247) | c2_1(a1247) | c0_1(a1247))),
% 1.03/0.92 inference(quant_inst,[status(thm)],[])).
% 1.03/0.92 tff(570,plain,
% 1.03/0.92 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c0_1(a1247)),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[569, 568])).
% 1.03/0.92 tff(571,plain,
% 1.03/0.92 ($false),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[570, 219, 177, 539, 564, 218, 558])).
% 1.03/0.92 tff(572,plain,((~hskp19) | hskp28 | hskp11 | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.03/0.92 tff(573,plain,
% 1.03/0.92 (hskp8),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[572, 522, 333, 219])).
% 1.03/0.92 tff(574,plain,
% 1.03/0.92 (((~hskp8) | (~c0_1(a1217))) <=> ((~hskp8) | (~c0_1(a1217)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(575,plain,
% 1.03/0.92 (((~c0_1(a1217)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a1217)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(576,axiom,((~c0_1(a1217)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 1.03/0.92 tff(577,plain,
% 1.03/0.92 ((~hskp8) | (~c0_1(a1217))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[576, 575])).
% 1.03/0.92 tff(578,plain,
% 1.03/0.92 ((~hskp8) | (~c0_1(a1217))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[577, 574])).
% 1.03/0.92 tff(579,plain,
% 1.03/0.92 (~c0_1(a1217)),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[578, 573])).
% 1.03/0.92 tff(580,plain,
% 1.03/0.92 (((~hskp8) | (~c3_1(a1217))) <=> ((~hskp8) | (~c3_1(a1217)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(581,plain,
% 1.03/0.92 (((~c3_1(a1217)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a1217)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(582,axiom,((~c3_1(a1217)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 1.03/0.92 tff(583,plain,
% 1.03/0.92 ((~hskp8) | (~c3_1(a1217))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[582, 581])).
% 1.03/0.92 tff(584,plain,
% 1.03/0.92 ((~hskp8) | (~c3_1(a1217))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[583, 580])).
% 1.03/0.92 tff(585,plain,
% 1.03/0.92 (~c3_1(a1217)),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[584, 573])).
% 1.03/0.92 tff(586,assumption,(~c0_1(a1217)), introduced(assumption)).
% 1.03/0.92 tff(587,assumption,(~c3_1(a1217)), introduced(assumption)).
% 1.03/0.92 tff(588,plain,
% 1.03/0.92 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(589,plain,
% 1.03/0.92 ((hskp11 | (~ndr1_0) | c3_1(a1217) | c0_1(a1217) | (~c2_1(a1217))) <=> (hskp11 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(590,plain,
% 1.03/0.92 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1217) | c0_1(a1217) | (~c2_1(a1217)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217))))),
% 1.03/0.92 inference(monotonicity,[status(thm)],[589])).
% 1.03/0.92 tff(591,plain,
% 1.03/0.92 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1217) | c0_1(a1217) | (~c2_1(a1217)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)))),
% 1.03/0.92 inference(transitivity,[status(thm)],[590, 588])).
% 1.03/0.92 tff(592,plain,
% 1.03/0.92 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1217) | c0_1(a1217) | (~c2_1(a1217)))),
% 1.03/0.92 inference(quant_inst,[status(thm)],[])).
% 1.03/0.92 tff(593,plain,
% 1.03/0.92 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217))),
% 1.03/0.92 inference(modus_ponens,[status(thm)],[592, 591])).
% 1.03/0.92 tff(594,plain,
% 1.03/0.92 (c0_1(a1217) | (~c2_1(a1217))),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[593, 177, 333, 587, 343])).
% 1.03/0.92 tff(595,plain,
% 1.03/0.92 (~c2_1(a1217)),
% 1.03/0.92 inference(unit_resolution,[status(thm)],[594, 586])).
% 1.03/0.92 tff(596,plain,
% 1.03/0.92 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | c2_1(a1217))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | c2_1(a1217))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(597,plain,
% 1.03/0.92 ((hskp28 | (~ndr1_0) | c3_1(a1217) | c2_1(a1217) | c0_1(a1217)) <=> (hskp28 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | c2_1(a1217))),
% 1.03/0.92 inference(rewrite,[status(thm)],[])).
% 1.03/0.92 tff(598,plain,
% 1.03/0.92 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1217) | c2_1(a1217) | c0_1(a1217))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | c2_1(a1217)))),
% 1.03/0.92 inference(monotonicity,[status(thm)],[597])).
% 1.03/0.92 tff(599,plain,
% 1.03/0.92 (((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1217) | c2_1(a1217) | c0_1(a1217))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | c2_1(a1217))),
% 1.03/0.93 inference(transitivity,[status(thm)],[598, 596])).
% 1.03/0.93 tff(600,plain,
% 1.03/0.93 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp28 | (~ndr1_0) | c3_1(a1217) | c2_1(a1217) | c0_1(a1217))),
% 1.03/0.93 inference(quant_inst,[status(thm)],[])).
% 1.03/0.93 tff(601,plain,
% 1.03/0.93 ((~![U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp28 | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | c2_1(a1217)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[600, 599])).
% 1.03/0.93 tff(602,plain,
% 1.03/0.93 (c0_1(a1217) | c2_1(a1217)),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[601, 219, 177, 587, 218])).
% 1.03/0.93 tff(603,plain,
% 1.03/0.93 ($false),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[602, 595, 586])).
% 1.03/0.93 tff(604,plain,(c0_1(a1217) | hskp28 | c3_1(a1217) | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.03/0.93 tff(605,plain,
% 1.03/0.93 ($false),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[604, 585, 579, 219, 333])).
% 1.03/0.93 tff(606,plain,(hskp11 | hskp28 | (~c2_1(a1215)) | c3_1(a1215) | (~c1_1(a1215)) | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.03/0.93 tff(607,plain,
% 1.03/0.93 (hskp11),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[606, 219, 115, 93, 104, 75])).
% 1.03/0.93 tff(608,plain,
% 1.03/0.93 (((~hskp11) | (~c2_1(a1224))) <=> ((~hskp11) | (~c2_1(a1224)))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(609,plain,
% 1.03/0.93 (((~c2_1(a1224)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a1224)))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(610,axiom,((~c2_1(a1224)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 1.03/0.93 tff(611,plain,
% 1.03/0.93 ((~hskp11) | (~c2_1(a1224))),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[610, 609])).
% 1.03/0.93 tff(612,plain,
% 1.03/0.93 ((~hskp11) | (~c2_1(a1224))),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[611, 608])).
% 1.03/0.93 tff(613,plain,
% 1.03/0.93 (~c2_1(a1224)),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[612, 607])).
% 1.03/0.93 tff(614,plain,
% 1.03/0.93 (((~hskp11) | c3_1(a1224)) <=> ((~hskp11) | c3_1(a1224))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(615,axiom,((~hskp11) | c3_1(a1224)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 1.03/0.93 tff(616,plain,
% 1.03/0.93 ((~hskp11) | c3_1(a1224)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[615, 614])).
% 1.03/0.93 tff(617,plain,
% 1.03/0.93 ((~hskp11) | c3_1(a1224)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[616, 614])).
% 1.03/0.93 tff(618,plain,
% 1.03/0.93 ((~hskp11) | c3_1(a1224)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[617, 614])).
% 1.03/0.93 tff(619,plain,
% 1.03/0.93 ((~hskp11) | c3_1(a1224)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[618, 614])).
% 1.03/0.93 tff(620,plain,
% 1.03/0.93 ((~hskp11) | c3_1(a1224)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[619, 614])).
% 1.03/0.93 tff(621,plain,
% 1.03/0.93 ((~hskp11) | c3_1(a1224)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[620, 614])).
% 1.03/0.93 tff(622,plain,
% 1.03/0.93 ((~hskp11) | c3_1(a1224)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[621, 614])).
% 1.03/0.93 tff(623,plain,
% 1.03/0.93 ((~hskp11) | c3_1(a1224)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[622, 614])).
% 1.03/0.93 tff(624,plain,
% 1.03/0.93 (c3_1(a1224)),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[623, 607])).
% 1.03/0.93 tff(625,plain,
% 1.03/0.93 (((~hskp11) | c1_1(a1224)) <=> ((~hskp11) | c1_1(a1224))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(626,axiom,((~hskp11) | c1_1(a1224)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 1.03/0.93 tff(627,plain,
% 1.03/0.93 ((~hskp11) | c1_1(a1224)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[626, 625])).
% 1.03/0.93 tff(628,plain,
% 1.03/0.93 ((~hskp11) | c1_1(a1224)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[627, 625])).
% 1.03/0.93 tff(629,plain,
% 1.03/0.93 ((~hskp11) | c1_1(a1224)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[628, 625])).
% 1.03/0.93 tff(630,plain,
% 1.03/0.93 ((~hskp11) | c1_1(a1224)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[629, 625])).
% 1.03/0.93 tff(631,plain,
% 1.03/0.93 ((~hskp11) | c1_1(a1224)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[630, 625])).
% 1.03/0.93 tff(632,plain,
% 1.03/0.93 ((~hskp11) | c1_1(a1224)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[631, 625])).
% 1.03/0.93 tff(633,plain,
% 1.03/0.93 ((~hskp11) | c1_1(a1224)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[632, 625])).
% 1.03/0.93 tff(634,plain,
% 1.03/0.93 ((~hskp11) | c1_1(a1224)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[633, 625])).
% 1.03/0.93 tff(635,plain,
% 1.03/0.93 (c1_1(a1224)),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[634, 607])).
% 1.03/0.93 tff(636,assumption,(~c2_1(a1224)), introduced(assumption)).
% 1.03/0.93 tff(637,assumption,(c3_1(a1224)), introduced(assumption)).
% 1.03/0.93 tff(638,assumption,(c1_1(a1224)), introduced(assumption)).
% 1.03/0.93 tff(639,plain,
% 1.03/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(640,plain,
% 1.03/0.93 (((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1224) | c0_1(a1224) | (~c3_1(a1224))) <=> (c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(641,plain,
% 1.03/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1224) | c0_1(a1224) | (~c3_1(a1224)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224))))),
% 1.03/0.93 inference(monotonicity,[status(thm)],[640])).
% 1.03/0.93 tff(642,plain,
% 1.03/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1224) | c0_1(a1224) | (~c3_1(a1224)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.03/0.93 inference(transitivity,[status(thm)],[641, 639])).
% 1.03/0.93 tff(643,plain,
% 1.03/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1224) | c0_1(a1224) | (~c3_1(a1224)))),
% 1.03/0.93 inference(quant_inst,[status(thm)],[])).
% 1.03/0.93 tff(644,plain,
% 1.03/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224))),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[643, 642])).
% 1.03/0.93 tff(645,plain,
% 1.03/0.93 ((~c0_1(a1215)) | c0_1(a1224)),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[644, 177, 638, 637, 140, 139, 636, 382])).
% 1.03/0.93 tff(646,plain,
% 1.03/0.93 (c0_1(a1224)),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[645, 372])).
% 1.03/0.93 tff(647,plain,
% 1.03/0.93 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(648,plain,
% 1.03/0.93 ((hskp5 | (~ndr1_0) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c0_1(a1224)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205))) <=> (hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(649,plain,
% 1.03/0.93 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c0_1(a1224)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224))))),
% 1.03/0.93 inference(monotonicity,[status(thm)],[648])).
% 1.03/0.93 tff(650,plain,
% 1.03/0.93 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c0_1(a1224)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.03/0.93 inference(transitivity,[status(thm)],[649, 647])).
% 1.03/0.93 tff(651,plain,
% 1.03/0.93 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c0_1(a1224)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))),
% 1.03/0.93 inference(quant_inst,[status(thm)],[])).
% 1.03/0.93 tff(652,plain,
% 1.03/0.93 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224))),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[651, 650])).
% 1.03/0.93 tff(653,plain,
% 1.03/0.93 ((~c3_1(a1205)) | (~c0_1(a1224))),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[652, 177, 21, 638, 637, 22, 23, 20])).
% 1.03/0.93 tff(654,plain,
% 1.03/0.93 (~c3_1(a1205)),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[653, 646])).
% 1.03/0.93 tff(655,plain,
% 1.03/0.93 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 1.03/0.93 inference(bind,[status(th)],[])).
% 1.03/0.93 tff(656,plain,
% 1.03/0.93 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.03/0.93 inference(quant_intro,[status(thm)],[655])).
% 1.03/0.93 tff(657,plain,
% 1.03/0.93 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(658,plain,
% 1.03/0.93 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 1.03/0.93 inference(bind,[status(th)],[])).
% 1.03/0.93 tff(659,plain,
% 1.03/0.93 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.03/0.93 inference(quant_intro,[status(thm)],[658])).
% 1.03/0.93 tff(660,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 1.03/0.93 tff(661,plain,
% 1.03/0.93 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[660, 659])).
% 1.03/0.93 tff(662,plain,
% 1.03/0.93 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[661, 657])).
% 1.03/0.93 tff(663,plain,(
% 1.03/0.93 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.03/0.93 inference(skolemize,[status(sab)],[662])).
% 1.03/0.93 tff(664,plain,
% 1.03/0.93 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[663, 656])).
% 1.03/0.93 tff(665,assumption,(c2_1(a1205)), introduced(assumption)).
% 1.03/0.93 tff(666,plain,
% 1.03/0.93 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a1224) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c3_1(a1224)) | (~c1_1(a1224)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(667,plain,
% 1.03/0.93 ((hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1205) | c1_1(a1205) | (~c2_1(a1205))) <=> (hskp14 | c2_1(a1224) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(668,plain,
% 1.03/0.93 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1205) | c1_1(a1205) | (~c2_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a1224) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c3_1(a1224)) | (~c1_1(a1224))))),
% 1.03/0.93 inference(monotonicity,[status(thm)],[667])).
% 1.03/0.93 tff(669,plain,
% 1.03/0.93 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1205) | c1_1(a1205) | (~c2_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.03/0.93 inference(transitivity,[status(thm)],[668, 666])).
% 1.03/0.93 tff(670,plain,
% 1.03/0.93 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1205) | c1_1(a1205) | (~c2_1(a1205)))),
% 1.03/0.93 inference(quant_inst,[status(thm)],[])).
% 1.03/0.93 tff(671,plain,
% 1.03/0.93 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c3_1(a1224)) | (~c1_1(a1224))),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[670, 669])).
% 1.03/0.93 tff(672,plain,
% 1.03/0.93 (hskp14),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[671, 177, 638, 637, 665, 636, 23, 664, 654])).
% 1.03/0.93 tff(673,plain,
% 1.03/0.93 (~c2_1(a1232)),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[418, 672])).
% 1.03/0.93 tff(674,plain,
% 1.03/0.93 (~c0_1(a1232)),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[453, 672])).
% 1.03/0.93 tff(675,plain,
% 1.03/0.93 (c3_1(a1232)),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[429, 672])).
% 1.03/0.93 tff(676,plain,
% 1.03/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(677,plain,
% 1.03/0.93 (((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232))) <=> (c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(678,plain,
% 1.03/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232))))),
% 1.03/0.93 inference(monotonicity,[status(thm)],[677])).
% 1.03/0.93 tff(679,plain,
% 1.03/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))),
% 1.03/0.93 inference(transitivity,[status(thm)],[678, 676])).
% 1.03/0.93 tff(680,plain,
% 1.03/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))),
% 1.07/0.93 inference(quant_inst,[status(thm)],[])).
% 1.07/0.93 tff(681,plain,
% 1.07/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232))),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[680, 679])).
% 1.07/0.93 tff(682,plain,
% 1.07/0.93 ($false),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[681, 177, 675, 638, 637, 140, 139, 674, 673, 636, 382, 372])).
% 1.07/0.93 tff(683,plain,((~c0_1(a1215)) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1224) | (~c2_1(a1205)) | c1_1(a1205) | hskp5 | c0_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 1.07/0.93 tff(684,plain,
% 1.07/0.93 (~c0_1(a1215)),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[683, 635, 624, 104, 115, 613, 332, 23, 21, 22])).
% 1.07/0.93 tff(685,assumption,(hskp26), introduced(assumption)).
% 1.07/0.93 tff(686,plain,
% 1.07/0.93 (((~hskp26) | c2_1(a1208)) <=> ((~hskp26) | c2_1(a1208))),
% 1.07/0.93 inference(rewrite,[status(thm)],[])).
% 1.07/0.93 tff(687,axiom,((~hskp26) | c2_1(a1208)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 1.07/0.93 tff(688,plain,
% 1.07/0.93 ((~hskp26) | c2_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[687, 686])).
% 1.07/0.93 tff(689,plain,
% 1.07/0.93 ((~hskp26) | c2_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[688, 686])).
% 1.07/0.93 tff(690,plain,
% 1.07/0.93 ((~hskp26) | c2_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[689, 686])).
% 1.07/0.93 tff(691,plain,
% 1.07/0.93 ((~hskp26) | c2_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[690, 686])).
% 1.07/0.93 tff(692,plain,
% 1.07/0.93 ((~hskp26) | c2_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[691, 686])).
% 1.07/0.93 tff(693,plain,
% 1.07/0.93 ((~hskp26) | c2_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[692, 686])).
% 1.07/0.93 tff(694,plain,
% 1.07/0.93 ((~hskp26) | c2_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[693, 686])).
% 1.07/0.93 tff(695,plain,
% 1.07/0.93 ((~hskp26) | c2_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[694, 686])).
% 1.07/0.93 tff(696,plain,
% 1.07/0.93 (c2_1(a1208)),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[695, 685])).
% 1.07/0.93 tff(697,plain,
% 1.07/0.93 (((~hskp26) | c1_1(a1208)) <=> ((~hskp26) | c1_1(a1208))),
% 1.07/0.93 inference(rewrite,[status(thm)],[])).
% 1.07/0.93 tff(698,axiom,((~hskp26) | c1_1(a1208)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 1.07/0.93 tff(699,plain,
% 1.07/0.93 ((~hskp26) | c1_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[698, 697])).
% 1.07/0.93 tff(700,plain,
% 1.07/0.93 ((~hskp26) | c1_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[699, 697])).
% 1.07/0.93 tff(701,plain,
% 1.07/0.93 ((~hskp26) | c1_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[700, 697])).
% 1.07/0.93 tff(702,plain,
% 1.07/0.93 ((~hskp26) | c1_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[701, 697])).
% 1.07/0.93 tff(703,plain,
% 1.07/0.93 ((~hskp26) | c1_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[702, 697])).
% 1.07/0.93 tff(704,plain,
% 1.07/0.93 ((~hskp26) | c1_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[703, 697])).
% 1.07/0.93 tff(705,plain,
% 1.07/0.93 ((~hskp26) | c1_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[704, 697])).
% 1.07/0.93 tff(706,plain,
% 1.07/0.93 ((~hskp26) | c1_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[705, 697])).
% 1.07/0.93 tff(707,plain,
% 1.07/0.93 (c1_1(a1208)),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[706, 685])).
% 1.07/0.93 tff(708,plain,
% 1.07/0.93 (((~hskp26) | c0_1(a1208)) <=> ((~hskp26) | c0_1(a1208))),
% 1.07/0.93 inference(rewrite,[status(thm)],[])).
% 1.07/0.93 tff(709,axiom,((~hskp26) | c0_1(a1208)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 1.07/0.93 tff(710,plain,
% 1.07/0.93 ((~hskp26) | c0_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[709, 708])).
% 1.07/0.93 tff(711,plain,
% 1.07/0.93 ((~hskp26) | c0_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[710, 708])).
% 1.07/0.93 tff(712,plain,
% 1.07/0.93 ((~hskp26) | c0_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[711, 708])).
% 1.07/0.93 tff(713,plain,
% 1.07/0.93 ((~hskp26) | c0_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[712, 708])).
% 1.07/0.93 tff(714,plain,
% 1.07/0.93 ((~hskp26) | c0_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[713, 708])).
% 1.07/0.93 tff(715,plain,
% 1.07/0.93 ((~hskp26) | c0_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[714, 708])).
% 1.07/0.93 tff(716,plain,
% 1.07/0.93 ((~hskp26) | c0_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[715, 708])).
% 1.07/0.93 tff(717,plain,
% 1.07/0.93 ((~hskp26) | c0_1(a1208)),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[716, 708])).
% 1.07/0.93 tff(718,plain,
% 1.07/0.93 (c0_1(a1208)),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[717, 685])).
% 1.07/0.93 tff(719,plain,
% 1.07/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.07/0.93 inference(rewrite,[status(thm)],[])).
% 1.07/0.93 tff(720,plain,
% 1.07/0.93 (((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1224) | c0_1(a1224) | (~c3_1(a1224))) <=> (c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.07/0.93 inference(rewrite,[status(thm)],[])).
% 1.07/0.93 tff(721,plain,
% 1.07/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1224) | c0_1(a1224) | (~c3_1(a1224)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224))))),
% 1.07/0.93 inference(monotonicity,[status(thm)],[720])).
% 1.07/0.93 tff(722,plain,
% 1.07/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1224) | c0_1(a1224) | (~c3_1(a1224)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.07/0.93 inference(transitivity,[status(thm)],[721, 719])).
% 1.07/0.93 tff(723,plain,
% 1.07/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1224) | c0_1(a1224) | (~c3_1(a1224)))),
% 1.07/0.93 inference(quant_inst,[status(thm)],[])).
% 1.07/0.93 tff(724,plain,
% 1.07/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | c0_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224))),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[723, 722])).
% 1.07/0.93 tff(725,plain,
% 1.07/0.93 (c0_1(a1224)),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[724, 177, 718, 707, 696, 638, 637, 636, 382])).
% 1.07/0.93 tff(726,plain,
% 1.07/0.93 (~c3_1(a1205)),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[653, 725])).
% 1.07/0.93 tff(727,plain,
% 1.07/0.93 (hskp14),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[671, 177, 638, 637, 665, 636, 23, 664, 726])).
% 1.07/0.93 tff(728,plain,
% 1.07/0.93 (~c2_1(a1232)),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[418, 727])).
% 1.07/0.93 tff(729,plain,
% 1.07/0.93 (~c0_1(a1232)),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[453, 727])).
% 1.07/0.93 tff(730,plain,
% 1.07/0.93 (c3_1(a1232)),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[429, 727])).
% 1.07/0.93 tff(731,plain,
% 1.07/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))),
% 1.07/0.93 inference(rewrite,[status(thm)],[])).
% 1.07/0.93 tff(732,plain,
% 1.07/0.93 (((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232))) <=> (c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))),
% 1.07/0.93 inference(rewrite,[status(thm)],[])).
% 1.07/0.93 tff(733,plain,
% 1.07/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232))))),
% 1.07/0.93 inference(monotonicity,[status(thm)],[732])).
% 1.07/0.93 tff(734,plain,
% 1.07/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))),
% 1.07/0.93 inference(transitivity,[status(thm)],[733, 731])).
% 1.07/0.93 tff(735,plain,
% 1.07/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))),
% 1.07/0.93 inference(quant_inst,[status(thm)],[])).
% 1.07/0.93 tff(736,plain,
% 1.07/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232))),
% 1.07/0.93 inference(modus_ponens,[status(thm)],[735, 734])).
% 1.07/0.93 tff(737,plain,
% 1.07/0.93 ($false),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[736, 177, 718, 707, 696, 730, 638, 637, 729, 728, 636, 382])).
% 1.07/0.93 tff(738,plain,((~hskp26) | (~c1_1(a1224)) | (~c3_1(a1224)) | c2_1(a1224) | (~c2_1(a1205)) | c1_1(a1205) | hskp5 | c0_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 1.07/0.93 tff(739,plain,
% 1.07/0.93 (~hskp26),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[738, 635, 624, 613, 332, 23, 21, 22])).
% 1.07/0.93 tff(740,plain,
% 1.07/0.93 (hskp24),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[175, 739, 219])).
% 1.07/0.93 tff(741,plain,
% 1.07/0.93 (~c2_1(a1267)),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[479, 740])).
% 1.07/0.93 tff(742,plain,
% 1.07/0.93 (~c1_1(a1267)),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[485, 740])).
% 1.07/0.93 tff(743,plain,
% 1.07/0.93 (c0_1(a1267)),
% 1.07/0.93 inference(unit_resolution,[status(thm)],[496, 740])).
% 1.07/0.93 tff(744,assumption,(hskp25), introduced(assumption)).
% 1.07/0.93 tff(745,plain,
% 1.07/0.93 (((~hskp25) | c0_1(a1204)) <=> ((~hskp25) | c0_1(a1204))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(746,axiom,((~hskp25) | c0_1(a1204)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 1.08/0.94 tff(747,plain,
% 1.08/0.94 ((~hskp25) | c0_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[746, 745])).
% 1.08/0.94 tff(748,plain,
% 1.08/0.94 ((~hskp25) | c0_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[747, 745])).
% 1.08/0.94 tff(749,plain,
% 1.08/0.94 ((~hskp25) | c0_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[748, 745])).
% 1.08/0.94 tff(750,plain,
% 1.08/0.94 ((~hskp25) | c0_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[749, 745])).
% 1.08/0.94 tff(751,plain,
% 1.08/0.94 ((~hskp25) | c0_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[750, 745])).
% 1.08/0.94 tff(752,plain,
% 1.08/0.94 ((~hskp25) | c0_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[751, 745])).
% 1.08/0.94 tff(753,plain,
% 1.08/0.94 ((~hskp25) | c0_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[752, 745])).
% 1.08/0.94 tff(754,plain,
% 1.08/0.94 ((~hskp25) | c0_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[753, 745])).
% 1.08/0.94 tff(755,plain,
% 1.08/0.94 (c0_1(a1204)),
% 1.08/0.94 inference(unit_resolution,[status(thm)],[754, 744])).
% 1.08/0.94 tff(756,assumption,(~c0_1(a1215)), introduced(assumption)).
% 1.08/0.94 tff(757,plain,
% 1.08/0.94 (((~hskp25) | c2_1(a1204)) <=> ((~hskp25) | c2_1(a1204))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(758,axiom,((~hskp25) | c2_1(a1204)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 1.08/0.94 tff(759,plain,
% 1.08/0.94 ((~hskp25) | c2_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[758, 757])).
% 1.08/0.94 tff(760,plain,
% 1.08/0.94 ((~hskp25) | c2_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[759, 757])).
% 1.08/0.94 tff(761,plain,
% 1.08/0.94 ((~hskp25) | c2_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[760, 757])).
% 1.08/0.94 tff(762,plain,
% 1.08/0.94 ((~hskp25) | c2_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[761, 757])).
% 1.08/0.94 tff(763,plain,
% 1.08/0.94 ((~hskp25) | c2_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[762, 757])).
% 1.08/0.94 tff(764,plain,
% 1.08/0.94 ((~hskp25) | c2_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[763, 757])).
% 1.08/0.94 tff(765,plain,
% 1.08/0.94 ((~hskp25) | c2_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[764, 757])).
% 1.08/0.94 tff(766,plain,
% 1.08/0.94 ((~hskp25) | c2_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[765, 757])).
% 1.08/0.94 tff(767,plain,
% 1.08/0.94 (c2_1(a1204)),
% 1.08/0.94 inference(unit_resolution,[status(thm)],[766, 744])).
% 1.08/0.94 tff(768,plain,
% 1.08/0.94 (((~hskp25) | c3_1(a1204)) <=> ((~hskp25) | c3_1(a1204))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(769,axiom,((~hskp25) | c3_1(a1204)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 1.08/0.94 tff(770,plain,
% 1.08/0.94 ((~hskp25) | c3_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[769, 768])).
% 1.08/0.94 tff(771,plain,
% 1.08/0.94 ((~hskp25) | c3_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[770, 768])).
% 1.08/0.94 tff(772,plain,
% 1.08/0.94 ((~hskp25) | c3_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[771, 768])).
% 1.08/0.94 tff(773,plain,
% 1.08/0.94 ((~hskp25) | c3_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[772, 768])).
% 1.08/0.94 tff(774,plain,
% 1.08/0.94 ((~hskp25) | c3_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[773, 768])).
% 1.08/0.94 tff(775,plain,
% 1.08/0.94 ((~hskp25) | c3_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[774, 768])).
% 1.08/0.94 tff(776,plain,
% 1.08/0.94 ((~hskp25) | c3_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[775, 768])).
% 1.08/0.94 tff(777,plain,
% 1.08/0.94 ((~hskp25) | c3_1(a1204)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[776, 768])).
% 1.08/0.94 tff(778,plain,
% 1.08/0.94 (c3_1(a1204)),
% 1.08/0.94 inference(unit_resolution,[status(thm)],[777, 744])).
% 1.08/0.94 tff(779,plain,
% 1.08/0.94 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.08/0.94 inference(bind,[status(th)],[])).
% 1.08/0.94 tff(780,plain,
% 1.08/0.94 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.08/0.94 inference(quant_intro,[status(thm)],[779])).
% 1.08/0.94 tff(781,plain,
% 1.08/0.94 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(782,plain,
% 1.08/0.94 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.08/0.94 inference(bind,[status(th)],[])).
% 1.08/0.94 tff(783,plain,
% 1.08/0.94 (![V: $i, U: $i] : (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.08/0.94 inference(quant_intro,[status(thm)],[782])).
% 1.08/0.94 tff(784,axiom,(![V: $i, U: $i] : (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 1.08/0.94 tff(785,plain,
% 1.08/0.94 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[784, 783])).
% 1.08/0.94 tff(786,plain,
% 1.08/0.94 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[785, 781])).
% 1.08/0.94 tff(787,plain,(
% 1.08/0.94 ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.08/0.94 inference(skolemize,[status(sab)],[786])).
% 1.08/0.94 tff(788,plain,
% 1.08/0.94 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[787, 780])).
% 1.08/0.94 tff(789,plain,
% 1.08/0.94 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.08/0.94 inference(bind,[status(th)],[])).
% 1.08/0.94 tff(790,plain,
% 1.08/0.94 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.08/0.94 inference(quant_intro,[status(thm)],[789])).
% 1.08/0.94 tff(791,plain,
% 1.08/0.94 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(792,plain,
% 1.08/0.94 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.08/0.94 inference(bind,[status(th)],[])).
% 1.08/0.94 tff(793,plain,
% 1.08/0.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.08/0.94 inference(quant_intro,[status(thm)],[792])).
% 1.08/0.94 tff(794,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 1.08/0.94 tff(795,plain,
% 1.08/0.94 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[794, 793])).
% 1.08/0.94 tff(796,plain,
% 1.08/0.94 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[795, 791])).
% 1.08/0.94 tff(797,plain,(
% 1.08/0.94 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.08/0.94 inference(skolemize,[status(sab)],[796])).
% 1.08/0.94 tff(798,plain,
% 1.08/0.94 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[797, 790])).
% 1.08/0.94 tff(799,assumption,(c3_1(a1204)), introduced(assumption)).
% 1.08/0.94 tff(800,assumption,(c2_1(a1204)), introduced(assumption)).
% 1.08/0.94 tff(801,assumption,(c0_1(a1204)), introduced(assumption)).
% 1.08/0.94 tff(802,plain,
% 1.08/0.94 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(803,plain,
% 1.08/0.94 ((hskp9 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215))) <=> (hskp9 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(804,plain,
% 1.08/0.94 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))))),
% 1.08/0.94 inference(monotonicity,[status(thm)],[803])).
% 1.08/0.94 tff(805,plain,
% 1.08/0.94 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.08/0.94 inference(transitivity,[status(thm)],[804, 802])).
% 1.08/0.94 tff(806,plain,
% 1.08/0.94 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.08/0.94 inference(quant_inst,[status(thm)],[])).
% 1.08/0.94 tff(807,plain,
% 1.08/0.94 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[806, 805])).
% 1.08/0.94 tff(808,plain,
% 1.08/0.94 (hskp9 | c0_1(a1215)),
% 1.08/0.94 inference(unit_resolution,[status(thm)],[807, 177, 801, 800, 799, 140, 138, 798])).
% 1.08/0.94 tff(809,plain,
% 1.08/0.94 (hskp9),
% 1.08/0.94 inference(unit_resolution,[status(thm)],[808, 756])).
% 1.08/0.94 tff(810,plain,
% 1.08/0.94 (((~hskp9) | c2_1(a1219)) <=> ((~hskp9) | c2_1(a1219))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(811,axiom,((~hskp9) | c2_1(a1219)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 1.08/0.94 tff(812,plain,
% 1.08/0.94 ((~hskp9) | c2_1(a1219)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[811, 810])).
% 1.08/0.94 tff(813,plain,
% 1.08/0.94 ((~hskp9) | c2_1(a1219)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[812, 810])).
% 1.08/0.94 tff(814,plain,
% 1.08/0.94 ((~hskp9) | c2_1(a1219)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[813, 810])).
% 1.08/0.94 tff(815,plain,
% 1.08/0.94 ((~hskp9) | c2_1(a1219)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[814, 810])).
% 1.08/0.94 tff(816,plain,
% 1.08/0.94 ((~hskp9) | c2_1(a1219)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[815, 810])).
% 1.08/0.94 tff(817,plain,
% 1.08/0.94 ((~hskp9) | c2_1(a1219)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[816, 810])).
% 1.08/0.94 tff(818,plain,
% 1.08/0.94 ((~hskp9) | c2_1(a1219)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[817, 810])).
% 1.08/0.94 tff(819,plain,
% 1.08/0.94 ((~hskp9) | c2_1(a1219)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[818, 810])).
% 1.08/0.94 tff(820,plain,
% 1.08/0.94 (c2_1(a1219)),
% 1.08/0.94 inference(unit_resolution,[status(thm)],[819, 809])).
% 1.08/0.94 tff(821,plain,
% 1.08/0.94 (((~hskp9) | c1_1(a1219)) <=> ((~hskp9) | c1_1(a1219))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(822,axiom,((~hskp9) | c1_1(a1219)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 1.08/0.94 tff(823,plain,
% 1.08/0.94 ((~hskp9) | c1_1(a1219)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[822, 821])).
% 1.08/0.94 tff(824,plain,
% 1.08/0.94 ((~hskp9) | c1_1(a1219)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[823, 821])).
% 1.08/0.94 tff(825,plain,
% 1.08/0.94 ((~hskp9) | c1_1(a1219)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[824, 821])).
% 1.08/0.94 tff(826,plain,
% 1.08/0.94 ((~hskp9) | c1_1(a1219)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[825, 821])).
% 1.08/0.94 tff(827,plain,
% 1.08/0.94 ((~hskp9) | c1_1(a1219)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[826, 821])).
% 1.08/0.94 tff(828,plain,
% 1.08/0.94 ((~hskp9) | c1_1(a1219)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[827, 821])).
% 1.08/0.94 tff(829,plain,
% 1.08/0.94 ((~hskp9) | c1_1(a1219)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[828, 821])).
% 1.08/0.94 tff(830,plain,
% 1.08/0.94 ((~hskp9) | c1_1(a1219)),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[829, 821])).
% 1.08/0.94 tff(831,plain,
% 1.08/0.94 (c1_1(a1219)),
% 1.08/0.94 inference(unit_resolution,[status(thm)],[830, 809])).
% 1.08/0.94 tff(832,plain,
% 1.08/0.94 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(833,plain,
% 1.08/0.94 (((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215))) <=> (c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(834,plain,
% 1.08/0.94 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219))))),
% 1.08/0.94 inference(monotonicity,[status(thm)],[833])).
% 1.08/0.94 tff(835,plain,
% 1.08/0.94 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)))),
% 1.08/0.94 inference(transitivity,[status(thm)],[834, 832])).
% 1.08/0.94 tff(836,plain,
% 1.08/0.94 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.08/0.94 inference(quant_inst,[status(thm)],[])).
% 1.08/0.94 tff(837,plain,
% 1.08/0.94 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219))),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[836, 835])).
% 1.08/0.94 tff(838,plain,
% 1.08/0.94 (~c3_1(a1219)),
% 1.08/0.94 inference(unit_resolution,[status(thm)],[837, 177, 831, 820, 140, 138, 788, 756])).
% 1.08/0.94 tff(839,plain,
% 1.08/0.94 (((~hskp9) | (~c0_1(a1219))) <=> ((~hskp9) | (~c0_1(a1219)))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(840,plain,
% 1.08/0.94 (((~c0_1(a1219)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a1219)))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(841,axiom,((~c0_1(a1219)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 1.08/0.94 tff(842,plain,
% 1.08/0.94 ((~hskp9) | (~c0_1(a1219))),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[841, 840])).
% 1.08/0.94 tff(843,plain,
% 1.08/0.94 ((~hskp9) | (~c0_1(a1219))),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[842, 839])).
% 1.08/0.94 tff(844,plain,
% 1.08/0.94 (~c0_1(a1219)),
% 1.08/0.94 inference(unit_resolution,[status(thm)],[843, 809])).
% 1.08/0.94 tff(845,plain,
% 1.08/0.94 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (c3_1(a1215) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(846,plain,
% 1.08/0.94 (((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c3_1(a1208)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215))) <=> (c3_1(a1215) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(847,plain,
% 1.08/0.94 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c3_1(a1208)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (c3_1(a1215) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | c0_1(a1215) | (~c1_1(a1215))))),
% 1.08/0.94 inference(monotonicity,[status(thm)],[846])).
% 1.08/0.94 tff(848,plain,
% 1.08/0.94 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c3_1(a1208)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.08/0.94 inference(transitivity,[status(thm)],[847, 845])).
% 1.08/0.94 tff(849,plain,
% 1.08/0.94 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c3_1(a1208)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.08/0.94 inference(quant_inst,[status(thm)],[])).
% 1.08/0.94 tff(850,plain,
% 1.08/0.94 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | c0_1(a1215) | (~c1_1(a1215))),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[849, 848])).
% 1.08/0.94 tff(851,plain,
% 1.08/0.94 (~c3_1(a1208)),
% 1.08/0.94 inference(unit_resolution,[status(thm)],[850, 177, 707, 696, 140, 138, 788, 756])).
% 1.08/0.94 tff(852,plain,
% 1.08/0.94 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(853,plain,
% 1.08/0.94 (((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215))) <=> (c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(854,plain,
% 1.08/0.94 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204))))),
% 1.08/0.94 inference(monotonicity,[status(thm)],[853])).
% 1.08/0.94 tff(855,plain,
% 1.08/0.94 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)))),
% 1.08/0.94 inference(transitivity,[status(thm)],[854, 852])).
% 1.08/0.94 tff(856,plain,
% 1.08/0.94 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.08/0.94 inference(quant_inst,[status(thm)],[])).
% 1.08/0.94 tff(857,plain,
% 1.08/0.94 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204))),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[856, 855])).
% 1.08/0.94 tff(858,plain,
% 1.08/0.94 (c0_1(a1215) | (~c1_1(a1204))),
% 1.08/0.94 inference(unit_resolution,[status(thm)],[857, 177, 800, 799, 140, 138, 788])).
% 1.08/0.94 tff(859,plain,
% 1.08/0.94 (~c1_1(a1204)),
% 1.08/0.94 inference(unit_resolution,[status(thm)],[858, 756])).
% 1.08/0.94 tff(860,plain,
% 1.08/0.94 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.08/0.94 inference(bind,[status(th)],[])).
% 1.08/0.94 tff(861,plain,
% 1.08/0.94 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.08/0.94 inference(quant_intro,[status(thm)],[860])).
% 1.08/0.94 tff(862,plain,
% 1.08/0.94 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(863,plain,
% 1.08/0.94 (^[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)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp19) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp19))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.08/0.94 inference(bind,[status(th)],[])).
% 1.08/0.94 tff(864,plain,
% 1.08/0.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.08/0.94 inference(quant_intro,[status(thm)],[863])).
% 1.08/0.94 tff(865,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 1.08/0.94 tff(866,plain,
% 1.08/0.94 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[865, 864])).
% 1.08/0.94 tff(867,plain,
% 1.08/0.94 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[866, 862])).
% 1.08/0.94 tff(868,plain,(
% 1.08/0.94 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.08/0.94 inference(skolemize,[status(sab)],[867])).
% 1.08/0.94 tff(869,plain,
% 1.08/0.94 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.08/0.94 inference(modus_ponens,[status(thm)],[868, 861])).
% 1.08/0.94 tff(870,plain,
% 1.08/0.94 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1224)) | (~c1_1(a1224)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1224)) | (~c1_1(a1224)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(871,plain,
% 1.08/0.94 ((hskp19 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c0_1(a1224)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204))) <=> (hskp19 | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1224)) | (~c1_1(a1224)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))),
% 1.08/0.94 inference(rewrite,[status(thm)],[])).
% 1.08/0.94 tff(872,plain,
% 1.08/0.94 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c0_1(a1224)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1224)) | (~c1_1(a1224)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204))))),
% 1.08/0.94 inference(monotonicity,[status(thm)],[871])).
% 1.08/0.94 tff(873,plain,
% 1.08/0.94 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c0_1(a1224)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1224)) | (~c1_1(a1224)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))),
% 1.08/0.94 inference(transitivity,[status(thm)],[872, 870])).
% 1.08/0.94 tff(874,plain,
% 1.08/0.94 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c0_1(a1224)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204)))),
% 1.08/0.95 inference(quant_inst,[status(thm)],[])).
% 1.08/0.95 tff(875,plain,
% 1.08/0.95 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c2_1(a1224) | (~ndr1_0) | (~c0_1(a1224)) | (~c1_1(a1224)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204))),
% 1.08/0.95 inference(modus_ponens,[status(thm)],[874, 873])).
% 1.08/0.95 tff(876,plain,
% 1.08/0.95 (hskp19 | (~c0_1(a1224))),
% 1.08/0.95 inference(unit_resolution,[status(thm)],[875, 177, 800, 799, 638, 636, 869, 859])).
% 1.08/0.95 tff(877,plain,
% 1.08/0.95 (hskp19),
% 1.08/0.95 inference(unit_resolution,[status(thm)],[876, 725])).
% 1.08/0.95 tff(878,plain,
% 1.08/0.95 (~c3_1(a1247)),
% 1.08/0.95 inference(unit_resolution,[status(thm)],[563, 877])).
% 1.08/0.95 tff(879,plain,
% 1.08/0.95 (~c2_1(a1247)),
% 1.08/0.95 inference(unit_resolution,[status(thm)],[538, 877])).
% 1.08/0.95 tff(880,plain,
% 1.08/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)) | c0_1(a1247))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)) | c0_1(a1247))),
% 1.08/0.95 inference(rewrite,[status(thm)],[])).
% 1.08/0.95 tff(881,plain,
% 1.08/0.95 (((~ndr1_0) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c0_1(a1224)) | c3_1(a1208) | (~c1_1(a1208)) | (~c2_1(a1208)) | c2_1(a1247) | c0_1(a1247) | c3_1(a1247)) <=> (c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)) | c0_1(a1247))),
% 1.08/0.95 inference(rewrite,[status(thm)],[])).
% 1.08/0.95 tff(882,plain,
% 1.08/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c0_1(a1224)) | c3_1(a1208) | (~c1_1(a1208)) | (~c2_1(a1208)) | c2_1(a1247) | c0_1(a1247) | c3_1(a1247))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)) | c0_1(a1247)))),
% 1.08/0.95 inference(monotonicity,[status(thm)],[881])).
% 1.08/0.95 tff(883,plain,
% 1.08/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c0_1(a1224)) | c3_1(a1208) | (~c1_1(a1208)) | (~c2_1(a1208)) | c2_1(a1247) | c0_1(a1247) | c3_1(a1247))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)) | c0_1(a1247))),
% 1.08/0.95 inference(transitivity,[status(thm)],[882, 880])).
% 1.08/0.95 tff(884,plain,
% 1.08/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c0_1(a1224)) | c3_1(a1208) | (~c1_1(a1208)) | (~c2_1(a1208)) | c2_1(a1247) | c0_1(a1247) | c3_1(a1247))),
% 1.08/0.95 inference(quant_inst,[status(thm)],[])).
% 1.08/0.95 tff(885,plain,
% 1.08/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c3_1(a1224)) | (~c1_1(a1224)) | c0_1(a1247)),
% 1.08/0.95 inference(modus_ponens,[status(thm)],[884, 883])).
% 1.08/0.95 tff(886,plain,
% 1.08/0.95 (c0_1(a1247)),
% 1.08/0.95 inference(unit_resolution,[status(thm)],[885, 177, 707, 696, 638, 637, 879, 878, 74, 725, 851])).
% 1.08/0.95 tff(887,plain,
% 1.08/0.95 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 1.08/0.95 inference(bind,[status(th)],[])).
% 1.08/0.95 tff(888,plain,
% 1.08/0.95 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.08/0.95 inference(quant_intro,[status(thm)],[887])).
% 1.08/0.95 tff(889,plain,
% 1.08/0.95 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.08/0.95 inference(rewrite,[status(thm)],[])).
% 1.08/0.95 tff(890,plain,
% 1.08/0.95 (^[V: $i, U: $i] : 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))) | 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))) | (~c2_1(U))) | (~ndr1_0)) | (~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))) | (~c2_1(U))) | (~ndr1_0)) | (~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)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 1.08/0.95 inference(bind,[status(th)],[])).
% 1.08/0.95 tff(891,plain,
% 1.08/0.95 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.08/0.95 inference(quant_intro,[status(thm)],[890])).
% 1.08/0.95 tff(892,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 1.08/0.95 tff(893,plain,
% 1.08/0.95 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.08/0.95 inference(modus_ponens,[status(thm)],[892, 891])).
% 1.08/0.95 tff(894,plain,
% 1.08/0.95 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.08/0.95 inference(modus_ponens,[status(thm)],[893, 889])).
% 1.08/0.95 tff(895,plain,(
% 1.08/0.95 ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.08/0.95 inference(skolemize,[status(sab)],[894])).
% 1.08/0.95 tff(896,plain,
% 1.08/0.95 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.08/0.95 inference(modus_ponens,[status(thm)],[895, 888])).
% 1.08/0.95 tff(897,plain,
% 1.08/0.95 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1247)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1247)))),
% 1.08/0.95 inference(rewrite,[status(thm)],[])).
% 1.08/0.95 tff(898,plain,
% 1.08/0.95 (((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c3_1(a1247) | c2_1(a1247) | (~c0_1(a1247))) <=> (c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1247)))),
% 1.08/0.95 inference(rewrite,[status(thm)],[])).
% 1.08/0.95 tff(899,plain,
% 1.08/0.95 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c3_1(a1247) | c2_1(a1247) | (~c0_1(a1247)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1247))))),
% 1.08/0.95 inference(monotonicity,[status(thm)],[898])).
% 1.08/0.95 tff(900,plain,
% 1.08/0.95 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c3_1(a1247) | c2_1(a1247) | (~c0_1(a1247)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1247)))),
% 1.08/0.95 inference(transitivity,[status(thm)],[899, 897])).
% 1.08/0.95 tff(901,plain,
% 1.08/0.95 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c3_1(a1247) | c2_1(a1247) | (~c0_1(a1247)))),
% 1.08/0.95 inference(quant_inst,[status(thm)],[])).
% 1.08/0.95 tff(902,plain,
% 1.08/0.95 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1247))),
% 1.08/0.95 inference(modus_ponens,[status(thm)],[901, 900])).
% 1.08/0.95 tff(903,plain,
% 1.08/0.95 ($false),
% 1.08/0.95 inference(unit_resolution,[status(thm)],[902, 177, 718, 707, 696, 879, 878, 896, 886])).
% 1.08/0.95 tff(904,plain,((~hskp26) | (~c1_1(a1224)) | (~c3_1(a1224)) | (~c2_1(a1204)) | (~c3_1(a1204)) | c2_1(a1224) | (~c1_1(a1215)) | c3_1(a1215) | c0_1(a1215)), inference(lemma,lemma(discharge,[]))).
% 1.08/0.95 tff(905,plain,
% 1.08/0.95 (~hskp26),
% 1.08/0.95 inference(unit_resolution,[status(thm)],[904, 756, 637, 800, 799, 636, 140, 138, 638])).
% 1.08/0.95 tff(906,plain,
% 1.08/0.95 (hskp24),
% 1.08/0.95 inference(unit_resolution,[status(thm)],[175, 905, 219])).
% 1.08/0.95 tff(907,plain,
% 1.08/0.95 (~c2_1(a1267)),
% 1.08/0.95 inference(unit_resolution,[status(thm)],[479, 906])).
% 1.08/0.95 tff(908,plain,
% 1.08/0.95 (~c1_1(a1267)),
% 1.08/0.95 inference(unit_resolution,[status(thm)],[485, 906])).
% 1.08/0.95 tff(909,plain,
% 1.08/0.95 (c0_1(a1267)),
% 1.08/0.95 inference(unit_resolution,[status(thm)],[496, 906])).
% 1.08/0.95 tff(910,assumption,(~c3_1(a1267)), introduced(assumption)).
% 1.08/0.95 tff(911,assumption,(~c3_1(a1219)), introduced(assumption)).
% 1.08/0.95 tff(912,plain,
% 1.08/0.95 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))))),
% 1.08/0.95 inference(bind,[status(th)],[])).
% 1.08/0.95 tff(913,plain,
% 1.08/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.08/0.95 inference(quant_intro,[status(thm)],[912])).
% 1.08/0.95 tff(914,plain,
% 1.08/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.08/0.95 inference(rewrite,[status(thm)],[])).
% 1.08/0.95 tff(915,plain,
% 1.08/0.95 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~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))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | 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(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | 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)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | 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)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))))),
% 1.08/0.95 inference(bind,[status(th)],[])).
% 1.08/0.95 tff(916,plain,
% 1.08/0.95 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.08/0.95 inference(quant_intro,[status(thm)],[915])).
% 1.08/0.95 tff(917,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 1.08/0.95 tff(918,plain,
% 1.08/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.08/0.95 inference(modus_ponens,[status(thm)],[917, 916])).
% 1.08/0.95 tff(919,plain,
% 1.08/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.08/0.95 inference(modus_ponens,[status(thm)],[918, 914])).
% 1.08/0.95 tff(920,plain,(
% 1.08/0.95 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.08/0.95 inference(skolemize,[status(sab)],[919])).
% 1.08/0.95 tff(921,plain,
% 1.08/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.08/0.95 inference(modus_ponens,[status(thm)],[920, 913])).
% 1.08/0.95 tff(922,assumption,(~c0_1(a1219)), introduced(assumption)).
% 1.08/0.95 tff(923,assumption,(~c2_1(a1267)), introduced(assumption)).
% 1.08/0.95 tff(924,assumption,(~c1_1(a1267)), introduced(assumption)).
% 1.08/0.95 tff(925,assumption,(c1_1(a1219)), introduced(assumption)).
% 1.08/0.95 tff(926,assumption,(c0_1(a1267)), introduced(assumption)).
% 1.08/0.95 tff(927,plain,
% 1.08/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1267)) | c3_1(a1267))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1267) | c2_1(a1267) | c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1267)) | c3_1(a1267))),
% 1.08/0.95 inference(rewrite,[status(thm)],[])).
% 1.08/0.95 tff(928,plain,
% 1.08/0.95 (((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219))) <=> (c1_1(a1267) | c2_1(a1267) | c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1267)) | c3_1(a1267))),
% 1.08/0.95 inference(rewrite,[status(thm)],[])).
% 1.08/0.95 tff(929,plain,
% 1.08/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1267)) | c3_1(a1267)))),
% 1.08/0.95 inference(monotonicity,[status(thm)],[928])).
% 1.08/0.95 tff(930,plain,
% 1.08/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1267) | c2_1(a1267) | c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1267)) | c3_1(a1267))),
% 1.08/0.95 inference(transitivity,[status(thm)],[929, 927])).
% 1.08/0.95 tff(931,plain,
% 1.08/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219)))),
% 1.08/0.95 inference(quant_inst,[status(thm)],[])).
% 1.08/0.95 tff(932,plain,
% 1.08/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1267) | c2_1(a1267) | c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1267)) | c3_1(a1267)),
% 1.08/0.95 inference(modus_ponens,[status(thm)],[931, 930])).
% 1.08/0.95 tff(933,plain,
% 1.08/0.95 ($false),
% 1.08/0.95 inference(unit_resolution,[status(thm)],[932, 177, 926, 925, 924, 923, 922, 921, 911, 910])).
% 1.08/0.95 tff(934,plain,(c3_1(a1267) | (~c0_1(a1267)) | (~c1_1(a1219)) | c1_1(a1267) | c2_1(a1267) | c0_1(a1219) | c3_1(a1219)), inference(lemma,lemma(discharge,[]))).
% 1.08/0.95 tff(935,plain,
% 1.08/0.95 (c3_1(a1267)),
% 1.08/0.95 inference(unit_resolution,[status(thm)],[934, 909, 831, 908, 907, 844, 838])).
% 1.08/0.95 tff(936,plain,
% 1.08/0.95 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.08/0.95 inference(bind,[status(th)],[])).
% 1.08/0.95 tff(937,plain,
% 1.08/0.95 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.08/0.95 inference(quant_intro,[status(thm)],[936])).
% 1.08/0.95 tff(938,plain,
% 1.08/0.95 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.08/0.95 inference(rewrite,[status(thm)],[])).
% 1.08/0.95 tff(939,plain,
% 1.08/0.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | 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)) | c1_1(U)) | c2_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)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.08/0.95 inference(bind,[status(th)],[])).
% 1.08/0.95 tff(940,plain,
% 1.08/0.95 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.08/0.95 inference(quant_intro,[status(thm)],[939])).
% 1.08/0.95 tff(941,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 1.08/0.95 tff(942,plain,
% 1.08/0.95 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.08/0.95 inference(modus_ponens,[status(thm)],[941, 940])).
% 1.08/0.95 tff(943,plain,
% 1.08/0.95 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.08/0.95 inference(modus_ponens,[status(thm)],[942, 938])).
% 1.08/0.95 tff(944,plain,(
% 1.08/0.95 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.08/0.95 inference(skolemize,[status(sab)],[943])).
% 1.08/0.95 tff(945,plain,
% 1.08/0.95 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.08/0.95 inference(modus_ponens,[status(thm)],[944, 937])).
% 1.08/0.95 tff(946,plain,
% 1.08/0.95 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.08/0.95 inference(bind,[status(th)],[])).
% 1.08/0.95 tff(947,plain,
% 1.08/0.95 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.08/0.95 inference(quant_intro,[status(thm)],[946])).
% 1.08/0.95 tff(948,plain,
% 1.08/0.95 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.08/0.95 inference(rewrite,[status(thm)],[])).
% 1.08/0.95 tff(949,plain,
% 1.08/0.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp8))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.08/0.95 inference(bind,[status(th)],[])).
% 1.08/0.95 tff(950,plain,
% 1.08/0.95 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.08/0.95 inference(quant_intro,[status(thm)],[949])).
% 1.08/0.95 tff(951,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 1.08/0.95 tff(952,plain,
% 1.08/0.95 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.08/0.95 inference(modus_ponens,[status(thm)],[951, 950])).
% 1.08/0.95 tff(953,plain,
% 1.08/0.95 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.08/0.95 inference(modus_ponens,[status(thm)],[952, 948])).
% 1.08/0.95 tff(954,plain,(
% 1.08/0.95 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.08/0.95 inference(skolemize,[status(sab)],[953])).
% 1.08/0.95 tff(955,plain,
% 1.08/0.95 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.08/0.95 inference(modus_ponens,[status(thm)],[954, 947])).
% 1.08/0.95 tff(956,plain,
% 1.08/0.95 (((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | c1_1(a1267) | c2_1(a1267) | (~ndr1_0) | (~c3_1(a1267)))) <=> ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp15 | hskp4 | c1_1(a1267) | c2_1(a1267) | (~ndr1_0) | (~c3_1(a1267)))),
% 1.08/0.95 inference(rewrite,[status(thm)],[])).
% 1.08/0.95 tff(957,plain,
% 1.08/0.95 ((hskp15 | hskp4 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267))) <=> (hskp15 | hskp4 | c1_1(a1267) | c2_1(a1267) | (~ndr1_0) | (~c3_1(a1267)))),
% 1.08/0.95 inference(rewrite,[status(thm)],[])).
% 1.08/0.95 tff(958,plain,
% 1.08/0.95 (((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)))) <=> ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | c1_1(a1267) | c2_1(a1267) | (~ndr1_0) | (~c3_1(a1267))))),
% 1.08/0.95 inference(monotonicity,[status(thm)],[957])).
% 1.08/0.95 tff(959,plain,
% 1.08/0.95 (((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)))) <=> ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp15 | hskp4 | c1_1(a1267) | c2_1(a1267) | (~ndr1_0) | (~c3_1(a1267)))),
% 1.08/0.95 inference(transitivity,[status(thm)],[958, 956])).
% 1.08/0.95 tff(960,plain,
% 1.08/0.95 ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp15 | hskp4 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)))),
% 1.08/0.96 inference(quant_inst,[status(thm)],[])).
% 1.08/0.96 tff(961,plain,
% 1.08/0.96 ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp15 | hskp4 | c1_1(a1267) | c2_1(a1267) | (~ndr1_0) | (~c3_1(a1267))),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[960, 959])).
% 1.08/0.96 tff(962,plain,
% 1.08/0.96 (hskp4 | (~c3_1(a1267))),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[961, 177, 75, 908, 907, 412])).
% 1.08/0.96 tff(963,plain,
% 1.08/0.96 (hskp4),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[962, 935])).
% 1.08/0.96 tff(964,plain,
% 1.08/0.96 (~c2_1(a1211)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[357, 963])).
% 1.08/0.96 tff(965,plain,
% 1.08/0.96 (~c0_1(a1211)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[363, 963])).
% 1.08/0.96 tff(966,plain,
% 1.08/0.96 (c1_1(a1211)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[392, 963])).
% 1.08/0.96 tff(967,plain,
% 1.08/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c3_1(a1215) | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c1_1(a1211)) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c3_1(a1215) | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c1_1(a1211)) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(968,plain,
% 1.08/0.96 ((hskp8 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1211) | c2_1(a1211) | (~c1_1(a1211))) <=> (hskp8 | c3_1(a1215) | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c1_1(a1211)) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(969,plain,
% 1.08/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1211) | c2_1(a1211) | (~c1_1(a1211)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c3_1(a1215) | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c1_1(a1211)) | c0_1(a1215) | (~c1_1(a1215))))),
% 1.08/0.96 inference(monotonicity,[status(thm)],[968])).
% 1.08/0.96 tff(970,plain,
% 1.08/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1211) | c2_1(a1211) | (~c1_1(a1211)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c3_1(a1215) | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c1_1(a1211)) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.08/0.96 inference(transitivity,[status(thm)],[969, 967])).
% 1.08/0.96 tff(971,plain,
% 1.08/0.96 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1211) | c2_1(a1211) | (~c1_1(a1211)))),
% 1.08/0.96 inference(quant_inst,[status(thm)],[])).
% 1.08/0.96 tff(972,plain,
% 1.08/0.96 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c3_1(a1215) | c0_1(a1211) | c2_1(a1211) | (~ndr1_0) | (~c1_1(a1211)) | c0_1(a1215) | (~c1_1(a1215))),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[971, 970])).
% 1.08/0.96 tff(973,plain,
% 1.08/0.96 (hskp8),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[972, 177, 140, 966, 138, 965, 964, 955, 756])).
% 1.08/0.96 tff(974,plain,
% 1.08/0.96 (~c3_1(a1217)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[584, 973])).
% 1.08/0.96 tff(975,plain,
% 1.08/0.96 (((~hskp8) | (~c1_1(a1217))) <=> ((~hskp8) | (~c1_1(a1217)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(976,plain,
% 1.08/0.96 (((~c1_1(a1217)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a1217)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(977,axiom,((~c1_1(a1217)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 1.08/0.96 tff(978,plain,
% 1.08/0.96 ((~hskp8) | (~c1_1(a1217))),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[977, 976])).
% 1.08/0.96 tff(979,plain,
% 1.08/0.96 ((~hskp8) | (~c1_1(a1217))),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[978, 975])).
% 1.08/0.96 tff(980,plain,
% 1.08/0.96 (~c1_1(a1217)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[979, 973])).
% 1.08/0.96 tff(981,plain,
% 1.08/0.96 (~c0_1(a1217)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[578, 973])).
% 1.08/0.96 tff(982,plain,
% 1.08/0.96 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1217) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c3_1(a1267)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1217) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c3_1(a1267)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(983,plain,
% 1.08/0.96 ((hskp26 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)) | c3_1(a1217) | c1_1(a1217) | c0_1(a1217)) <=> (hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1217) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c3_1(a1267)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(984,plain,
% 1.08/0.96 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)) | c3_1(a1217) | c1_1(a1217) | c0_1(a1217))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1217) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c3_1(a1267))))),
% 1.08/0.96 inference(monotonicity,[status(thm)],[983])).
% 1.08/0.96 tff(985,plain,
% 1.08/0.96 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)) | c3_1(a1217) | c1_1(a1217) | c0_1(a1217))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1217) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c3_1(a1267)))),
% 1.08/0.96 inference(transitivity,[status(thm)],[984, 982])).
% 1.08/0.96 tff(986,plain,
% 1.08/0.96 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)) | c3_1(a1217) | c1_1(a1217) | c0_1(a1217))),
% 1.08/0.96 inference(quant_inst,[status(thm)],[])).
% 1.08/0.96 tff(987,plain,
% 1.08/0.96 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1217) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c3_1(a1267))),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[986, 985])).
% 1.08/0.96 tff(988,plain,
% 1.08/0.96 ($false),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[987, 177, 905, 908, 907, 981, 980, 974, 945, 935])).
% 1.08/0.96 tff(989,plain,(c0_1(a1215) | (~c1_1(a1215)) | c3_1(a1215) | hskp15 | hskp28 | (~c3_1(a1224)) | (~c2_1(a1204)) | (~c3_1(a1204)) | c2_1(a1224) | (~c1_1(a1224)) | (~c0_1(a1204))), inference(lemma,lemma(discharge,[]))).
% 1.08/0.96 tff(990,plain,
% 1.08/0.96 ($false),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[989, 778, 767, 138, 75, 219, 637, 140, 756, 636, 638, 755])).
% 1.08/0.96 tff(991,plain,((~hskp25) | c3_1(a1215) | hskp15 | hskp28 | (~c3_1(a1224)) | (~c1_1(a1215)) | c0_1(a1215) | c2_1(a1224) | (~c1_1(a1224))), inference(lemma,lemma(discharge,[]))).
% 1.08/0.96 tff(992,plain,
% 1.08/0.96 (~hskp25),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[991, 219, 75, 93, 624, 104, 684, 613, 635])).
% 1.08/0.96 tff(993,plain,
% 1.08/0.96 ((hskp25 | hskp26 | hskp1) <=> (hskp25 | hskp26 | hskp1)),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(994,plain,
% 1.08/0.96 (((hskp25 | hskp26) | hskp1) <=> (hskp25 | hskp26 | hskp1)),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(995,plain,
% 1.08/0.96 ((hskp26 | hskp25) <=> (hskp25 | hskp26)),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(996,plain,
% 1.08/0.96 (((hskp26 | hskp25) | hskp1) <=> ((hskp25 | hskp26) | hskp1)),
% 1.08/0.96 inference(monotonicity,[status(thm)],[995])).
% 1.08/0.96 tff(997,plain,
% 1.08/0.96 (((hskp26 | hskp25) | hskp1) <=> (hskp25 | hskp26 | hskp1)),
% 1.08/0.96 inference(transitivity,[status(thm)],[996, 994])).
% 1.08/0.96 tff(998,axiom,((hskp26 | hskp25) | hskp1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause32')).
% 1.08/0.96 tff(999,plain,
% 1.08/0.96 (hskp25 | hskp26 | hskp1),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[998, 997])).
% 1.08/0.96 tff(1000,plain,
% 1.08/0.96 (hskp25 | hskp26 | hskp1),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[999, 993])).
% 1.08/0.96 tff(1001,plain,
% 1.08/0.96 (hskp25 | hskp26 | hskp1),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1000, 993])).
% 1.08/0.96 tff(1002,plain,
% 1.08/0.96 (hskp25 | hskp26 | hskp1),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1001, 993])).
% 1.08/0.96 tff(1003,plain,
% 1.08/0.96 (hskp25 | hskp26 | hskp1),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1002, 993])).
% 1.08/0.96 tff(1004,plain,
% 1.08/0.96 (hskp25 | hskp26 | hskp1),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1003, 993])).
% 1.08/0.96 tff(1005,plain,
% 1.08/0.96 (hskp25 | hskp26 | hskp1),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1004, 993])).
% 1.08/0.96 tff(1006,plain,
% 1.08/0.96 (hskp25 | hskp26 | hskp1),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1005, 993])).
% 1.08/0.96 tff(1007,plain,
% 1.08/0.96 (hskp1),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[1006, 992, 739])).
% 1.08/0.96 tff(1008,assumption,(hskp1), introduced(assumption)).
% 1.08/0.96 tff(1009,plain,
% 1.08/0.96 (((~hskp1) | (~c3_1(a1206))) <=> ((~hskp1) | (~c3_1(a1206)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(1010,plain,
% 1.08/0.96 (((~c3_1(a1206)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a1206)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(1011,axiom,((~c3_1(a1206)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 1.08/0.96 tff(1012,plain,
% 1.08/0.96 ((~hskp1) | (~c3_1(a1206))),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1011, 1010])).
% 1.08/0.96 tff(1013,plain,
% 1.08/0.96 ((~hskp1) | (~c3_1(a1206))),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1012, 1009])).
% 1.08/0.96 tff(1014,plain,
% 1.08/0.96 (~c3_1(a1206)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[1013, 1008])).
% 1.08/0.96 tff(1015,plain,
% 1.08/0.96 (((~hskp1) | c2_1(a1206)) <=> ((~hskp1) | c2_1(a1206))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(1016,axiom,((~hskp1) | c2_1(a1206)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 1.08/0.96 tff(1017,plain,
% 1.08/0.96 ((~hskp1) | c2_1(a1206)),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1016, 1015])).
% 1.08/0.96 tff(1018,plain,
% 1.08/0.96 ((~hskp1) | c2_1(a1206)),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1017, 1015])).
% 1.08/0.96 tff(1019,plain,
% 1.08/0.96 ((~hskp1) | c2_1(a1206)),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1018, 1015])).
% 1.08/0.96 tff(1020,plain,
% 1.08/0.96 ((~hskp1) | c2_1(a1206)),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1019, 1015])).
% 1.08/0.96 tff(1021,plain,
% 1.08/0.96 ((~hskp1) | c2_1(a1206)),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1020, 1015])).
% 1.08/0.96 tff(1022,plain,
% 1.08/0.96 ((~hskp1) | c2_1(a1206)),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1021, 1015])).
% 1.08/0.96 tff(1023,plain,
% 1.08/0.96 ((~hskp1) | c2_1(a1206)),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1022, 1015])).
% 1.08/0.96 tff(1024,plain,
% 1.08/0.96 ((~hskp1) | c2_1(a1206)),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1023, 1015])).
% 1.08/0.96 tff(1025,plain,
% 1.08/0.96 (c2_1(a1206)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[1024, 1008])).
% 1.08/0.96 tff(1026,plain,
% 1.08/0.96 (((~hskp1) | c0_1(a1206)) <=> ((~hskp1) | c0_1(a1206))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(1027,axiom,((~hskp1) | c0_1(a1206)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 1.08/0.96 tff(1028,plain,
% 1.08/0.96 ((~hskp1) | c0_1(a1206)),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1027, 1026])).
% 1.08/0.96 tff(1029,plain,
% 1.08/0.96 ((~hskp1) | c0_1(a1206)),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1028, 1026])).
% 1.08/0.96 tff(1030,plain,
% 1.08/0.96 ((~hskp1) | c0_1(a1206)),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1029, 1026])).
% 1.08/0.96 tff(1031,plain,
% 1.08/0.96 ((~hskp1) | c0_1(a1206)),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1030, 1026])).
% 1.08/0.96 tff(1032,plain,
% 1.08/0.96 ((~hskp1) | c0_1(a1206)),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1031, 1026])).
% 1.08/0.96 tff(1033,plain,
% 1.08/0.96 ((~hskp1) | c0_1(a1206)),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1032, 1026])).
% 1.08/0.96 tff(1034,plain,
% 1.08/0.96 ((~hskp1) | c0_1(a1206)),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1033, 1026])).
% 1.08/0.96 tff(1035,plain,
% 1.08/0.96 ((~hskp1) | c0_1(a1206)),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1034, 1026])).
% 1.08/0.96 tff(1036,plain,
% 1.08/0.96 (c0_1(a1206)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[1035, 1008])).
% 1.08/0.96 tff(1037,plain,
% 1.08/0.96 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1267)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1267)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(1038,plain,
% 1.08/0.96 ((hskp14 | (~ndr1_0) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1267) | c2_1(a1267) | (~c0_1(a1267))) <=> (hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1267)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(1039,plain,
% 1.08/0.96 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1267) | c2_1(a1267) | (~c0_1(a1267)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1267))))),
% 1.08/0.96 inference(monotonicity,[status(thm)],[1038])).
% 1.08/0.96 tff(1040,plain,
% 1.08/0.96 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1267) | c2_1(a1267) | (~c0_1(a1267)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1267)))),
% 1.08/0.96 inference(transitivity,[status(thm)],[1039, 1037])).
% 1.08/0.96 tff(1041,plain,
% 1.08/0.96 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1267) | c2_1(a1267) | (~c0_1(a1267)))),
% 1.08/0.96 inference(quant_inst,[status(thm)],[])).
% 1.08/0.96 tff(1042,plain,
% 1.08/0.96 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp14 | c1_1(a1267) | c2_1(a1267) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1267))),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1041, 1040])).
% 1.08/0.96 tff(1043,plain,
% 1.08/0.96 ($false),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[1042, 177, 498, 926, 1036, 1025, 924, 923, 1014, 473])).
% 1.08/0.96 tff(1044,plain,((~hskp1) | hskp14 | (~c0_1(a1267)) | c1_1(a1267) | c2_1(a1267)), inference(lemma,lemma(discharge,[]))).
% 1.08/0.96 tff(1045,plain,
% 1.08/0.96 (hskp14),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[1044, 1007, 743, 742, 741])).
% 1.08/0.96 tff(1046,plain,
% 1.08/0.96 (~c2_1(a1232)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[418, 1045])).
% 1.08/0.96 tff(1047,plain,
% 1.08/0.96 (~c0_1(a1232)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[453, 1045])).
% 1.08/0.96 tff(1048,plain,
% 1.08/0.96 (c3_1(a1232)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[429, 1045])).
% 1.08/0.96 tff(1049,plain,
% 1.08/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1232) | c2_1(a1232) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | c1_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1232) | c2_1(a1232) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | c1_1(a1232) | (~c3_1(a1232)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(1050,plain,
% 1.08/0.96 (((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1232) | c2_1(a1232) | (~c3_1(a1232)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232)) <=> (c0_1(a1232) | c2_1(a1232) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | c1_1(a1232) | (~c3_1(a1232)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(1051,plain,
% 1.08/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1232) | c2_1(a1232) | (~c3_1(a1232)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1232) | c2_1(a1232) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | c1_1(a1232) | (~c3_1(a1232))))),
% 1.08/0.96 inference(monotonicity,[status(thm)],[1050])).
% 1.08/0.96 tff(1052,plain,
% 1.08/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1232) | c2_1(a1232) | (~c3_1(a1232)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1232) | c2_1(a1232) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | c1_1(a1232) | (~c3_1(a1232)))),
% 1.08/0.96 inference(transitivity,[status(thm)],[1051, 1049])).
% 1.08/0.96 tff(1053,plain,
% 1.08/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1232) | c2_1(a1232) | (~c3_1(a1232)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))),
% 1.08/0.96 inference(quant_inst,[status(thm)],[])).
% 1.08/0.96 tff(1054,plain,
% 1.08/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1232) | c2_1(a1232) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | c1_1(a1232) | (~c3_1(a1232))),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 1.08/0.96 tff(1055,plain,
% 1.08/0.96 (c1_1(a1232)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[1054, 177, 1048, 104, 1047, 1046, 93, 237, 684])).
% 1.08/0.96 tff(1056,plain,
% 1.08/0.96 (c2_1(a1206)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[1024, 1007])).
% 1.08/0.96 tff(1057,plain,
% 1.08/0.96 (c0_1(a1206)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[1035, 1007])).
% 1.08/0.96 tff(1058,plain,
% 1.08/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1232)) | (~c1_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(1059,plain,
% 1.08/0.96 (((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232))) <=> (c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(1060,plain,
% 1.08/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1232)) | (~c1_1(a1232))))),
% 1.08/0.96 inference(monotonicity,[status(thm)],[1059])).
% 1.08/0.96 tff(1061,plain,
% 1.08/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 1.08/0.96 inference(transitivity,[status(thm)],[1060, 1058])).
% 1.08/0.96 tff(1062,plain,
% 1.08/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))),
% 1.08/0.96 inference(quant_inst,[status(thm)],[])).
% 1.08/0.96 tff(1063,plain,
% 1.08/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1232)) | (~c1_1(a1232))),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1062, 1061])).
% 1.08/0.96 tff(1064,plain,
% 1.08/0.96 (~c1_1(a1206)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[1063, 177, 1048, 1057, 1056, 1047, 1046, 382, 1055])).
% 1.08/0.96 tff(1065,plain,
% 1.08/0.96 (^[V: $i, U: $i] : refl((hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.08/0.96 inference(bind,[status(th)],[])).
% 1.08/0.96 tff(1066,plain,
% 1.08/0.96 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.08/0.96 inference(quant_intro,[status(thm)],[1065])).
% 1.08/0.96 tff(1067,plain,
% 1.08/0.96 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(1068,plain,
% 1.08/0.96 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_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)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_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)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp25) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp25))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.08/0.96 inference(bind,[status(th)],[])).
% 1.08/0.96 tff(1069,plain,
% 1.08/0.96 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp25) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.08/0.96 inference(quant_intro,[status(thm)],[1068])).
% 1.08/0.96 tff(1070,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 1.08/0.96 tff(1071,plain,
% 1.08/0.96 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1070, 1069])).
% 1.08/0.96 tff(1072,plain,
% 1.08/0.96 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1071, 1067])).
% 1.08/0.96 tff(1073,plain,(
% 1.08/0.96 ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.08/0.96 inference(skolemize,[status(sab)],[1072])).
% 1.08/0.96 tff(1074,plain,
% 1.08/0.96 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1073, 1066])).
% 1.08/0.96 tff(1075,plain,
% 1.08/0.96 (~c3_1(a1206)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[1013, 1007])).
% 1.08/0.96 tff(1076,plain,
% 1.08/0.96 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | c0_1(a1232) | c2_1(a1232) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | (~c1_1(a1232)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp25 | c0_1(a1232) | c2_1(a1232) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | (~c1_1(a1232)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(1077,plain,
% 1.08/0.96 ((hskp25 | (~ndr1_0) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)) | c0_1(a1232) | c2_1(a1232) | (~c1_1(a1232))) <=> (hskp25 | c0_1(a1232) | c2_1(a1232) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | (~c1_1(a1232)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(1078,plain,
% 1.08/0.96 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)) | c0_1(a1232) | c2_1(a1232) | (~c1_1(a1232)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | c0_1(a1232) | c2_1(a1232) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | (~c1_1(a1232))))),
% 1.08/0.96 inference(monotonicity,[status(thm)],[1077])).
% 1.08/0.96 tff(1079,plain,
% 1.08/0.96 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)) | c0_1(a1232) | c2_1(a1232) | (~c1_1(a1232)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp25 | c0_1(a1232) | c2_1(a1232) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | (~c1_1(a1232)))),
% 1.08/0.96 inference(transitivity,[status(thm)],[1078, 1076])).
% 1.08/0.96 tff(1080,plain,
% 1.08/0.96 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)) | c0_1(a1232) | c2_1(a1232) | (~c1_1(a1232)))),
% 1.08/0.96 inference(quant_inst,[status(thm)],[])).
% 1.08/0.96 tff(1081,plain,
% 1.08/0.96 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp25 | c0_1(a1232) | c2_1(a1232) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | (~c1_1(a1232))),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 1.08/0.96 tff(1082,plain,
% 1.08/0.96 (c1_1(a1206) | (~c1_1(a1232))),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[1081, 992, 177, 1057, 1047, 1046, 1075, 1074])).
% 1.08/0.96 tff(1083,plain,
% 1.08/0.96 ($false),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[1082, 1064, 1055])).
% 1.08/0.96 tff(1084,plain,(hskp28 | hskp15 | c1_1(a1205) | hskp5 | c0_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 1.08/0.96 tff(1085,plain,
% 1.08/0.96 (hskp28),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[1084, 75, 23, 21, 22])).
% 1.08/0.96 tff(1086,plain,
% 1.08/0.96 (c3_1(a1214)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[300, 1085])).
% 1.08/0.96 tff(1087,plain,
% 1.08/0.96 (c1_1(a1214)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[311, 1085])).
% 1.08/0.96 tff(1088,plain,
% 1.08/0.96 (c0_1(a1214)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[322, 1085])).
% 1.08/0.96 tff(1089,plain,
% 1.08/0.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(1090,plain,
% 1.08/0.96 ((hskp5 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205))) <=> (hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(1091,plain,
% 1.08/0.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 1.08/0.96 inference(monotonicity,[status(thm)],[1090])).
% 1.08/0.96 tff(1092,plain,
% 1.08/0.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.08/0.96 inference(transitivity,[status(thm)],[1091, 1089])).
% 1.08/0.96 tff(1093,plain,
% 1.08/0.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))),
% 1.08/0.96 inference(quant_inst,[status(thm)],[])).
% 1.08/0.96 tff(1094,plain,
% 1.08/0.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 1.08/0.96 inference(modus_ponens,[status(thm)],[1093, 1092])).
% 1.08/0.96 tff(1095,plain,
% 1.08/0.96 (~c3_1(a1205)),
% 1.08/0.96 inference(unit_resolution,[status(thm)],[1094, 177, 21, 1088, 1087, 1086, 22, 23, 20])).
% 1.08/0.96 tff(1096,plain,
% 1.08/0.96 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)))),
% 1.08/0.96 inference(rewrite,[status(thm)],[])).
% 1.08/0.96 tff(1097,plain,
% 1.08/0.96 ((hskp11 | (~ndr1_0) | c3_1(a1205) | c0_1(a1205) | (~c2_1(a1205))) <=> (hskp11 | c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1098,plain,
% 1.08/0.97 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1205) | c0_1(a1205) | (~c2_1(a1205)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205))))),
% 1.08/0.97 inference(monotonicity,[status(thm)],[1097])).
% 1.08/0.97 tff(1099,plain,
% 1.08/0.97 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1205) | c0_1(a1205) | (~c2_1(a1205)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)))),
% 1.08/0.97 inference(transitivity,[status(thm)],[1098, 1096])).
% 1.08/0.97 tff(1100,plain,
% 1.08/0.97 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1205) | c0_1(a1205) | (~c2_1(a1205)))),
% 1.08/0.97 inference(quant_inst,[status(thm)],[])).
% 1.08/0.97 tff(1101,plain,
% 1.08/0.97 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1100, 1099])).
% 1.08/0.97 tff(1102,plain,
% 1.08/0.97 (hskp11 | c3_1(a1205) | (~c2_1(a1205))),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[1101, 177, 22, 343])).
% 1.08/0.97 tff(1103,plain,
% 1.08/0.97 (hskp11),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[1102, 1095, 332])).
% 1.08/0.97 tff(1104,plain,
% 1.08/0.97 (~c2_1(a1224)),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[612, 1103])).
% 1.08/0.97 tff(1105,plain,
% 1.08/0.97 (c3_1(a1224)),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[623, 1103])).
% 1.08/0.97 tff(1106,plain,
% 1.08/0.97 (c1_1(a1224)),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[634, 1103])).
% 1.08/0.97 tff(1107,plain,
% 1.08/0.97 (~c0_1(a1215)),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[683, 1106, 1105, 104, 115, 1104, 332, 23, 21, 22])).
% 1.08/0.97 tff(1108,assumption,(hskp2), introduced(assumption)).
% 1.08/0.97 tff(1109,plain,
% 1.08/0.97 (((~hskp2) | (~c2_1(a1207))) <=> ((~hskp2) | (~c2_1(a1207)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1110,plain,
% 1.08/0.97 (((~c2_1(a1207)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a1207)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1111,axiom,((~c2_1(a1207)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 1.08/0.97 tff(1112,plain,
% 1.08/0.97 ((~hskp2) | (~c2_1(a1207))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1111, 1110])).
% 1.08/0.97 tff(1113,plain,
% 1.08/0.97 ((~hskp2) | (~c2_1(a1207))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1112, 1109])).
% 1.08/0.97 tff(1114,plain,
% 1.08/0.97 (~c2_1(a1207)),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[1113, 1108])).
% 1.08/0.97 tff(1115,plain,
% 1.08/0.97 (((~hskp2) | (~c1_1(a1207))) <=> ((~hskp2) | (~c1_1(a1207)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1116,plain,
% 1.08/0.97 (((~c1_1(a1207)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a1207)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1117,axiom,((~c1_1(a1207)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 1.08/0.97 tff(1118,plain,
% 1.08/0.97 ((~hskp2) | (~c1_1(a1207))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1117, 1116])).
% 1.08/0.97 tff(1119,plain,
% 1.08/0.97 ((~hskp2) | (~c1_1(a1207))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1118, 1115])).
% 1.08/0.97 tff(1120,plain,
% 1.08/0.97 (~c1_1(a1207)),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[1119, 1108])).
% 1.08/0.97 tff(1121,plain,
% 1.08/0.97 (((~hskp2) | (~c0_1(a1207))) <=> ((~hskp2) | (~c0_1(a1207)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1122,plain,
% 1.08/0.97 (((~c0_1(a1207)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a1207)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1123,axiom,((~c0_1(a1207)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 1.08/0.97 tff(1124,plain,
% 1.08/0.97 ((~hskp2) | (~c0_1(a1207))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1123, 1122])).
% 1.08/0.97 tff(1125,plain,
% 1.08/0.97 ((~hskp2) | (~c0_1(a1207))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1124, 1121])).
% 1.08/0.97 tff(1126,plain,
% 1.08/0.97 (~c0_1(a1207)),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[1125, 1108])).
% 1.08/0.97 tff(1127,plain,
% 1.08/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a1215) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1215) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1128,plain,
% 1.08/0.97 (((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1207) | c2_1(a1207) | (~c3_1(a1207)) | c2_1(a1207) | c1_1(a1207) | c0_1(a1207)) <=> (c3_1(a1215) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1129,plain,
% 1.08/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1207) | c2_1(a1207) | (~c3_1(a1207)) | c2_1(a1207) | c1_1(a1207) | c0_1(a1207))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a1215) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1215) | (~c1_1(a1215))))),
% 1.08/0.97 inference(monotonicity,[status(thm)],[1128])).
% 1.08/0.97 tff(1130,plain,
% 1.08/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1207) | c2_1(a1207) | (~c3_1(a1207)) | c2_1(a1207) | c1_1(a1207) | c0_1(a1207))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1215) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.08/0.97 inference(transitivity,[status(thm)],[1129, 1127])).
% 1.08/0.97 tff(1131,plain,
% 1.08/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)) | c0_1(a1207) | c2_1(a1207) | (~c3_1(a1207)) | c2_1(a1207) | c1_1(a1207) | c0_1(a1207))),
% 1.08/0.97 inference(quant_inst,[status(thm)],[])).
% 1.08/0.97 tff(1132,plain,
% 1.08/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1215) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1215) | (~c1_1(a1215))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 1.08/0.97 tff(1133,plain,
% 1.08/0.97 (~c3_1(a1207)),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[1132, 177, 140, 138, 1126, 1120, 1114, 237, 756])).
% 1.08/0.97 tff(1134,assumption,(c3_1(a1214)), introduced(assumption)).
% 1.08/0.97 tff(1135,assumption,(c1_1(a1214)), introduced(assumption)).
% 1.08/0.97 tff(1136,assumption,(c0_1(a1214)), introduced(assumption)).
% 1.08/0.97 tff(1137,plain,
% 1.08/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1215) | c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1215) | c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1138,plain,
% 1.08/0.97 (((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1207) | c0_1(a1207) | c3_1(a1207)) <=> (c3_1(a1215) | c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1139,plain,
% 1.08/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1207) | c0_1(a1207) | c3_1(a1207))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a1215) | c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 1.08/0.97 inference(monotonicity,[status(thm)],[1138])).
% 1.08/0.97 tff(1140,plain,
% 1.08/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1207) | c0_1(a1207) | c3_1(a1207))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1215) | c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.08/0.97 inference(transitivity,[status(thm)],[1139, 1137])).
% 1.08/0.97 tff(1141,plain,
% 1.08/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1207) | c0_1(a1207) | c3_1(a1207))),
% 1.08/0.97 inference(quant_inst,[status(thm)],[])).
% 1.08/0.97 tff(1142,plain,
% 1.08/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a1215) | c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1141, 1140])).
% 1.08/0.97 tff(1143,plain,
% 1.08/0.97 ($false),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[1142, 177, 1136, 1135, 1134, 140, 139, 138, 1126, 1114, 74, 1133])).
% 1.08/0.97 tff(1144,plain,((~hskp2) | (~c0_1(a1214)) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c1_1(a1215)) | (~c2_1(a1215)) | c3_1(a1215) | c0_1(a1215)), inference(lemma,lemma(discharge,[]))).
% 1.08/0.97 tff(1145,plain,
% 1.08/0.97 (~hskp2),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[1144, 1088, 1087, 1086, 104, 115, 93, 1107])).
% 1.08/0.97 tff(1146,plain,
% 1.08/0.97 (^[U: $i] : refl((hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 1.08/0.97 inference(bind,[status(th)],[])).
% 1.08/0.97 tff(1147,plain,
% 1.08/0.97 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.08/0.97 inference(quant_intro,[status(thm)],[1146])).
% 1.08/0.97 tff(1148,plain,
% 1.08/0.97 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1149,plain,
% 1.08/0.97 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp2))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) | hskp7) <=> ((hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp7))), rewrite(((hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) | hskp7) <=> (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.08/0.97 inference(bind,[status(th)],[])).
% 1.08/0.97 tff(1150,plain,
% 1.08/0.97 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) | hskp7) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.08/0.97 inference(quant_intro,[status(thm)],[1149])).
% 1.08/0.97 tff(1151,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 1.08/0.97 tff(1152,plain,
% 1.08/0.97 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 1.08/0.97 tff(1153,plain,
% 1.08/0.97 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1152, 1148])).
% 1.08/0.97 tff(1154,plain,(
% 1.08/0.97 ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.08/0.97 inference(skolemize,[status(sab)],[1153])).
% 1.08/0.97 tff(1155,plain,
% 1.08/0.97 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1154, 1147])).
% 1.08/0.97 tff(1156,plain,
% 1.08/0.97 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1157,plain,
% 1.08/0.97 ((hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214))) <=> (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1158,plain,
% 1.08/0.97 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 1.08/0.97 inference(monotonicity,[status(thm)],[1157])).
% 1.08/0.97 tff(1159,plain,
% 1.08/0.97 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.08/0.97 inference(transitivity,[status(thm)],[1158, 1156])).
% 1.08/0.97 tff(1160,plain,
% 1.08/0.97 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)))),
% 1.08/0.97 inference(quant_inst,[status(thm)],[])).
% 1.08/0.97 tff(1161,plain,
% 1.08/0.97 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp2 | (~ndr1_0) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1160, 1159])).
% 1.08/0.97 tff(1162,plain,
% 1.08/0.97 (hskp7 | hskp2),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[1161, 177, 1088, 1087, 1086, 1155])).
% 1.08/0.97 tff(1163,plain,
% 1.08/0.97 (hskp7),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[1162, 1145])).
% 1.08/0.97 tff(1164,plain,
% 1.08/0.97 (((~hskp7) | (~c3_1(a1216))) <=> ((~hskp7) | (~c3_1(a1216)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1165,plain,
% 1.08/0.97 (((~c3_1(a1216)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a1216)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1166,axiom,((~c3_1(a1216)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 1.08/0.97 tff(1167,plain,
% 1.08/0.97 ((~hskp7) | (~c3_1(a1216))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 1.08/0.97 tff(1168,plain,
% 1.08/0.97 ((~hskp7) | (~c3_1(a1216))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1167, 1164])).
% 1.08/0.97 tff(1169,plain,
% 1.08/0.97 (~c3_1(a1216)),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[1168, 1163])).
% 1.08/0.97 tff(1170,plain,
% 1.08/0.97 (((~hskp7) | (~c2_1(a1216))) <=> ((~hskp7) | (~c2_1(a1216)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1171,plain,
% 1.08/0.97 (((~c2_1(a1216)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a1216)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1172,axiom,((~c2_1(a1216)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.08/0.97 tff(1173,plain,
% 1.08/0.97 ((~hskp7) | (~c2_1(a1216))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1172, 1171])).
% 1.08/0.97 tff(1174,plain,
% 1.08/0.97 ((~hskp7) | (~c2_1(a1216))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1173, 1170])).
% 1.08/0.97 tff(1175,plain,
% 1.08/0.97 (~c2_1(a1216)),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[1174, 1163])).
% 1.08/0.97 tff(1176,plain,
% 1.08/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1216) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1216) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1177,plain,
% 1.08/0.97 (((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1216) | c0_1(a1216) | c3_1(a1216)) <=> (c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1216) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1178,plain,
% 1.08/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1216) | c0_1(a1216) | c3_1(a1216))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1216) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 1.08/0.97 inference(monotonicity,[status(thm)],[1177])).
% 1.08/0.97 tff(1179,plain,
% 1.08/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1216) | c0_1(a1216) | c3_1(a1216))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1216) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.08/0.97 inference(transitivity,[status(thm)],[1178, 1176])).
% 1.08/0.97 tff(1180,plain,
% 1.08/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c1_1(a1215)) | (~c2_1(a1215)) | c2_1(a1216) | c0_1(a1216) | c3_1(a1216))),
% 1.08/0.97 inference(quant_inst,[status(thm)],[])).
% 1.08/0.97 tff(1181,plain,
% 1.08/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | (~c1_1(a1215)) | (~c2_1(a1215)) | c0_1(a1216) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 1.08/0.97 tff(1182,plain,
% 1.08/0.97 (c0_1(a1216)),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[1181, 177, 1088, 1087, 1086, 104, 115, 1175, 1169, 93, 74])).
% 1.08/0.97 tff(1183,plain,
% 1.08/0.97 (~hskp26),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[738, 1106, 1105, 1104, 332, 23, 21, 22])).
% 1.08/0.97 tff(1184,plain,
% 1.08/0.97 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.08/0.97 inference(bind,[status(th)],[])).
% 1.08/0.97 tff(1185,plain,
% 1.08/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.08/0.97 inference(quant_intro,[status(thm)],[1184])).
% 1.08/0.97 tff(1186,plain,
% 1.08/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1187,plain,
% 1.08/0.97 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.08/0.97 inference(bind,[status(th)],[])).
% 1.08/0.97 tff(1188,plain,
% 1.08/0.97 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.08/0.97 inference(quant_intro,[status(thm)],[1187])).
% 1.08/0.97 tff(1189,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 1.08/0.97 tff(1190,plain,
% 1.08/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 1.08/0.97 tff(1191,plain,
% 1.08/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1190, 1186])).
% 1.08/0.97 tff(1192,plain,(
% 1.08/0.97 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.08/0.97 inference(skolemize,[status(sab)],[1191])).
% 1.08/0.97 tff(1193,plain,
% 1.08/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1192, 1185])).
% 1.08/0.97 tff(1194,assumption,(~hskp26), introduced(assumption)).
% 1.08/0.97 tff(1195,assumption,(~hskp25), introduced(assumption)).
% 1.08/0.97 tff(1196,plain,
% 1.08/0.97 (hskp1),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[1006, 1195, 1194])).
% 1.08/0.97 tff(1197,plain,
% 1.08/0.97 (~c3_1(a1206)),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[1013, 1196])).
% 1.08/0.97 tff(1198,plain,
% 1.08/0.97 ((hskp25 | hskp21) <=> (hskp25 | hskp21)),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1199,axiom,(hskp25 | hskp21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 1.08/0.97 tff(1200,plain,
% 1.08/0.97 (hskp25 | hskp21),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1199, 1198])).
% 1.08/0.97 tff(1201,plain,
% 1.08/0.97 (hskp25 | hskp21),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1200, 1198])).
% 1.08/0.97 tff(1202,plain,
% 1.08/0.97 (hskp25 | hskp21),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1201, 1198])).
% 1.08/0.97 tff(1203,plain,
% 1.08/0.97 (hskp25 | hskp21),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1202, 1198])).
% 1.08/0.97 tff(1204,plain,
% 1.08/0.97 (hskp25 | hskp21),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1203, 1198])).
% 1.08/0.97 tff(1205,plain,
% 1.08/0.97 (hskp25 | hskp21),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1204, 1198])).
% 1.08/0.97 tff(1206,plain,
% 1.08/0.97 (hskp25 | hskp21),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1205, 1198])).
% 1.08/0.97 tff(1207,plain,
% 1.08/0.97 (hskp25 | hskp21),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1206, 1198])).
% 1.08/0.97 tff(1208,plain,
% 1.08/0.97 (hskp21),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[1207, 1195])).
% 1.08/0.97 tff(1209,plain,
% 1.08/0.97 (~c1_1(a1257)),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[190, 1208])).
% 1.08/0.97 tff(1210,plain,
% 1.08/0.97 (~c0_1(a1257)),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[196, 1208])).
% 1.08/0.97 tff(1211,plain,
% 1.08/0.97 (c2_1(a1206)),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[1024, 1196])).
% 1.08/0.97 tff(1212,plain,
% 1.08/0.97 (c0_1(a1206)),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[1035, 1196])).
% 1.08/0.97 tff(1213,plain,
% 1.08/0.97 (c3_1(a1257)),
% 1.08/0.97 inference(unit_resolution,[status(thm)],[207, 1208])).
% 1.08/0.97 tff(1214,plain,
% 1.08/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1215,plain,
% 1.08/0.97 (((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257))) <=> (c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.08/0.97 inference(rewrite,[status(thm)],[])).
% 1.08/0.97 tff(1216,plain,
% 1.08/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 1.08/0.97 inference(monotonicity,[status(thm)],[1215])).
% 1.08/0.97 tff(1217,plain,
% 1.08/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.08/0.97 inference(transitivity,[status(thm)],[1216, 1214])).
% 1.08/0.97 tff(1218,plain,
% 1.08/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))),
% 1.08/0.97 inference(quant_inst,[status(thm)],[])).
% 1.08/0.97 tff(1219,plain,
% 1.08/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 1.08/0.97 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 1.08/0.98 tff(1220,plain,
% 1.08/0.98 ($false),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1219, 177, 1136, 1135, 1134, 1213, 1212, 1211, 1210, 1209, 1197, 1193])).
% 1.08/0.98 tff(1221,plain,(hskp25 | (~c0_1(a1214)) | (~c1_1(a1214)) | (~c3_1(a1214)) | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.08/0.98 tff(1222,plain,
% 1.08/0.98 (hskp25),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1221, 1088, 1087, 1086, 1183])).
% 1.08/0.98 tff(1223,plain,
% 1.08/0.98 (c3_1(a1204)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[777, 1222])).
% 1.08/0.98 tff(1224,plain,
% 1.08/0.98 (c2_1(a1204)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[766, 1222])).
% 1.08/0.98 tff(1225,plain,
% 1.08/0.98 (c0_1(a1204)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[754, 1222])).
% 1.08/0.98 tff(1226,plain,
% 1.08/0.98 (hskp9),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[807, 177, 1225, 1224, 1223, 104, 93, 798, 1107])).
% 1.08/0.98 tff(1227,plain,
% 1.08/0.98 (c2_1(a1219)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[819, 1226])).
% 1.08/0.98 tff(1228,plain,
% 1.08/0.98 (c1_1(a1219)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[830, 1226])).
% 1.08/0.98 tff(1229,plain,
% 1.08/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1230,plain,
% 1.08/0.98 (((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1205) | c3_1(a1205) | (~c2_1(a1205))) <=> (c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1231,plain,
% 1.08/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1205) | c3_1(a1205) | (~c2_1(a1205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 1.08/0.98 inference(monotonicity,[status(thm)],[1230])).
% 1.08/0.98 tff(1232,plain,
% 1.08/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1205) | c3_1(a1205) | (~c2_1(a1205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.08/0.98 inference(transitivity,[status(thm)],[1231, 1229])).
% 1.08/0.98 tff(1233,plain,
% 1.08/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1205) | c3_1(a1205) | (~c2_1(a1205)))),
% 1.08/0.98 inference(quant_inst,[status(thm)],[])).
% 1.08/0.98 tff(1234,plain,
% 1.08/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1233, 1232])).
% 1.08/0.98 tff(1235,plain,
% 1.08/0.98 (~c3_1(a1219)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1234, 177, 1088, 1087, 1086, 1228, 1227, 332, 22, 10, 1095])).
% 1.08/0.98 tff(1236,plain,
% 1.08/0.98 (((~hskp7) | (~c1_1(a1216))) <=> ((~hskp7) | (~c1_1(a1216)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1237,plain,
% 1.08/0.98 (((~c1_1(a1216)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a1216)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1238,axiom,((~c1_1(a1216)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 1.08/0.98 tff(1239,plain,
% 1.08/0.98 ((~hskp7) | (~c1_1(a1216))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 1.08/0.98 tff(1240,plain,
% 1.08/0.98 ((~hskp7) | (~c1_1(a1216))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1239, 1236])).
% 1.08/0.98 tff(1241,plain,
% 1.08/0.98 (~c1_1(a1216)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1240, 1163])).
% 1.08/0.98 tff(1242,plain,
% 1.08/0.98 (~c0_1(a1219)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[843, 1226])).
% 1.08/0.98 tff(1243,plain,
% 1.08/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a1219) | c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | c3_1(a1219) | (~c1_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a1219) | c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | c3_1(a1219) | (~c1_1(a1219)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1244,plain,
% 1.08/0.98 (((~ndr1_0) | c3_1(a1216) | c2_1(a1216) | (~c0_1(a1216)) | c3_1(a1216) | c1_1(a1216) | (~c0_1(a1216)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219))) <=> (c0_1(a1219) | c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | c3_1(a1219) | (~c1_1(a1219)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1245,plain,
% 1.08/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1216) | c2_1(a1216) | (~c0_1(a1216)) | c3_1(a1216) | c1_1(a1216) | (~c0_1(a1216)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a1219) | c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | c3_1(a1219) | (~c1_1(a1219))))),
% 1.08/0.98 inference(monotonicity,[status(thm)],[1244])).
% 1.08/0.98 tff(1246,plain,
% 1.08/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1216) | c2_1(a1216) | (~c0_1(a1216)) | c3_1(a1216) | c1_1(a1216) | (~c0_1(a1216)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a1219) | c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | c3_1(a1219) | (~c1_1(a1219)))),
% 1.08/0.98 inference(transitivity,[status(thm)],[1245, 1243])).
% 1.08/0.98 tff(1247,plain,
% 1.08/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1216) | c2_1(a1216) | (~c0_1(a1216)) | c3_1(a1216) | c1_1(a1216) | (~c0_1(a1216)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219)))),
% 1.08/0.98 inference(quant_inst,[status(thm)],[])).
% 1.08/0.98 tff(1248,plain,
% 1.08/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a1219) | c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | c3_1(a1219) | (~c1_1(a1219))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 1.08/0.98 tff(1249,plain,
% 1.08/0.98 ($false),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1248, 177, 1228, 1242, 1241, 1175, 1169, 921, 1235, 1182])).
% 1.08/0.98 tff(1250,plain,(hskp15 | c0_1(a1205) | c1_1(a1205) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.08/0.98 tff(1251,plain,
% 1.08/0.98 (hskp15),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1250, 23, 22, 21])).
% 1.08/0.98 tff(1252,plain,
% 1.08/0.98 (((~hskp15) | (~c2_1(a1233))) <=> ((~hskp15) | (~c2_1(a1233)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1253,plain,
% 1.08/0.98 (((~c2_1(a1233)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a1233)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1254,axiom,((~c2_1(a1233)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 1.08/0.98 tff(1255,plain,
% 1.08/0.98 ((~hskp15) | (~c2_1(a1233))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1254, 1253])).
% 1.08/0.98 tff(1256,plain,
% 1.08/0.98 ((~hskp15) | (~c2_1(a1233))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1255, 1252])).
% 1.08/0.98 tff(1257,plain,
% 1.08/0.98 (~c2_1(a1233)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1256, 1251])).
% 1.08/0.98 tff(1258,plain,
% 1.08/0.98 (((~hskp15) | c1_1(a1233)) <=> ((~hskp15) | c1_1(a1233))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1259,axiom,((~hskp15) | c1_1(a1233)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 1.08/0.98 tff(1260,plain,
% 1.08/0.98 ((~hskp15) | c1_1(a1233)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1259, 1258])).
% 1.08/0.98 tff(1261,plain,
% 1.08/0.98 ((~hskp15) | c1_1(a1233)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1260, 1258])).
% 1.08/0.98 tff(1262,plain,
% 1.08/0.98 ((~hskp15) | c1_1(a1233)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1261, 1258])).
% 1.08/0.98 tff(1263,plain,
% 1.08/0.98 ((~hskp15) | c1_1(a1233)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1262, 1258])).
% 1.08/0.98 tff(1264,plain,
% 1.08/0.98 ((~hskp15) | c1_1(a1233)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1263, 1258])).
% 1.08/0.98 tff(1265,plain,
% 1.08/0.98 ((~hskp15) | c1_1(a1233)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1264, 1258])).
% 1.08/0.98 tff(1266,plain,
% 1.08/0.98 ((~hskp15) | c1_1(a1233)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1265, 1258])).
% 1.08/0.98 tff(1267,plain,
% 1.08/0.98 ((~hskp15) | c1_1(a1233)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1266, 1258])).
% 1.08/0.98 tff(1268,plain,
% 1.08/0.98 (c1_1(a1233)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1267, 1251])).
% 1.08/0.98 tff(1269,plain,
% 1.08/0.98 (((~hskp15) | c0_1(a1233)) <=> ((~hskp15) | c0_1(a1233))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1270,axiom,((~hskp15) | c0_1(a1233)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 1.08/0.98 tff(1271,plain,
% 1.08/0.98 ((~hskp15) | c0_1(a1233)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1270, 1269])).
% 1.08/0.98 tff(1272,plain,
% 1.08/0.98 ((~hskp15) | c0_1(a1233)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1271, 1269])).
% 1.08/0.98 tff(1273,plain,
% 1.08/0.98 ((~hskp15) | c0_1(a1233)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1272, 1269])).
% 1.08/0.98 tff(1274,plain,
% 1.08/0.98 ((~hskp15) | c0_1(a1233)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1273, 1269])).
% 1.08/0.98 tff(1275,plain,
% 1.08/0.98 ((~hskp15) | c0_1(a1233)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1274, 1269])).
% 1.08/0.98 tff(1276,plain,
% 1.08/0.98 ((~hskp15) | c0_1(a1233)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1275, 1269])).
% 1.08/0.98 tff(1277,plain,
% 1.08/0.98 ((~hskp15) | c0_1(a1233)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1276, 1269])).
% 1.08/0.98 tff(1278,plain,
% 1.08/0.98 ((~hskp15) | c0_1(a1233)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1277, 1269])).
% 1.08/0.98 tff(1279,plain,
% 1.08/0.98 (c0_1(a1233)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1278, 1251])).
% 1.08/0.98 tff(1280,plain,
% 1.08/0.98 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1281,plain,
% 1.08/0.98 ((hskp10 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233))) <=> (hskp10 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1282,plain,
% 1.08/0.98 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))))),
% 1.08/0.98 inference(monotonicity,[status(thm)],[1281])).
% 1.08/0.98 tff(1283,plain,
% 1.08/0.98 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.08/0.98 inference(transitivity,[status(thm)],[1282, 1280])).
% 1.08/0.98 tff(1284,plain,
% 1.08/0.98 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)))),
% 1.08/0.98 inference(quant_inst,[status(thm)],[])).
% 1.08/0.98 tff(1285,plain,
% 1.08/0.98 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 1.08/0.98 tff(1286,plain,
% 1.08/0.98 (hskp10),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1285, 177, 755, 767, 778, 1279, 1268, 1257, 64])).
% 1.08/0.98 tff(1287,plain,
% 1.08/0.98 (((~hskp10) | (~c3_1(a1223))) <=> ((~hskp10) | (~c3_1(a1223)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1288,plain,
% 1.08/0.98 (((~c3_1(a1223)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a1223)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1289,axiom,((~c3_1(a1223)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 1.08/0.98 tff(1290,plain,
% 1.08/0.98 ((~hskp10) | (~c3_1(a1223))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1289, 1288])).
% 1.08/0.98 tff(1291,plain,
% 1.08/0.98 ((~hskp10) | (~c3_1(a1223))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1290, 1287])).
% 1.08/0.98 tff(1292,plain,
% 1.08/0.98 (~c3_1(a1223)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1291, 1286])).
% 1.08/0.98 tff(1293,plain,
% 1.08/0.98 (((~hskp10) | (~c1_1(a1223))) <=> ((~hskp10) | (~c1_1(a1223)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1294,plain,
% 1.08/0.98 (((~c1_1(a1223)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a1223)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1295,axiom,((~c1_1(a1223)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 1.08/0.98 tff(1296,plain,
% 1.08/0.98 ((~hskp10) | (~c1_1(a1223))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1295, 1294])).
% 1.08/0.98 tff(1297,plain,
% 1.08/0.98 ((~hskp10) | (~c1_1(a1223))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1296, 1293])).
% 1.08/0.98 tff(1298,plain,
% 1.08/0.98 (~c1_1(a1223)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1297, 1286])).
% 1.08/0.98 tff(1299,plain,
% 1.08/0.98 (((~hskp10) | c2_1(a1223)) <=> ((~hskp10) | c2_1(a1223))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1300,axiom,((~hskp10) | c2_1(a1223)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 1.08/0.98 tff(1301,plain,
% 1.08/0.98 ((~hskp10) | c2_1(a1223)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 1.08/0.98 tff(1302,plain,
% 1.08/0.98 ((~hskp10) | c2_1(a1223)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1301, 1299])).
% 1.08/0.98 tff(1303,plain,
% 1.08/0.98 ((~hskp10) | c2_1(a1223)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1302, 1299])).
% 1.08/0.98 tff(1304,plain,
% 1.08/0.98 ((~hskp10) | c2_1(a1223)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1303, 1299])).
% 1.08/0.98 tff(1305,plain,
% 1.08/0.98 ((~hskp10) | c2_1(a1223)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1304, 1299])).
% 1.08/0.98 tff(1306,plain,
% 1.08/0.98 ((~hskp10) | c2_1(a1223)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1305, 1299])).
% 1.08/0.98 tff(1307,plain,
% 1.08/0.98 ((~hskp10) | c2_1(a1223)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1306, 1299])).
% 1.08/0.98 tff(1308,plain,
% 1.08/0.98 ((~hskp10) | c2_1(a1223)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1307, 1299])).
% 1.08/0.98 tff(1309,plain,
% 1.08/0.98 (c2_1(a1223)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1308, 1286])).
% 1.08/0.98 tff(1310,plain,
% 1.08/0.98 (((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)))) <=> ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp13 | hskp6 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1311,plain,
% 1.08/0.98 ((hskp13 | hskp6 | (~ndr1_0) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223))) <=> (hskp13 | hskp6 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1312,plain,
% 1.08/0.98 (((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223)))) <=> ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223))))),
% 1.08/0.98 inference(monotonicity,[status(thm)],[1311])).
% 1.08/0.98 tff(1313,plain,
% 1.08/0.98 (((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223)))) <=> ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp13 | hskp6 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)))),
% 1.08/0.98 inference(transitivity,[status(thm)],[1312, 1310])).
% 1.08/0.98 tff(1314,plain,
% 1.08/0.98 ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223)))),
% 1.08/0.98 inference(quant_inst,[status(thm)],[])).
% 1.08/0.98 tff(1315,plain,
% 1.08/0.98 ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp13 | hskp6 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 1.08/0.98 tff(1316,plain,
% 1.08/0.98 (hskp13),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1315, 177, 24, 1309, 1298, 1292, 54])).
% 1.08/0.98 tff(1317,plain,
% 1.08/0.98 (((~hskp13) | (~c1_1(a1229))) <=> ((~hskp13) | (~c1_1(a1229)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1318,plain,
% 1.08/0.98 (((~c1_1(a1229)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a1229)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1319,axiom,((~c1_1(a1229)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 1.08/0.98 tff(1320,plain,
% 1.08/0.98 ((~hskp13) | (~c1_1(a1229))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1319, 1318])).
% 1.08/0.98 tff(1321,plain,
% 1.08/0.98 ((~hskp13) | (~c1_1(a1229))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1320, 1317])).
% 1.08/0.98 tff(1322,plain,
% 1.08/0.98 (~c1_1(a1229)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1321, 1316])).
% 1.08/0.98 tff(1323,plain,
% 1.08/0.98 (((~hskp13) | c2_1(a1229)) <=> ((~hskp13) | c2_1(a1229))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1324,axiom,((~hskp13) | c2_1(a1229)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 1.08/0.98 tff(1325,plain,
% 1.08/0.98 ((~hskp13) | c2_1(a1229)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 1.08/0.98 tff(1326,plain,
% 1.08/0.98 ((~hskp13) | c2_1(a1229)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1325, 1323])).
% 1.08/0.98 tff(1327,plain,
% 1.08/0.98 ((~hskp13) | c2_1(a1229)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1326, 1323])).
% 1.08/0.98 tff(1328,plain,
% 1.08/0.98 ((~hskp13) | c2_1(a1229)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1327, 1323])).
% 1.08/0.98 tff(1329,plain,
% 1.08/0.98 ((~hskp13) | c2_1(a1229)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1328, 1323])).
% 1.08/0.98 tff(1330,plain,
% 1.08/0.98 ((~hskp13) | c2_1(a1229)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1329, 1323])).
% 1.08/0.98 tff(1331,plain,
% 1.08/0.98 ((~hskp13) | c2_1(a1229)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1330, 1323])).
% 1.08/0.98 tff(1332,plain,
% 1.08/0.98 ((~hskp13) | c2_1(a1229)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1331, 1323])).
% 1.08/0.98 tff(1333,plain,
% 1.08/0.98 (c2_1(a1229)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1332, 1316])).
% 1.08/0.98 tff(1334,plain,
% 1.08/0.98 (((~hskp13) | c0_1(a1229)) <=> ((~hskp13) | c0_1(a1229))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1335,axiom,((~hskp13) | c0_1(a1229)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 1.08/0.98 tff(1336,plain,
% 1.08/0.98 ((~hskp13) | c0_1(a1229)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1335, 1334])).
% 1.08/0.98 tff(1337,plain,
% 1.08/0.98 ((~hskp13) | c0_1(a1229)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1336, 1334])).
% 1.08/0.98 tff(1338,plain,
% 1.08/0.98 ((~hskp13) | c0_1(a1229)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1337, 1334])).
% 1.08/0.98 tff(1339,plain,
% 1.08/0.98 ((~hskp13) | c0_1(a1229)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1338, 1334])).
% 1.08/0.98 tff(1340,plain,
% 1.08/0.98 ((~hskp13) | c0_1(a1229)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1339, 1334])).
% 1.08/0.98 tff(1341,plain,
% 1.08/0.98 ((~hskp13) | c0_1(a1229)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1340, 1334])).
% 1.08/0.98 tff(1342,plain,
% 1.08/0.98 ((~hskp13) | c0_1(a1229)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1341, 1334])).
% 1.08/0.98 tff(1343,plain,
% 1.08/0.98 ((~hskp13) | c0_1(a1229)),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1342, 1334])).
% 1.08/0.98 tff(1344,plain,
% 1.08/0.98 (c0_1(a1229)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1343, 1316])).
% 1.08/0.98 tff(1345,plain,
% 1.08/0.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c2_1(a1233) | c1_1(a1229) | (~ndr1_0) | (~c0_1(a1229)) | (~c2_1(a1229)) | (~c0_1(a1233)) | (~c3_1(a1233)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c2_1(a1233) | c1_1(a1229) | (~ndr1_0) | (~c0_1(a1229)) | (~c2_1(a1229)) | (~c0_1(a1233)) | (~c3_1(a1233)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1346,plain,
% 1.08/0.98 ((hskp6 | (~ndr1_0) | c2_1(a1233) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1229) | (~c2_1(a1229)) | (~c0_1(a1229))) <=> (hskp6 | c2_1(a1233) | c1_1(a1229) | (~ndr1_0) | (~c0_1(a1229)) | (~c2_1(a1229)) | (~c0_1(a1233)) | (~c3_1(a1233)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1347,plain,
% 1.08/0.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1233) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1229) | (~c2_1(a1229)) | (~c0_1(a1229)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c2_1(a1233) | c1_1(a1229) | (~ndr1_0) | (~c0_1(a1229)) | (~c2_1(a1229)) | (~c0_1(a1233)) | (~c3_1(a1233))))),
% 1.08/0.98 inference(monotonicity,[status(thm)],[1346])).
% 1.08/0.98 tff(1348,plain,
% 1.08/0.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1233) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1229) | (~c2_1(a1229)) | (~c0_1(a1229)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c2_1(a1233) | c1_1(a1229) | (~ndr1_0) | (~c0_1(a1229)) | (~c2_1(a1229)) | (~c0_1(a1233)) | (~c3_1(a1233)))),
% 1.08/0.98 inference(transitivity,[status(thm)],[1347, 1345])).
% 1.08/0.98 tff(1349,plain,
% 1.08/0.98 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1233) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1229) | (~c2_1(a1229)) | (~c0_1(a1229)))),
% 1.08/0.98 inference(quant_inst,[status(thm)],[])).
% 1.08/0.98 tff(1350,plain,
% 1.08/0.98 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c2_1(a1233) | c1_1(a1229) | (~ndr1_0) | (~c0_1(a1229)) | (~c2_1(a1229)) | (~c0_1(a1233)) | (~c3_1(a1233))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1349, 1348])).
% 1.08/0.98 tff(1351,plain,
% 1.08/0.98 (~c3_1(a1233)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1350, 177, 24, 1279, 1344, 1333, 1257, 1322, 44])).
% 1.08/0.98 tff(1352,plain,
% 1.08/0.98 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1353,plain,
% 1.08/0.98 (((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233))) <=> (c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1354,plain,
% 1.08/0.98 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204))))),
% 1.08/0.98 inference(monotonicity,[status(thm)],[1353])).
% 1.08/0.98 tff(1355,plain,
% 1.08/0.98 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 1.08/0.98 inference(transitivity,[status(thm)],[1354, 1352])).
% 1.08/0.98 tff(1356,plain,
% 1.08/0.98 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)))),
% 1.08/0.98 inference(quant_inst,[status(thm)],[])).
% 1.08/0.98 tff(1357,plain,
% 1.08/0.98 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 1.08/0.98 tff(1358,plain,
% 1.08/0.98 (~c1_1(a1204)),
% 1.08/0.98 inference(unit_resolution,[status(thm)],[1357, 177, 755, 767, 1279, 1257, 896, 1351])).
% 1.08/0.98 tff(1359,plain,
% 1.08/0.98 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 1.08/0.98 inference(bind,[status(th)],[])).
% 1.08/0.98 tff(1360,plain,
% 1.08/0.98 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.08/0.98 inference(quant_intro,[status(thm)],[1359])).
% 1.08/0.98 tff(1361,plain,
% 1.08/0.98 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1362,plain,
% 1.08/0.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 1.08/0.98 inference(bind,[status(th)],[])).
% 1.08/0.98 tff(1363,plain,
% 1.08/0.98 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.08/0.98 inference(quant_intro,[status(thm)],[1362])).
% 1.08/0.98 tff(1364,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 1.08/0.98 tff(1365,plain,
% 1.08/0.98 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1364, 1363])).
% 1.08/0.98 tff(1366,plain,
% 1.08/0.98 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1365, 1361])).
% 1.08/0.98 tff(1367,plain,(
% 1.08/0.98 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.08/0.98 inference(skolemize,[status(sab)],[1366])).
% 1.08/0.98 tff(1368,plain,
% 1.08/0.98 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.08/0.98 inference(modus_ponens,[status(thm)],[1367, 1360])).
% 1.08/0.98 tff(1369,plain,
% 1.08/0.98 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1370,plain,
% 1.08/0.98 ((hskp9 | (~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223))) <=> (hskp9 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.08/0.98 inference(rewrite,[status(thm)],[])).
% 1.08/0.98 tff(1371,plain,
% 1.08/0.98 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204))))),
% 1.08/0.99 inference(monotonicity,[status(thm)],[1370])).
% 1.08/0.99 tff(1372,plain,
% 1.08/0.99 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.08/0.99 inference(transitivity,[status(thm)],[1371, 1369])).
% 1.08/0.99 tff(1373,plain,
% 1.08/0.99 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223)))),
% 1.08/0.99 inference(quant_inst,[status(thm)],[])).
% 1.08/0.99 tff(1374,plain,
% 1.08/0.99 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204))),
% 1.08/0.99 inference(modus_ponens,[status(thm)],[1373, 1372])).
% 1.08/0.99 tff(1375,plain,
% 1.08/0.99 (hskp9),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1374, 177, 755, 778, 1309, 1298, 1292, 1368, 1358])).
% 1.08/0.99 tff(1376,plain,
% 1.08/0.99 (~c0_1(a1219)),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[843, 1375])).
% 1.08/0.99 tff(1377,plain,
% 1.08/0.99 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.08/0.99 inference(bind,[status(th)],[])).
% 1.08/0.99 tff(1378,plain,
% 1.08/0.99 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.08/0.99 inference(quant_intro,[status(thm)],[1377])).
% 1.08/0.99 tff(1379,plain,
% 1.08/0.99 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.08/0.99 inference(rewrite,[status(thm)],[])).
% 1.08/0.99 tff(1380,plain,
% 1.08/0.99 (^[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)) | (~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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.08/0.99 inference(bind,[status(th)],[])).
% 1.08/0.99 tff(1381,plain,
% 1.08/0.99 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.08/0.99 inference(quant_intro,[status(thm)],[1380])).
% 1.08/0.99 tff(1382,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 1.08/0.99 tff(1383,plain,
% 1.08/0.99 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.08/0.99 inference(modus_ponens,[status(thm)],[1382, 1381])).
% 1.08/0.99 tff(1384,plain,
% 1.08/0.99 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.08/0.99 inference(modus_ponens,[status(thm)],[1383, 1379])).
% 1.08/0.99 tff(1385,plain,(
% 1.08/0.99 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.08/0.99 inference(skolemize,[status(sab)],[1384])).
% 1.08/0.99 tff(1386,plain,
% 1.08/0.99 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.08/0.99 inference(modus_ponens,[status(thm)],[1385, 1378])).
% 1.08/0.99 tff(1387,plain,
% 1.08/0.99 (c2_1(a1219)),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[819, 1375])).
% 1.08/0.99 tff(1388,plain,
% 1.08/0.99 (c1_1(a1219)),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[830, 1375])).
% 1.08/0.99 tff(1389,plain,
% 1.08/0.99 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | c2_1(a1233) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c0_1(a1233)) | (~c1_1(a1233)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp1 | c2_1(a1233) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 1.08/0.99 inference(rewrite,[status(thm)],[])).
% 1.08/0.99 tff(1390,plain,
% 1.08/0.99 ((hskp1 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219))) <=> (hskp1 | c2_1(a1233) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 1.08/0.99 inference(rewrite,[status(thm)],[])).
% 1.08/0.99 tff(1391,plain,
% 1.08/0.99 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | c2_1(a1233) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c0_1(a1233)) | (~c1_1(a1233))))),
% 1.08/0.99 inference(monotonicity,[status(thm)],[1390])).
% 1.08/0.99 tff(1392,plain,
% 1.08/0.99 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp1 | c2_1(a1233) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 1.08/0.99 inference(transitivity,[status(thm)],[1391, 1389])).
% 1.08/0.99 tff(1393,plain,
% 1.08/0.99 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)))),
% 1.08/0.99 inference(quant_inst,[status(thm)],[])).
% 1.08/0.99 tff(1394,plain,
% 1.08/0.99 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp1 | c2_1(a1233) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c0_1(a1233)) | (~c1_1(a1233))),
% 1.08/0.99 inference(modus_ponens,[status(thm)],[1393, 1392])).
% 1.08/0.99 tff(1395,plain,
% 1.08/0.99 (hskp1),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1394, 177, 1279, 1268, 1388, 1387, 1257, 1376, 1386])).
% 1.08/0.99 tff(1396,plain,
% 1.08/0.99 (c2_1(a1206)),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1024, 1395])).
% 1.08/0.99 tff(1397,plain,
% 1.08/0.99 (c0_1(a1206)),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1035, 1395])).
% 1.08/0.99 tff(1398,plain,
% 1.08/0.99 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1233) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | c3_1(a1233))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1233) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | c3_1(a1233))),
% 1.08/0.99 inference(rewrite,[status(thm)],[])).
% 1.08/0.99 tff(1399,plain,
% 1.08/0.99 (((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233))) <=> (c2_1(a1233) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | c3_1(a1233))),
% 1.08/0.99 inference(rewrite,[status(thm)],[])).
% 1.08/0.99 tff(1400,plain,
% 1.08/0.99 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1233) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | c3_1(a1233)))),
% 1.08/0.99 inference(monotonicity,[status(thm)],[1399])).
% 1.08/0.99 tff(1401,plain,
% 1.08/0.99 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1233) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | c3_1(a1233))),
% 1.08/0.99 inference(transitivity,[status(thm)],[1400, 1398])).
% 1.08/0.99 tff(1402,plain,
% 1.08/0.99 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)))),
% 1.08/0.99 inference(quant_inst,[status(thm)],[])).
% 1.08/0.99 tff(1403,plain,
% 1.08/0.99 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1233) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | c3_1(a1233)),
% 1.08/0.99 inference(modus_ponens,[status(thm)],[1402, 1401])).
% 1.08/0.99 tff(1404,plain,
% 1.08/0.99 (~c1_1(a1206)),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1403, 177, 1279, 1397, 1396, 1257, 896, 1351])).
% 1.08/0.99 tff(1405,plain,
% 1.08/0.99 (^[U: $i] : refl((hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.08/0.99 inference(bind,[status(th)],[])).
% 1.08/0.99 tff(1406,plain,
% 1.08/0.99 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.08/0.99 inference(quant_intro,[status(thm)],[1405])).
% 1.08/0.99 tff(1407,plain,
% 1.08/0.99 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.08/0.99 inference(rewrite,[status(thm)],[])).
% 1.08/0.99 tff(1408,plain,
% 1.08/0.99 (^[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)) | hskp17) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp17))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp17) | hskp5) <=> ((hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp5))), rewrite(((hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp5) <=> (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp17) | hskp5) <=> (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.08/0.99 inference(bind,[status(th)],[])).
% 1.08/0.99 tff(1409,plain,
% 1.08/0.99 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp17) | hskp5) <=> ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.08/0.99 inference(quant_intro,[status(thm)],[1408])).
% 1.08/0.99 tff(1410,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp17) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 1.08/0.99 tff(1411,plain,
% 1.08/0.99 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.08/0.99 inference(modus_ponens,[status(thm)],[1410, 1409])).
% 1.08/0.99 tff(1412,plain,
% 1.08/0.99 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.08/0.99 inference(modus_ponens,[status(thm)],[1411, 1407])).
% 1.08/0.99 tff(1413,plain,(
% 1.08/0.99 ![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.08/0.99 inference(skolemize,[status(sab)],[1412])).
% 1.08/0.99 tff(1414,plain,
% 1.08/0.99 (![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.08/0.99 inference(modus_ponens,[status(thm)],[1413, 1406])).
% 1.08/0.99 tff(1415,plain,
% 1.08/0.99 (~c3_1(a1206)),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1013, 1395])).
% 1.08/0.99 tff(1416,plain,
% 1.08/0.99 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp5 | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp5 | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)))),
% 1.08/0.99 inference(rewrite,[status(thm)],[])).
% 1.08/0.99 tff(1417,plain,
% 1.08/0.99 ((hskp17 | hskp5 | (~ndr1_0) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206))) <=> (hskp17 | hskp5 | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)))),
% 1.08/0.99 inference(rewrite,[status(thm)],[])).
% 1.08/0.99 tff(1418,plain,
% 1.08/0.99 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp5 | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206))))),
% 1.08/0.99 inference(monotonicity,[status(thm)],[1417])).
% 1.08/0.99 tff(1419,plain,
% 1.08/0.99 (((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)))) <=> ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp5 | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)))),
% 1.08/0.99 inference(transitivity,[status(thm)],[1418, 1416])).
% 1.08/0.99 tff(1420,plain,
% 1.08/0.99 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp5 | (~ndr1_0) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)))),
% 1.08/0.99 inference(quant_inst,[status(thm)],[])).
% 1.08/0.99 tff(1421,plain,
% 1.08/0.99 ((~![U: $i] : (hskp17 | hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp5 | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206))),
% 1.08/0.99 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 1.08/0.99 tff(1422,plain,
% 1.08/0.99 (hskp17 | c1_1(a1206)),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1421, 177, 21, 1397, 1415, 1414])).
% 1.08/0.99 tff(1423,plain,
% 1.08/0.99 (hskp17),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1422, 1404])).
% 1.08/0.99 tff(1424,plain,
% 1.08/0.99 (((~hskp17) | (~c1_1(a1237))) <=> ((~hskp17) | (~c1_1(a1237)))),
% 1.08/0.99 inference(rewrite,[status(thm)],[])).
% 1.08/0.99 tff(1425,plain,
% 1.08/0.99 (((~c1_1(a1237)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a1237)))),
% 1.08/0.99 inference(rewrite,[status(thm)],[])).
% 1.08/0.99 tff(1426,axiom,((~c1_1(a1237)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 1.08/0.99 tff(1427,plain,
% 1.08/0.99 ((~hskp17) | (~c1_1(a1237))),
% 1.08/0.99 inference(modus_ponens,[status(thm)],[1426, 1425])).
% 1.08/0.99 tff(1428,plain,
% 1.08/0.99 ((~hskp17) | (~c1_1(a1237))),
% 1.08/0.99 inference(modus_ponens,[status(thm)],[1427, 1424])).
% 1.08/0.99 tff(1429,plain,
% 1.08/0.99 (~c1_1(a1237)),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1428, 1423])).
% 1.08/0.99 tff(1430,plain,
% 1.08/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a1233) | c0_1(a1219) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1233)) | c3_1(a1233))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a1233) | c0_1(a1219) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1233)) | c3_1(a1233))),
% 1.08/0.99 inference(rewrite,[status(thm)],[])).
% 1.08/0.99 tff(1431,plain,
% 1.08/0.99 (((~ndr1_0) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219))) <=> (c2_1(a1233) | c0_1(a1219) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1233)) | c3_1(a1233))),
% 1.08/0.99 inference(rewrite,[status(thm)],[])).
% 1.08/0.99 tff(1432,plain,
% 1.08/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a1233) | c0_1(a1219) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1233)) | c3_1(a1233)))),
% 1.08/0.99 inference(monotonicity,[status(thm)],[1431])).
% 1.08/0.99 tff(1433,plain,
% 1.08/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a1233) | c0_1(a1219) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1233)) | c3_1(a1233))),
% 1.08/0.99 inference(transitivity,[status(thm)],[1432, 1430])).
% 1.08/0.99 tff(1434,plain,
% 1.08/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)) | c3_1(a1206) | c1_1(a1206) | (~c0_1(a1206)) | c0_1(a1219) | c3_1(a1219) | (~c1_1(a1219)))),
% 1.08/0.99 inference(quant_inst,[status(thm)],[])).
% 1.08/0.99 tff(1435,plain,
% 1.08/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a1233) | c0_1(a1219) | c3_1(a1206) | (~ndr1_0) | c1_1(a1206) | (~c0_1(a1206)) | c3_1(a1219) | (~c1_1(a1219)) | (~c0_1(a1233)) | c3_1(a1233)),
% 1.08/0.99 inference(modus_ponens,[status(thm)],[1434, 1433])).
% 1.08/0.99 tff(1436,plain,
% 1.08/0.99 (c3_1(a1219)),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1435, 177, 1279, 1388, 1397, 1257, 1376, 1415, 921, 1351, 1404])).
% 1.08/0.99 tff(1437,assumption,(c3_1(a1233)), introduced(assumption)).
% 1.08/0.99 tff(1438,plain,
% 1.08/0.99 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)))),
% 1.08/0.99 inference(rewrite,[status(thm)],[])).
% 1.08/0.99 tff(1439,plain,
% 1.08/0.99 ((hskp5 | (~ndr1_0) | (~c1_1(a1233)) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205))) <=> (hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)))),
% 1.08/0.99 inference(rewrite,[status(thm)],[])).
% 1.08/0.99 tff(1440,plain,
% 1.08/0.99 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1233)) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233))))),
% 1.08/0.99 inference(monotonicity,[status(thm)],[1439])).
% 1.08/0.99 tff(1441,plain,
% 1.08/0.99 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1233)) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)))),
% 1.08/0.99 inference(transitivity,[status(thm)],[1440, 1438])).
% 1.08/0.99 tff(1442,plain,
% 1.08/0.99 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c1_1(a1233)) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))),
% 1.08/0.99 inference(quant_inst,[status(thm)],[])).
% 1.08/0.99 tff(1443,plain,
% 1.08/0.99 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c3_1(a1205)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233))),
% 1.08/0.99 inference(modus_ponens,[status(thm)],[1442, 1441])).
% 1.08/0.99 tff(1444,plain,
% 1.08/0.99 ((~c3_1(a1205)) | (~c3_1(a1233))),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1443, 177, 21, 1279, 1268, 22, 23, 20])).
% 1.08/0.99 tff(1445,plain,
% 1.08/0.99 (~c3_1(a1205)),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1444, 1437])).
% 1.08/0.99 tff(1446,plain,
% 1.08/0.99 (c2_1(a1205)),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[226, 1445, 219])).
% 1.08/0.99 tff(1447,plain,
% 1.08/0.99 (((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)))) <=> ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp13 | hskp6 | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)))),
% 1.08/0.99 inference(rewrite,[status(thm)],[])).
% 1.08/0.99 tff(1448,plain,
% 1.08/0.99 ((hskp13 | hskp6 | (~ndr1_0) | c3_1(a1205) | c1_1(a1205) | (~c2_1(a1205))) <=> (hskp13 | hskp6 | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)))),
% 1.08/0.99 inference(rewrite,[status(thm)],[])).
% 1.08/0.99 tff(1449,plain,
% 1.08/0.99 (((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c3_1(a1205) | c1_1(a1205) | (~c2_1(a1205)))) <=> ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205))))),
% 1.08/0.99 inference(monotonicity,[status(thm)],[1448])).
% 1.08/0.99 tff(1450,plain,
% 1.08/0.99 (((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c3_1(a1205) | c1_1(a1205) | (~c2_1(a1205)))) <=> ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp13 | hskp6 | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205)))),
% 1.08/0.99 inference(transitivity,[status(thm)],[1449, 1447])).
% 1.08/0.99 tff(1451,plain,
% 1.08/0.99 ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp13 | hskp6 | (~ndr1_0) | c3_1(a1205) | c1_1(a1205) | (~c2_1(a1205)))),
% 1.08/0.99 inference(quant_inst,[status(thm)],[])).
% 1.08/0.99 tff(1452,plain,
% 1.08/0.99 ((~![U: $i] : (hskp13 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp13 | hskp6 | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c2_1(a1205))),
% 1.08/0.99 inference(modus_ponens,[status(thm)],[1451, 1450])).
% 1.08/0.99 tff(1453,plain,
% 1.08/0.99 (hskp13 | hskp6 | c3_1(a1205) | (~c2_1(a1205))),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1452, 177, 23, 54])).
% 1.08/0.99 tff(1454,plain,
% 1.08/0.99 (hskp13),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1453, 1446, 24, 1445])).
% 1.08/0.99 tff(1455,plain,
% 1.08/0.99 (~c1_1(a1229)),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1321, 1454])).
% 1.08/0.99 tff(1456,plain,
% 1.08/0.99 (c2_1(a1229)),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1332, 1454])).
% 1.08/0.99 tff(1457,plain,
% 1.08/0.99 (c0_1(a1229)),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1343, 1454])).
% 1.08/0.99 tff(1458,plain,
% 1.08/0.99 ($false),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1350, 177, 24, 1279, 1457, 1456, 1257, 1455, 44, 1437])).
% 1.08/0.99 tff(1459,plain,((~c3_1(a1233)) | hskp6 | c1_1(a1205) | hskp28 | c0_1(a1205) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.08/0.99 tff(1460,plain,
% 1.08/0.99 (~c3_1(a1233)),
% 1.08/0.99 inference(unit_resolution,[status(thm)],[1459, 219, 23, 24, 22, 21])).
% 1.08/0.99 tff(1461,assumption,(~c2_1(a1233)), introduced(assumption)).
% 1.08/0.99 tff(1462,assumption,(~c3_1(a1233)), introduced(assumption)).
% 1.08/0.99 tff(1463,assumption,(c1_1(a1233)), introduced(assumption)).
% 1.08/0.99 tff(1464,assumption,(c0_1(a1233)), introduced(assumption)).
% 1.08/0.99 tff(1465,plain,
% 1.08/0.99 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))))),
% 1.08/0.99 inference(bind,[status(th)],[])).
% 1.08/0.99 tff(1466,plain,
% 1.08/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.08/0.99 inference(quant_intro,[status(thm)],[1465])).
% 1.08/0.99 tff(1467,plain,
% 1.08/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.08/0.99 inference(rewrite,[status(thm)],[])).
% 1.08/0.99 tff(1468,plain,
% 1.08/0.99 (^[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))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | 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(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))))),
% 1.08/0.99 inference(bind,[status(th)],[])).
% 1.08/0.99 tff(1469,plain,
% 1.08/0.99 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.08/0.99 inference(quant_intro,[status(thm)],[1468])).
% 1.08/0.99 tff(1470,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 1.08/0.99 tff(1471,plain,
% 1.08/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1470, 1469])).
% 1.08/1.00 tff(1472,plain,
% 1.08/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1471, 1467])).
% 1.08/1.00 tff(1473,plain,(
% 1.08/1.00 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.08/1.00 inference(skolemize,[status(sab)],[1472])).
% 1.08/1.00 tff(1474,plain,
% 1.08/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1473, 1466])).
% 1.08/1.00 tff(1475,plain,
% 1.08/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1267) | c2_1(a1267) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1267)))),
% 1.08/1.00 inference(rewrite,[status(thm)],[])).
% 1.08/1.00 tff(1476,plain,
% 1.08/1.00 (((~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c3_1(a1233) | c2_1(a1233) | (~c1_1(a1233)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267))) <=> (c1_1(a1267) | c2_1(a1267) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1267)))),
% 1.08/1.00 inference(rewrite,[status(thm)],[])).
% 1.08/1.00 tff(1477,plain,
% 1.08/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c3_1(a1233) | c2_1(a1233) | (~c1_1(a1233)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1267))))),
% 1.08/1.00 inference(monotonicity,[status(thm)],[1476])).
% 1.08/1.00 tff(1478,plain,
% 1.08/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c3_1(a1233) | c2_1(a1233) | (~c1_1(a1233)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1267) | c2_1(a1267) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1267)))),
% 1.08/1.00 inference(transitivity,[status(thm)],[1477, 1475])).
% 1.08/1.00 tff(1479,plain,
% 1.08/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c3_1(a1233) | c2_1(a1233) | (~c1_1(a1233)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)))),
% 1.08/1.00 inference(quant_inst,[status(thm)],[])).
% 1.08/1.00 tff(1480,plain,
% 1.08/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1267) | c2_1(a1267) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1267))),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1479, 1478])).
% 1.08/1.00 tff(1481,plain,
% 1.08/1.00 ($false),
% 1.08/1.00 inference(unit_resolution,[status(thm)],[1480, 177, 926, 1464, 1463, 924, 923, 1461, 1474, 1462])).
% 1.08/1.00 tff(1482,plain,(c3_1(a1233) | (~c0_1(a1267)) | (~c0_1(a1233)) | (~c1_1(a1233)) | c1_1(a1267) | c2_1(a1267) | c2_1(a1233)), inference(lemma,lemma(discharge,[]))).
% 1.08/1.00 tff(1483,plain,
% 1.08/1.00 ($false),
% 1.08/1.00 inference(unit_resolution,[status(thm)],[1482, 486, 497, 1464, 1463, 1462, 480, 1461])).
% 1.08/1.00 tff(1484,plain,((~hskp24) | (~c0_1(a1233)) | (~c1_1(a1233)) | c3_1(a1233) | c2_1(a1233)), inference(lemma,lemma(discharge,[]))).
% 1.08/1.00 tff(1485,plain,
% 1.08/1.00 (~hskp24),
% 1.08/1.00 inference(unit_resolution,[status(thm)],[1484, 1460, 1268, 1279, 1257])).
% 1.08/1.00 tff(1486,plain,
% 1.08/1.00 (hskp26),
% 1.08/1.00 inference(unit_resolution,[status(thm)],[175, 1485, 219])).
% 1.08/1.00 tff(1487,plain,
% 1.08/1.00 (c2_1(a1208)),
% 1.08/1.00 inference(unit_resolution,[status(thm)],[695, 1486])).
% 1.08/1.00 tff(1488,plain,
% 1.08/1.00 (c1_1(a1208)),
% 1.08/1.00 inference(unit_resolution,[status(thm)],[706, 1486])).
% 1.08/1.00 tff(1489,plain,
% 1.08/1.00 (c0_1(a1208)),
% 1.08/1.00 inference(unit_resolution,[status(thm)],[717, 1486])).
% 1.08/1.00 tff(1490,plain,
% 1.08/1.00 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | c3_1(a1233))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | c3_1(a1233))),
% 1.08/1.00 inference(rewrite,[status(thm)],[])).
% 1.08/1.00 tff(1491,plain,
% 1.08/1.00 (((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233))) <=> (c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | c3_1(a1233))),
% 1.08/1.00 inference(rewrite,[status(thm)],[])).
% 1.08/1.00 tff(1492,plain,
% 1.08/1.00 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | c3_1(a1233)))),
% 1.08/1.00 inference(monotonicity,[status(thm)],[1491])).
% 1.08/1.00 tff(1493,plain,
% 1.08/1.00 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | c3_1(a1233))),
% 1.08/1.00 inference(transitivity,[status(thm)],[1492, 1490])).
% 1.08/1.00 tff(1494,plain,
% 1.08/1.00 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)))),
% 1.08/1.00 inference(quant_inst,[status(thm)],[])).
% 1.08/1.00 tff(1495,plain,
% 1.08/1.00 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | c3_1(a1233)),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1494, 1493])).
% 1.08/1.00 tff(1496,plain,
% 1.08/1.00 ($false),
% 1.08/1.00 inference(unit_resolution,[status(thm)],[1495, 177, 1489, 1488, 1487, 1279, 1257, 896, 1460])).
% 1.08/1.00 tff(1497,plain,(hskp28 | c1_1(a1205) | hskp6 | c0_1(a1205) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.08/1.00 tff(1498,plain,
% 1.08/1.00 (hskp28),
% 1.08/1.00 inference(unit_resolution,[status(thm)],[1497, 24, 23, 22, 21])).
% 1.08/1.00 tff(1499,plain,
% 1.08/1.00 (c3_1(a1214)),
% 1.08/1.00 inference(unit_resolution,[status(thm)],[300, 1498])).
% 1.08/1.00 tff(1500,plain,
% 1.08/1.00 (c1_1(a1214)),
% 1.08/1.00 inference(unit_resolution,[status(thm)],[311, 1498])).
% 1.08/1.00 tff(1501,plain,
% 1.08/1.00 (c0_1(a1214)),
% 1.08/1.00 inference(unit_resolution,[status(thm)],[322, 1498])).
% 1.08/1.00 tff(1502,plain,
% 1.08/1.00 (~c3_1(a1205)),
% 1.08/1.00 inference(unit_resolution,[status(thm)],[1094, 177, 21, 1501, 1500, 1499, 22, 23, 20])).
% 1.08/1.00 tff(1503,plain,
% 1.08/1.00 ((~c2_1(a1205)) | (~c3_1(a1219))),
% 1.08/1.00 inference(unit_resolution,[status(thm)],[1234, 177, 1501, 1500, 1499, 1388, 1387, 22, 10, 1502])).
% 1.08/1.00 tff(1504,plain,
% 1.08/1.00 (~c2_1(a1205)),
% 1.08/1.00 inference(unit_resolution,[status(thm)],[1503, 1436])).
% 1.08/1.00 tff(1505,plain,
% 1.08/1.00 (((~hskp17) | c3_1(a1237)) <=> ((~hskp17) | c3_1(a1237))),
% 1.08/1.00 inference(rewrite,[status(thm)],[])).
% 1.08/1.00 tff(1506,axiom,((~hskp17) | c3_1(a1237)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 1.08/1.00 tff(1507,plain,
% 1.08/1.00 ((~hskp17) | c3_1(a1237)),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1506, 1505])).
% 1.08/1.00 tff(1508,plain,
% 1.08/1.00 ((~hskp17) | c3_1(a1237)),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1507, 1505])).
% 1.08/1.00 tff(1509,plain,
% 1.08/1.00 ((~hskp17) | c3_1(a1237)),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1508, 1505])).
% 1.08/1.00 tff(1510,plain,
% 1.08/1.00 ((~hskp17) | c3_1(a1237)),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1509, 1505])).
% 1.08/1.00 tff(1511,plain,
% 1.08/1.00 ((~hskp17) | c3_1(a1237)),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1510, 1505])).
% 1.08/1.00 tff(1512,plain,
% 1.08/1.00 ((~hskp17) | c3_1(a1237)),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1511, 1505])).
% 1.08/1.00 tff(1513,plain,
% 1.08/1.00 ((~hskp17) | c3_1(a1237)),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1512, 1505])).
% 1.08/1.00 tff(1514,plain,
% 1.08/1.00 ((~hskp17) | c3_1(a1237)),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1513, 1505])).
% 1.08/1.00 tff(1515,plain,
% 1.08/1.00 (c3_1(a1237)),
% 1.08/1.00 inference(unit_resolution,[status(thm)],[1514, 1423])).
% 1.08/1.00 tff(1516,plain,
% 1.08/1.00 (((~hskp17) | c0_1(a1237)) <=> ((~hskp17) | c0_1(a1237))),
% 1.08/1.00 inference(rewrite,[status(thm)],[])).
% 1.08/1.00 tff(1517,axiom,((~hskp17) | c0_1(a1237)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 1.08/1.00 tff(1518,plain,
% 1.08/1.00 ((~hskp17) | c0_1(a1237)),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1517, 1516])).
% 1.08/1.00 tff(1519,plain,
% 1.08/1.00 ((~hskp17) | c0_1(a1237)),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1518, 1516])).
% 1.08/1.00 tff(1520,plain,
% 1.08/1.00 ((~hskp17) | c0_1(a1237)),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1519, 1516])).
% 1.08/1.00 tff(1521,plain,
% 1.08/1.00 ((~hskp17) | c0_1(a1237)),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1520, 1516])).
% 1.08/1.00 tff(1522,plain,
% 1.08/1.00 ((~hskp17) | c0_1(a1237)),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1521, 1516])).
% 1.08/1.00 tff(1523,plain,
% 1.08/1.00 ((~hskp17) | c0_1(a1237)),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1522, 1516])).
% 1.08/1.00 tff(1524,plain,
% 1.08/1.00 ((~hskp17) | c0_1(a1237)),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1523, 1516])).
% 1.08/1.00 tff(1525,plain,
% 1.08/1.00 ((~hskp17) | c0_1(a1237)),
% 1.08/1.00 inference(modus_ponens,[status(thm)],[1524, 1516])).
% 1.08/1.00 tff(1526,plain,
% 1.08/1.00 (c0_1(a1237)),
% 1.08/1.00 inference(unit_resolution,[status(thm)],[1525, 1423])).
% 1.08/1.00 tff(1527,plain,
% 1.08/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1205) | c1_1(a1237) | c0_1(a1219) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1237)) | (~c0_1(a1237)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1205) | c1_1(a1237) | c0_1(a1219) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1237)) | (~c0_1(a1237)))),
% 1.08/1.00 inference(rewrite,[status(thm)],[])).
% 1.08/1.00 tff(1528,plain,
% 1.08/1.00 (((~ndr1_0) | c1_1(a1237) | (~c3_1(a1237)) | (~c0_1(a1237)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1205) | c1_1(a1205) | c0_1(a1205)) <=> (c2_1(a1205) | c1_1(a1237) | c0_1(a1219) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1237)) | (~c0_1(a1237)))),
% 1.08/1.00 inference(rewrite,[status(thm)],[])).
% 1.08/1.00 tff(1529,plain,
% 1.08/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1237) | (~c3_1(a1237)) | (~c0_1(a1237)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1205) | c1_1(a1205) | c0_1(a1205))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a1205) | c1_1(a1237) | c0_1(a1219) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1237)) | (~c0_1(a1237))))),
% 1.08/1.00 inference(monotonicity,[status(thm)],[1528])).
% 1.08/1.00 tff(1530,plain,
% 1.08/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1237) | (~c3_1(a1237)) | (~c0_1(a1237)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1205) | c1_1(a1205) | c0_1(a1205))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1205) | c1_1(a1237) | c0_1(a1219) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1237)) | (~c0_1(a1237)))),
% 1.14/1.00 inference(transitivity,[status(thm)],[1529, 1527])).
% 1.14/1.00 tff(1531,plain,
% 1.14/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1237) | (~c3_1(a1237)) | (~c0_1(a1237)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1205) | c1_1(a1205) | c0_1(a1205))),
% 1.14/1.00 inference(quant_inst,[status(thm)],[])).
% 1.14/1.00 tff(1532,plain,
% 1.14/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a1205) | c1_1(a1237) | c0_1(a1219) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1237)) | (~c0_1(a1237))),
% 1.14/1.00 inference(modus_ponens,[status(thm)],[1531, 1530])).
% 1.14/1.00 tff(1533,plain,
% 1.14/1.00 ($false),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1532, 177, 1526, 1515, 1388, 1387, 1504, 1429, 1376, 22, 23, 34])).
% 1.14/1.00 tff(1534,plain,((~hskp25) | c0_1(a1205) | c1_1(a1205) | hskp5 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.14/1.00 tff(1535,plain,
% 1.14/1.00 (~hskp25),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1534, 24, 23, 21, 22])).
% 1.14/1.00 tff(1536,plain,
% 1.14/1.00 (hskp21),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1207, 1535])).
% 1.14/1.00 tff(1537,plain,
% 1.14/1.00 (~c1_1(a1257)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[190, 1536])).
% 1.14/1.00 tff(1538,plain,
% 1.14/1.00 (~c0_1(a1257)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[196, 1536])).
% 1.14/1.00 tff(1539,plain,
% 1.14/1.00 (c3_1(a1257)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[207, 1536])).
% 1.14/1.00 tff(1540,plain,
% 1.14/1.00 ($false),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[329, 177, 21, 1501, 1500, 1499, 1539, 1538, 1537, 20])).
% 1.14/1.00 tff(1541,plain,(hskp6 | hskp5 | c1_1(a1205) | c0_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.00 tff(1542,plain,
% 1.14/1.00 (hskp6),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1541, 23, 21, 22])).
% 1.14/1.00 tff(1543,plain,
% 1.14/1.00 (~c3_1(a1215)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[92, 1542])).
% 1.14/1.00 tff(1544,plain,
% 1.14/1.00 (c1_1(a1215)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[103, 1542])).
% 1.14/1.00 tff(1545,plain,
% 1.14/1.00 (c2_1(a1215)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[114, 1542])).
% 1.14/1.00 tff(1546,plain,
% 1.14/1.00 (c2_1(a1205)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[331, 1545, 21, 1544, 1543, 22, 23])).
% 1.14/1.00 tff(1547,plain,
% 1.14/1.00 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.14/1.00 inference(bind,[status(th)],[])).
% 1.14/1.00 tff(1548,plain,
% 1.14/1.00 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.14/1.00 inference(quant_intro,[status(thm)],[1547])).
% 1.14/1.00 tff(1549,plain,
% 1.14/1.00 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.14/1.00 inference(rewrite,[status(thm)],[])).
% 1.14/1.00 tff(1550,plain,
% 1.14/1.00 (^[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)) | hskp8) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp8) <=> (hskp8 | (~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)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.14/1.00 inference(bind,[status(th)],[])).
% 1.14/1.00 tff(1551,plain,
% 1.14/1.00 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.14/1.00 inference(quant_intro,[status(thm)],[1550])).
% 1.14/1.00 tff(1552,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)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 1.14/1.00 tff(1553,plain,
% 1.14/1.00 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.14/1.00 inference(modus_ponens,[status(thm)],[1552, 1551])).
% 1.14/1.00 tff(1554,plain,
% 1.14/1.00 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.14/1.00 inference(modus_ponens,[status(thm)],[1553, 1549])).
% 1.14/1.00 tff(1555,plain,(
% 1.14/1.00 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.14/1.00 inference(skolemize,[status(sab)],[1554])).
% 1.14/1.00 tff(1556,plain,
% 1.14/1.00 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.14/1.00 inference(modus_ponens,[status(thm)],[1555, 1548])).
% 1.14/1.00 tff(1557,plain,
% 1.14/1.00 (hskp24),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[175, 1194, 219])).
% 1.14/1.00 tff(1558,plain,
% 1.14/1.00 (c3_1(a1233)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1484, 1557, 1268, 1279, 1257])).
% 1.14/1.00 tff(1559,plain,
% 1.14/1.00 (~c3_1(a1205)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1444, 1558])).
% 1.14/1.00 tff(1560,plain,
% 1.14/1.00 (~c2_1(a1267)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[479, 1557])).
% 1.14/1.00 tff(1561,plain,
% 1.14/1.00 (~c1_1(a1267)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[485, 1557])).
% 1.14/1.00 tff(1562,plain,
% 1.14/1.00 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c3_1(a1267)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c3_1(a1267)))),
% 1.14/1.00 inference(rewrite,[status(thm)],[])).
% 1.14/1.00 tff(1563,plain,
% 1.14/1.00 ((hskp26 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)) | c3_1(a1205) | c1_1(a1205) | c0_1(a1205)) <=> (hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c3_1(a1267)))),
% 1.14/1.00 inference(rewrite,[status(thm)],[])).
% 1.14/1.00 tff(1564,plain,
% 1.14/1.00 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)) | c3_1(a1205) | c1_1(a1205) | c0_1(a1205))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c3_1(a1267))))),
% 1.14/1.00 inference(monotonicity,[status(thm)],[1563])).
% 1.14/1.00 tff(1565,plain,
% 1.14/1.00 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)) | c3_1(a1205) | c1_1(a1205) | c0_1(a1205))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c3_1(a1267)))),
% 1.14/1.00 inference(transitivity,[status(thm)],[1564, 1562])).
% 1.14/1.00 tff(1566,plain,
% 1.14/1.00 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp26 | (~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c3_1(a1267)) | c3_1(a1205) | c1_1(a1205) | c0_1(a1205))),
% 1.14/1.00 inference(quant_inst,[status(thm)],[])).
% 1.14/1.00 tff(1567,plain,
% 1.14/1.00 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp26 | c1_1(a1267) | c2_1(a1267) | c0_1(a1205) | c1_1(a1205) | (~ndr1_0) | c3_1(a1205) | (~c3_1(a1267))),
% 1.14/1.00 inference(modus_ponens,[status(thm)],[1566, 1565])).
% 1.14/1.00 tff(1568,plain,
% 1.14/1.00 (~c3_1(a1267)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1567, 177, 1194, 1561, 1560, 22, 23, 945, 1559])).
% 1.14/1.00 tff(1569,plain,
% 1.14/1.00 (hskp11),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1102, 1559, 1546])).
% 1.14/1.00 tff(1570,plain,
% 1.14/1.00 (c1_1(a1224)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[634, 1569])).
% 1.14/1.00 tff(1571,plain,
% 1.14/1.00 (~c2_1(a1224)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[612, 1569])).
% 1.14/1.00 tff(1572,plain,
% 1.14/1.00 (c3_1(a1224)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[623, 1569])).
% 1.14/1.00 tff(1573,plain,
% 1.14/1.00 (~c0_1(a1215)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[683, 1572, 1544, 1546, 1545, 1571, 1570, 23, 21, 22])).
% 1.14/1.00 tff(1574,plain,
% 1.14/1.00 (c0_1(a1267)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[496, 1557])).
% 1.14/1.00 tff(1575,plain,
% 1.14/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267))),
% 1.14/1.00 inference(rewrite,[status(thm)],[])).
% 1.14/1.00 tff(1576,plain,
% 1.14/1.00 (((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1215) | c3_1(a1215) | (~c1_1(a1215))) <=> (c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267))),
% 1.14/1.00 inference(rewrite,[status(thm)],[])).
% 1.14/1.00 tff(1577,plain,
% 1.14/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1215) | c3_1(a1215) | (~c1_1(a1215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267)))),
% 1.14/1.00 inference(monotonicity,[status(thm)],[1576])).
% 1.14/1.00 tff(1578,plain,
% 1.14/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1215) | c3_1(a1215) | (~c1_1(a1215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267))),
% 1.14/1.00 inference(transitivity,[status(thm)],[1577, 1575])).
% 1.14/1.00 tff(1579,plain,
% 1.14/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1215) | c3_1(a1215) | (~c1_1(a1215)))),
% 1.14/1.00 inference(quant_inst,[status(thm)],[])).
% 1.14/1.00 tff(1580,plain,
% 1.14/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1267) | c2_1(a1267) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267)),
% 1.14/1.00 inference(modus_ponens,[status(thm)],[1579, 1578])).
% 1.14/1.00 tff(1581,plain,
% 1.14/1.00 ($false),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1580, 177, 1574, 1544, 1561, 1560, 1543, 921, 1573, 1568])).
% 1.14/1.00 tff(1582,plain,(hskp26 | c0_1(a1205) | c1_1(a1205) | hskp5 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.14/1.00 tff(1583,plain,
% 1.14/1.00 (hskp26),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1582, 219, 23, 21, 22])).
% 1.14/1.00 tff(1584,plain,
% 1.14/1.00 (c2_1(a1208)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[695, 1583])).
% 1.14/1.00 tff(1585,plain,
% 1.14/1.00 (c1_1(a1208)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[706, 1583])).
% 1.14/1.00 tff(1586,plain,
% 1.14/1.00 (c0_1(a1208)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[717, 1583])).
% 1.14/1.00 tff(1587,plain,
% 1.14/1.00 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | (~c1_1(a1233)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 1.14/1.00 inference(rewrite,[status(thm)],[])).
% 1.14/1.00 tff(1588,plain,
% 1.14/1.00 ((hskp8 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233))) <=> (hskp8 | c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 1.14/1.00 inference(rewrite,[status(thm)],[])).
% 1.14/1.00 tff(1589,plain,
% 1.14/1.00 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | (~c1_1(a1233))))),
% 1.14/1.00 inference(monotonicity,[status(thm)],[1588])).
% 1.14/1.00 tff(1590,plain,
% 1.14/1.00 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 1.14/1.00 inference(transitivity,[status(thm)],[1589, 1587])).
% 1.14/1.00 tff(1591,plain,
% 1.14/1.00 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)))),
% 1.14/1.00 inference(quant_inst,[status(thm)],[])).
% 1.14/1.00 tff(1592,plain,
% 1.14/1.00 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a1233) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1233)) | (~c1_1(a1233))),
% 1.14/1.00 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 1.14/1.00 tff(1593,plain,
% 1.14/1.00 (hskp8),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1592, 177, 1586, 1585, 1584, 1279, 1268, 1257, 1556])).
% 1.14/1.00 tff(1594,plain,
% 1.14/1.00 (~c0_1(a1217)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[578, 1593])).
% 1.14/1.00 tff(1595,plain,
% 1.14/1.00 (~c3_1(a1217)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[584, 1593])).
% 1.14/1.00 tff(1596,plain,
% 1.14/1.00 (hskp11),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[604, 1595, 219, 1594])).
% 1.14/1.00 tff(1597,plain,
% 1.14/1.00 (~c2_1(a1224)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[612, 1596])).
% 1.14/1.00 tff(1598,plain,
% 1.14/1.00 (c1_1(a1224)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[634, 1596])).
% 1.14/1.00 tff(1599,plain,
% 1.14/1.00 (c3_1(a1224)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[623, 1596])).
% 1.14/1.00 tff(1600,plain,
% 1.14/1.00 ($false),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[738, 1599, 1598, 1583, 1597, 1546, 23, 21, 22])).
% 1.14/1.00 tff(1601,plain,(hskp28 | c1_1(a1205) | hskp5 | c0_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.00 tff(1602,plain,
% 1.14/1.00 (hskp28),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1601, 23, 21, 22])).
% 1.14/1.00 tff(1603,plain,
% 1.14/1.00 (c3_1(a1214)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[300, 1602])).
% 1.14/1.00 tff(1604,plain,
% 1.14/1.00 (c1_1(a1214)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[311, 1602])).
% 1.14/1.00 tff(1605,plain,
% 1.14/1.00 (c0_1(a1214)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[322, 1602])).
% 1.14/1.00 tff(1606,plain,
% 1.14/1.00 (~c3_1(a1205)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1094, 177, 21, 1605, 1604, 1603, 22, 23, 20])).
% 1.14/1.00 tff(1607,plain,
% 1.14/1.00 (hskp11),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1102, 1606, 1546])).
% 1.14/1.00 tff(1608,plain,
% 1.14/1.00 (c1_1(a1224)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[634, 1607])).
% 1.14/1.00 tff(1609,plain,
% 1.14/1.00 (~c2_1(a1224)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[612, 1607])).
% 1.14/1.00 tff(1610,plain,
% 1.14/1.00 (c3_1(a1224)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[623, 1607])).
% 1.14/1.00 tff(1611,plain,
% 1.14/1.00 (~c0_1(a1215)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[683, 1610, 1544, 1546, 1545, 1609, 1608, 23, 21, 22])).
% 1.14/1.00 tff(1612,plain,
% 1.14/1.00 (~hskp2),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1144, 1611, 1604, 1603, 1544, 1545, 1543, 1605])).
% 1.14/1.00 tff(1613,plain,
% 1.14/1.00 (hskp7 | hskp2),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1161, 177, 1605, 1604, 1603, 1155])).
% 1.14/1.00 tff(1614,plain,
% 1.14/1.00 (hskp7),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1613, 1612])).
% 1.14/1.00 tff(1615,plain,
% 1.14/1.00 (~c3_1(a1216)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1168, 1614])).
% 1.14/1.00 tff(1616,plain,
% 1.14/1.00 (~c2_1(a1216)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1174, 1614])).
% 1.14/1.00 tff(1617,plain,
% 1.14/1.00 (~c1_1(a1216)),
% 1.14/1.00 inference(unit_resolution,[status(thm)],[1240, 1614])).
% 1.14/1.00 tff(1618,plain,
% 1.14/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1216)))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1619,plain,
% 1.14/1.01 (((~ndr1_0) | c3_1(a1216) | c2_1(a1216) | (~c0_1(a1216)) | c3_1(a1216) | c1_1(a1216) | (~c0_1(a1216)) | c0_1(a1215) | c3_1(a1215) | (~c1_1(a1215))) <=> (c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1216)))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1620,plain,
% 1.14/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1216) | c2_1(a1216) | (~c0_1(a1216)) | c3_1(a1216) | c1_1(a1216) | (~c0_1(a1216)) | c0_1(a1215) | c3_1(a1215) | (~c1_1(a1215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1216))))),
% 1.14/1.01 inference(monotonicity,[status(thm)],[1619])).
% 1.14/1.01 tff(1621,plain,
% 1.14/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1216) | c2_1(a1216) | (~c0_1(a1216)) | c3_1(a1216) | c1_1(a1216) | (~c0_1(a1216)) | c0_1(a1215) | c3_1(a1215) | (~c1_1(a1215)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1216)))),
% 1.14/1.01 inference(transitivity,[status(thm)],[1620, 1618])).
% 1.14/1.01 tff(1622,plain,
% 1.14/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1216) | c2_1(a1216) | (~c0_1(a1216)) | c3_1(a1216) | c1_1(a1216) | (~c0_1(a1216)) | c0_1(a1215) | c3_1(a1215) | (~c1_1(a1215)))),
% 1.14/1.01 inference(quant_inst,[status(thm)],[])).
% 1.14/1.01 tff(1623,plain,
% 1.14/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1216) | c2_1(a1216) | c3_1(a1216) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c0_1(a1216))),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1622, 1621])).
% 1.14/1.01 tff(1624,plain,
% 1.14/1.01 (~c0_1(a1216)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1623, 177, 1544, 1617, 1616, 1615, 1543, 921, 1611])).
% 1.14/1.01 tff(1625,plain,
% 1.14/1.01 ($false),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1181, 177, 1605, 1604, 1603, 1544, 1545, 1616, 1615, 1543, 74, 1624])).
% 1.14/1.01 tff(1626,plain,(c1_1(a1205) | hskp5 | c0_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.01 tff(1627,plain,
% 1.14/1.01 (c1_1(a1205)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1626, 22, 21])).
% 1.14/1.01 tff(1628,plain,
% 1.14/1.01 (((~hskp0) | (~c1_1(a1205))) <=> ((~hskp0) | (~c1_1(a1205)))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1629,plain,
% 1.14/1.01 (((~c1_1(a1205)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a1205)))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1630,axiom,((~c1_1(a1205)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 1.14/1.01 tff(1631,plain,
% 1.14/1.01 ((~hskp0) | (~c1_1(a1205))),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1630, 1629])).
% 1.14/1.01 tff(1632,plain,
% 1.14/1.01 ((~hskp0) | (~c1_1(a1205))),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1631, 1628])).
% 1.14/1.01 tff(1633,plain,
% 1.14/1.01 (~hskp0),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1632, 1627])).
% 1.14/1.01 tff(1634,assumption,(hskp6), introduced(assumption)).
% 1.14/1.01 tff(1635,plain,
% 1.14/1.01 (~c3_1(a1215)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[92, 1634])).
% 1.14/1.01 tff(1636,assumption,(~hskp0), introduced(assumption)).
% 1.14/1.01 tff(1637,plain,
% 1.14/1.01 (c1_1(a1215)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[103, 1634])).
% 1.14/1.01 tff(1638,plain,
% 1.14/1.01 (c2_1(a1215)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[114, 1634])).
% 1.14/1.01 tff(1639,plain,
% 1.14/1.01 (^[U: $i] : refl((hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))),
% 1.14/1.01 inference(bind,[status(th)],[])).
% 1.14/1.01 tff(1640,plain,
% 1.14/1.01 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.14/1.01 inference(quant_intro,[status(thm)],[1639])).
% 1.14/1.01 tff(1641,plain,
% 1.14/1.01 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1642,plain,
% 1.14/1.01 (^[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)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) | hskp0) <=> ((hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp0))), rewrite(((hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp0) <=> (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) | hskp0) <=> (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))))),
% 1.14/1.01 inference(bind,[status(th)],[])).
% 1.14/1.01 tff(1643,plain,
% 1.14/1.01 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) | hskp0) <=> ![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.14/1.01 inference(quant_intro,[status(thm)],[1642])).
% 1.14/1.01 tff(1644,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 1.14/1.01 tff(1645,plain,
% 1.14/1.01 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1644, 1643])).
% 1.14/1.01 tff(1646,plain,
% 1.14/1.01 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1645, 1641])).
% 1.14/1.01 tff(1647,plain,(
% 1.14/1.01 ![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.14/1.01 inference(skolemize,[status(sab)],[1646])).
% 1.14/1.01 tff(1648,plain,
% 1.14/1.01 (![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1647, 1640])).
% 1.14/1.01 tff(1649,plain,
% 1.14/1.01 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp0 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp0 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1650,plain,
% 1.14/1.01 ((hskp27 | hskp0 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215))) <=> (hskp27 | hskp0 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1651,plain,
% 1.14/1.01 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp0 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp0 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215))))),
% 1.14/1.01 inference(monotonicity,[status(thm)],[1650])).
% 1.14/1.01 tff(1652,plain,
% 1.14/1.01 (((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp0 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp0 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.14/1.01 inference(transitivity,[status(thm)],[1651, 1649])).
% 1.14/1.01 tff(1653,plain,
% 1.14/1.01 ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp0 | (~ndr1_0) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.14/1.01 inference(quant_inst,[status(thm)],[])).
% 1.14/1.01 tff(1654,plain,
% 1.14/1.01 ((~![U: $i] : (hskp27 | hskp0 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp0 | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215))),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1653, 1652])).
% 1.14/1.01 tff(1655,plain,
% 1.14/1.01 (hskp27 | hskp0 | c0_1(a1215)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1654, 177, 140, 138, 1648])).
% 1.14/1.01 tff(1656,plain,
% 1.14/1.01 (hskp27),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1655, 756, 1636])).
% 1.14/1.01 tff(1657,plain,
% 1.14/1.01 (((~hskp27) | c3_1(a1213)) <=> ((~hskp27) | c3_1(a1213))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1658,axiom,((~hskp27) | c3_1(a1213)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 1.14/1.01 tff(1659,plain,
% 1.14/1.01 ((~hskp27) | c3_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 1.14/1.01 tff(1660,plain,
% 1.14/1.01 ((~hskp27) | c3_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1659, 1657])).
% 1.14/1.01 tff(1661,plain,
% 1.14/1.01 ((~hskp27) | c3_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1660, 1657])).
% 1.14/1.01 tff(1662,plain,
% 1.14/1.01 ((~hskp27) | c3_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1661, 1657])).
% 1.14/1.01 tff(1663,plain,
% 1.14/1.01 ((~hskp27) | c3_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1662, 1657])).
% 1.14/1.01 tff(1664,plain,
% 1.14/1.01 ((~hskp27) | c3_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1663, 1657])).
% 1.14/1.01 tff(1665,plain,
% 1.14/1.01 ((~hskp27) | c3_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1664, 1657])).
% 1.14/1.01 tff(1666,plain,
% 1.14/1.01 ((~hskp27) | c3_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1665, 1657])).
% 1.14/1.01 tff(1667,plain,
% 1.14/1.01 (c3_1(a1213)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1666, 1656])).
% 1.14/1.01 tff(1668,plain,
% 1.14/1.01 (((~hskp27) | c2_1(a1213)) <=> ((~hskp27) | c2_1(a1213))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1669,axiom,((~hskp27) | c2_1(a1213)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 1.14/1.01 tff(1670,plain,
% 1.14/1.01 ((~hskp27) | c2_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1669, 1668])).
% 1.14/1.01 tff(1671,plain,
% 1.14/1.01 ((~hskp27) | c2_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1670, 1668])).
% 1.14/1.01 tff(1672,plain,
% 1.14/1.01 ((~hskp27) | c2_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1671, 1668])).
% 1.14/1.01 tff(1673,plain,
% 1.14/1.01 ((~hskp27) | c2_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1672, 1668])).
% 1.14/1.01 tff(1674,plain,
% 1.14/1.01 ((~hskp27) | c2_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1673, 1668])).
% 1.14/1.01 tff(1675,plain,
% 1.14/1.01 ((~hskp27) | c2_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1674, 1668])).
% 1.14/1.01 tff(1676,plain,
% 1.14/1.01 ((~hskp27) | c2_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1675, 1668])).
% 1.14/1.01 tff(1677,plain,
% 1.14/1.01 ((~hskp27) | c2_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1676, 1668])).
% 1.14/1.01 tff(1678,plain,
% 1.14/1.01 (c2_1(a1213)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1677, 1656])).
% 1.14/1.01 tff(1679,plain,
% 1.14/1.01 (((~hskp27) | c1_1(a1213)) <=> ((~hskp27) | c1_1(a1213))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1680,axiom,((~hskp27) | c1_1(a1213)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 1.14/1.01 tff(1681,plain,
% 1.14/1.01 ((~hskp27) | c1_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1680, 1679])).
% 1.14/1.01 tff(1682,plain,
% 1.14/1.01 ((~hskp27) | c1_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1681, 1679])).
% 1.14/1.01 tff(1683,plain,
% 1.14/1.01 ((~hskp27) | c1_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1682, 1679])).
% 1.14/1.01 tff(1684,plain,
% 1.14/1.01 ((~hskp27) | c1_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1683, 1679])).
% 1.14/1.01 tff(1685,plain,
% 1.14/1.01 ((~hskp27) | c1_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1684, 1679])).
% 1.14/1.01 tff(1686,plain,
% 1.14/1.01 ((~hskp27) | c1_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1685, 1679])).
% 1.14/1.01 tff(1687,plain,
% 1.14/1.01 ((~hskp27) | c1_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1686, 1679])).
% 1.14/1.01 tff(1688,plain,
% 1.14/1.01 ((~hskp27) | c1_1(a1213)),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1687, 1679])).
% 1.14/1.01 tff(1689,plain,
% 1.14/1.01 (c1_1(a1213)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1688, 1656])).
% 1.14/1.01 tff(1690,plain,
% 1.14/1.01 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213)))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1691,plain,
% 1.14/1.01 (((~ndr1_0) | (~c2_1(a1213)) | (~c1_1(a1213)) | (~c3_1(a1213)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215))) <=> (c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213)))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1692,plain,
% 1.14/1.01 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1213)) | (~c1_1(a1213)) | (~c3_1(a1213)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213))))),
% 1.14/1.01 inference(monotonicity,[status(thm)],[1691])).
% 1.14/1.01 tff(1693,plain,
% 1.14/1.01 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1213)) | (~c1_1(a1213)) | (~c3_1(a1213)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213)))),
% 1.14/1.01 inference(transitivity,[status(thm)],[1692, 1690])).
% 1.14/1.01 tff(1694,plain,
% 1.14/1.01 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | ((~ndr1_0) | (~c2_1(a1213)) | (~c1_1(a1213)) | (~c3_1(a1213)) | c3_1(a1215) | c0_1(a1215) | (~c1_1(a1215)))),
% 1.14/1.01 inference(quant_inst,[status(thm)],[])).
% 1.14/1.01 tff(1695,plain,
% 1.14/1.01 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | c3_1(a1215) | (~ndr1_0) | c0_1(a1215) | (~c1_1(a1215)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213))),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1694, 1693])).
% 1.14/1.01 tff(1696,plain,
% 1.14/1.01 ($false),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1695, 177, 1689, 1678, 1667, 140, 138, 788, 756])).
% 1.14/1.01 tff(1697,plain,(c0_1(a1215) | (~c1_1(a1215)) | c3_1(a1215) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.14/1.01 tff(1698,plain,
% 1.14/1.01 (c0_1(a1215)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1697, 1636, 138, 140])).
% 1.14/1.01 tff(1699,plain,
% 1.14/1.01 (hskp21),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[184, 1636])).
% 1.14/1.01 tff(1700,plain,
% 1.14/1.01 (~c1_1(a1257)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[190, 1699])).
% 1.14/1.01 tff(1701,plain,
% 1.14/1.01 (~c0_1(a1257)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[196, 1699])).
% 1.14/1.01 tff(1702,plain,
% 1.14/1.01 (c3_1(a1257)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[207, 1699])).
% 1.14/1.01 tff(1703,plain,
% 1.14/1.01 (hskp23),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[262, 1698, 1636])).
% 1.14/1.01 tff(1704,plain,
% 1.14/1.01 (~c3_1(a1261)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[268, 1703])).
% 1.14/1.01 tff(1705,plain,
% 1.14/1.01 (~c2_1(a1261)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[274, 1703])).
% 1.14/1.01 tff(1706,plain,
% 1.14/1.01 (~c0_1(a1261)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[280, 1703])).
% 1.14/1.01 tff(1707,plain,
% 1.14/1.01 (hskp28),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[287, 177, 1706, 1705, 1704, 218])).
% 1.14/1.01 tff(1708,plain,
% 1.14/1.01 (c3_1(a1214)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[300, 1707])).
% 1.14/1.01 tff(1709,plain,
% 1.14/1.01 (c1_1(a1214)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[311, 1707])).
% 1.14/1.01 tff(1710,plain,
% 1.14/1.01 (c0_1(a1214)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[322, 1707])).
% 1.14/1.01 tff(1711,plain,
% 1.14/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1257) | c1_1(a1257) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1712,plain,
% 1.14/1.01 (((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c2_1(a1215)) | (~c0_1(a1215)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257))) <=> (c0_1(a1257) | c1_1(a1257) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1713,plain,
% 1.14/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c2_1(a1215)) | (~c0_1(a1215)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1257) | c1_1(a1257) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 1.14/1.01 inference(monotonicity,[status(thm)],[1712])).
% 1.14/1.01 tff(1714,plain,
% 1.14/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c2_1(a1215)) | (~c0_1(a1215)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.01 inference(transitivity,[status(thm)],[1713, 1711])).
% 1.14/1.01 tff(1715,plain,
% 1.14/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1215) | (~c2_1(a1215)) | (~c0_1(a1215)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))),
% 1.14/1.01 inference(quant_inst,[status(thm)],[])).
% 1.14/1.01 tff(1716,plain,
% 1.14/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | c3_1(a1215) | (~ndr1_0) | (~c0_1(a1215)) | (~c2_1(a1215)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1715, 1714])).
% 1.14/1.01 tff(1717,plain,
% 1.14/1.01 ($false),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1716, 177, 1710, 1709, 1708, 1702, 139, 1701, 1700, 138, 1193, 1698])).
% 1.14/1.01 tff(1718,plain,(hskp0 | (~c2_1(a1215)) | c3_1(a1215) | (~c1_1(a1215))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.01 tff(1719,plain,
% 1.14/1.01 ($false),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1718, 1638, 1637, 1636, 1635])).
% 1.14/1.01 tff(1720,plain,((~hskp6) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.14/1.01 tff(1721,plain,
% 1.14/1.01 (~hskp6),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1720, 1633])).
% 1.14/1.01 tff(1722,plain,
% 1.14/1.01 (hskp15),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[86, 1721, 21])).
% 1.14/1.01 tff(1723,plain,
% 1.14/1.01 (~c2_1(a1233)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1256, 1722])).
% 1.14/1.01 tff(1724,plain,
% 1.14/1.01 (c1_1(a1233)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1267, 1722])).
% 1.14/1.01 tff(1725,plain,
% 1.14/1.01 (c0_1(a1233)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1278, 1722])).
% 1.14/1.01 tff(1726,assumption,(c1_1(a1205)), introduced(assumption)).
% 1.14/1.01 tff(1727,plain,
% 1.14/1.01 (~hskp0),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1632, 1726])).
% 1.14/1.01 tff(1728,plain,
% 1.14/1.01 (~hskp6),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1720, 1727])).
% 1.14/1.01 tff(1729,plain,
% 1.14/1.01 (c3_1(a1205)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[226, 116, 219])).
% 1.14/1.01 tff(1730,plain,
% 1.14/1.01 (c3_1(a1233)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1484, 1557, 1463, 1461, 1464])).
% 1.14/1.01 tff(1731,plain,
% 1.14/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c3_1(a1257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c3_1(a1257)))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1732,plain,
% 1.14/1.01 (((~ndr1_0) | (~c1_1(a1233)) | (~c3_1(a1233)) | (~c0_1(a1233)) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257))) <=> (c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c3_1(a1257)))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1733,plain,
% 1.14/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1233)) | (~c3_1(a1233)) | (~c0_1(a1233)) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c3_1(a1257))))),
% 1.14/1.01 inference(monotonicity,[status(thm)],[1732])).
% 1.14/1.01 tff(1734,plain,
% 1.14/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1233)) | (~c3_1(a1233)) | (~c0_1(a1233)) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c3_1(a1257)))),
% 1.14/1.01 inference(transitivity,[status(thm)],[1733, 1731])).
% 1.14/1.01 tff(1735,plain,
% 1.14/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1233)) | (~c3_1(a1233)) | (~c0_1(a1233)) | c3_1(a1206) | (~c2_1(a1206)) | (~c0_1(a1206)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))),
% 1.14/1.01 inference(quant_inst,[status(thm)],[])).
% 1.14/1.01 tff(1736,plain,
% 1.14/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | c3_1(a1206) | (~ndr1_0) | (~c2_1(a1206)) | (~c0_1(a1206)) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c3_1(a1257))),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1735, 1734])).
% 1.14/1.01 tff(1737,plain,
% 1.14/1.01 ($false),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1736, 177, 1213, 1464, 1463, 1212, 1211, 1210, 1209, 1197, 1193, 1437])).
% 1.14/1.01 tff(1738,plain,(hskp25 | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c3_1(a1233)) | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.14/1.01 tff(1739,plain,
% 1.14/1.01 (hskp25),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1738, 1730, 1463, 1464, 1194])).
% 1.14/1.01 tff(1740,plain,
% 1.14/1.01 (c2_1(a1204)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[766, 1739])).
% 1.14/1.01 tff(1741,plain,
% 1.14/1.01 (c0_1(a1204)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[754, 1739])).
% 1.14/1.01 tff(1742,plain,
% 1.14/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1743,plain,
% 1.14/1.01 (((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c2_1(a1205) | (~c3_1(a1205)) | (~c1_1(a1205)) | c2_1(a1205) | c0_1(a1205) | (~c3_1(a1205))) <=> (c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1744,plain,
% 1.14/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c2_1(a1205) | (~c3_1(a1205)) | (~c1_1(a1205)) | c2_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204))))),
% 1.14/1.01 inference(monotonicity,[status(thm)],[1743])).
% 1.14/1.01 tff(1745,plain,
% 1.14/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c2_1(a1205) | (~c3_1(a1205)) | (~c1_1(a1205)) | c2_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 1.14/1.01 inference(transitivity,[status(thm)],[1744, 1742])).
% 1.14/1.01 tff(1746,plain,
% 1.14/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c2_1(a1205) | (~c3_1(a1205)) | (~c1_1(a1205)) | c2_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))),
% 1.14/1.01 inference(quant_inst,[status(thm)],[])).
% 1.14/1.01 tff(1747,plain,
% 1.14/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204))),
% 1.14/1.01 inference(modus_ponens,[status(thm)],[1746, 1745])).
% 1.14/1.01 tff(1748,plain,
% 1.14/1.01 (~c1_1(a1204)),
% 1.14/1.01 inference(unit_resolution,[status(thm)],[1747, 177, 1741, 1740, 116, 22, 1726, 382, 1729])).
% 1.14/1.01 tff(1749,plain,
% 1.14/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204)))),
% 1.14/1.01 inference(rewrite,[status(thm)],[])).
% 1.14/1.01 tff(1750,plain,
% 1.14/1.01 ((hskp6 | (~ndr1_0) | c2_1(a1233) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1204) | (~c2_1(a1204)) | (~c0_1(a1204))) <=> (hskp6 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204)))),
% 1.14/1.02 inference(rewrite,[status(thm)],[])).
% 1.14/1.02 tff(1751,plain,
% 1.14/1.02 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1233) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1204) | (~c2_1(a1204)) | (~c0_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204))))),
% 1.14/1.02 inference(monotonicity,[status(thm)],[1750])).
% 1.14/1.02 tff(1752,plain,
% 1.14/1.02 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1233) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1204) | (~c2_1(a1204)) | (~c0_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204)))),
% 1.14/1.02 inference(transitivity,[status(thm)],[1751, 1749])).
% 1.14/1.02 tff(1753,plain,
% 1.14/1.02 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1233) | (~c3_1(a1233)) | (~c0_1(a1233)) | c1_1(a1204) | (~c2_1(a1204)) | (~c0_1(a1204)))),
% 1.14/1.02 inference(quant_inst,[status(thm)],[])).
% 1.14/1.02 tff(1754,plain,
% 1.14/1.02 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c3_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204))),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 1.14/1.02 tff(1755,plain,
% 1.14/1.02 ($false),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1754, 177, 24, 1741, 1740, 1464, 1461, 44, 1748, 1730])).
% 1.14/1.02 tff(1756,plain,(hskp26 | hskp6 | (~c0_1(a1233)) | c2_1(a1233) | c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~c1_1(a1233)) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.14/1.02 tff(1757,plain,
% 1.14/1.02 (hskp26),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1756, 116, 1464, 1461, 24, 22, 1726, 1463, 219])).
% 1.14/1.02 tff(1758,plain,
% 1.14/1.02 (c2_1(a1208)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[695, 1757])).
% 1.14/1.02 tff(1759,plain,
% 1.14/1.02 (c1_1(a1208)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[706, 1757])).
% 1.14/1.02 tff(1760,plain,
% 1.14/1.02 (c0_1(a1208)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[717, 1757])).
% 1.14/1.02 tff(1761,plain,
% 1.14/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)))),
% 1.14/1.02 inference(rewrite,[status(thm)],[])).
% 1.14/1.02 tff(1762,plain,
% 1.14/1.02 (((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1205) | (~c3_1(a1205)) | (~c1_1(a1205)) | c2_1(a1205) | c0_1(a1205) | (~c3_1(a1205))) <=> (c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)))),
% 1.14/1.02 inference(rewrite,[status(thm)],[])).
% 1.14/1.02 tff(1763,plain,
% 1.14/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1205) | (~c3_1(a1205)) | (~c1_1(a1205)) | c2_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208))))),
% 1.14/1.02 inference(monotonicity,[status(thm)],[1762])).
% 1.14/1.02 tff(1764,plain,
% 1.14/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1205) | (~c3_1(a1205)) | (~c1_1(a1205)) | c2_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)))),
% 1.14/1.02 inference(transitivity,[status(thm)],[1763, 1761])).
% 1.14/1.02 tff(1765,plain,
% 1.14/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1205) | (~c3_1(a1205)) | (~c1_1(a1205)) | c2_1(a1205) | c0_1(a1205) | (~c3_1(a1205)))),
% 1.14/1.02 inference(quant_inst,[status(thm)],[])).
% 1.14/1.02 tff(1766,plain,
% 1.14/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c3_1(a1205)) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208))),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1765, 1764])).
% 1.14/1.02 tff(1767,plain,
% 1.14/1.02 ($false),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1766, 177, 1760, 1759, 1758, 116, 22, 1726, 382, 1729])).
% 1.14/1.02 tff(1768,plain,(c2_1(a1205) | c0_1(a1205) | (~c1_1(a1205)) | (~c0_1(a1233)) | c2_1(a1233) | hskp6 | (~c1_1(a1233)) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.14/1.02 tff(1769,plain,
% 1.14/1.02 (c2_1(a1205)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1768, 219, 1726, 22, 1461, 1728, 1463, 1464])).
% 1.14/1.02 tff(1770,plain,
% 1.14/1.02 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | c2_1(a1233) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c2_1(a1205)) | (~c0_1(a1233)) | (~c1_1(a1233)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp1 | c2_1(a1233) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c2_1(a1205)) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 1.14/1.02 inference(rewrite,[status(thm)],[])).
% 1.14/1.02 tff(1771,plain,
% 1.14/1.02 ((hskp1 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c0_1(a1205) | (~c1_1(a1205)) | (~c2_1(a1205))) <=> (hskp1 | c2_1(a1233) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c2_1(a1205)) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 1.14/1.02 inference(rewrite,[status(thm)],[])).
% 1.14/1.02 tff(1772,plain,
% 1.14/1.02 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c0_1(a1205) | (~c1_1(a1205)) | (~c2_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | c2_1(a1233) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c2_1(a1205)) | (~c0_1(a1233)) | (~c1_1(a1233))))),
% 1.14/1.02 inference(monotonicity,[status(thm)],[1771])).
% 1.14/1.02 tff(1773,plain,
% 1.14/1.02 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c0_1(a1205) | (~c1_1(a1205)) | (~c2_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp1 | c2_1(a1233) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c2_1(a1205)) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 1.14/1.02 inference(transitivity,[status(thm)],[1772, 1770])).
% 1.14/1.02 tff(1774,plain,
% 1.14/1.02 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c0_1(a1205) | (~c1_1(a1205)) | (~c2_1(a1205)))),
% 1.14/1.02 inference(quant_inst,[status(thm)],[])).
% 1.14/1.02 tff(1775,plain,
% 1.14/1.02 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp1 | c2_1(a1233) | c0_1(a1205) | (~c1_1(a1205)) | (~ndr1_0) | (~c2_1(a1205)) | (~c0_1(a1233)) | (~c1_1(a1233))),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1774, 1773])).
% 1.14/1.02 tff(1776,plain,
% 1.14/1.02 (hskp1 | (~c2_1(a1205))),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1775, 177, 1464, 1463, 1461, 22, 1726, 1386])).
% 1.14/1.02 tff(1777,plain,
% 1.14/1.02 (hskp1),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1776, 1769])).
% 1.14/1.02 tff(1778,plain,
% 1.14/1.02 (hskp14),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1044, 1574, 1008, 1561, 1560])).
% 1.14/1.02 tff(1779,plain,
% 1.14/1.02 (~c2_1(a1232)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[418, 1778])).
% 1.14/1.02 tff(1780,plain,
% 1.14/1.02 (~c0_1(a1232)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[453, 1778])).
% 1.14/1.02 tff(1781,plain,
% 1.14/1.02 (c3_1(a1232)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[429, 1778])).
% 1.14/1.02 tff(1782,plain,
% 1.14/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1233) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1233) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 1.14/1.02 inference(rewrite,[status(thm)],[])).
% 1.14/1.02 tff(1783,plain,
% 1.14/1.02 (((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c2_1(a1233) | (~c3_1(a1233)) | (~c1_1(a1233)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232))) <=> (c2_1(a1233) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 1.14/1.02 inference(rewrite,[status(thm)],[])).
% 1.14/1.02 tff(1784,plain,
% 1.14/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c2_1(a1233) | (~c3_1(a1233)) | (~c1_1(a1233)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a1233) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204))))),
% 1.14/1.02 inference(monotonicity,[status(thm)],[1783])).
% 1.14/1.02 tff(1785,plain,
% 1.14/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c2_1(a1233) | (~c3_1(a1233)) | (~c1_1(a1233)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1233) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 1.14/1.02 inference(transitivity,[status(thm)],[1784, 1782])).
% 1.14/1.02 tff(1786,plain,
% 1.14/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c2_1(a1233) | (~c3_1(a1233)) | (~c1_1(a1233)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))),
% 1.14/1.02 inference(quant_inst,[status(thm)],[])).
% 1.14/1.02 tff(1787,plain,
% 1.14/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a1233) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c3_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204))),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1786, 1785])).
% 1.14/1.02 tff(1788,plain,
% 1.14/1.02 (~c1_1(a1204)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1787, 177, 1741, 1740, 1463, 1781, 1461, 1780, 1779, 382, 1730])).
% 1.14/1.02 tff(1789,plain,
% 1.14/1.02 ($false),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1754, 177, 24, 1741, 1740, 1464, 1461, 44, 1788, 1730])).
% 1.14/1.02 tff(1790,plain,(hskp26 | hskp6 | (~c0_1(a1233)) | c2_1(a1233) | (~c1_1(a1233)) | (~hskp1) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.14/1.02 tff(1791,plain,
% 1.14/1.02 (hskp26),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1790, 1777, 1728, 1461, 1463, 1464, 219])).
% 1.14/1.02 tff(1792,plain,
% 1.14/1.02 (c2_1(a1208)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[695, 1791])).
% 1.14/1.02 tff(1793,plain,
% 1.14/1.02 (c1_1(a1208)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[706, 1791])).
% 1.14/1.02 tff(1794,plain,
% 1.14/1.02 (c0_1(a1208)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[717, 1791])).
% 1.14/1.02 tff(1795,assumption,(hskp23), introduced(assumption)).
% 1.14/1.02 tff(1796,plain,
% 1.14/1.02 (~c3_1(a1261)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[268, 1795])).
% 1.14/1.02 tff(1797,plain,
% 1.14/1.02 (~c2_1(a1261)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[274, 1795])).
% 1.14/1.02 tff(1798,plain,
% 1.14/1.02 (~c0_1(a1261)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[280, 1795])).
% 1.14/1.02 tff(1799,plain,
% 1.14/1.02 ($false),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[287, 219, 177, 1798, 1797, 1796, 218])).
% 1.14/1.02 tff(1800,plain,((~hskp23) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.14/1.02 tff(1801,plain,
% 1.14/1.02 (~hskp23),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1800, 219])).
% 1.14/1.02 tff(1802,plain,
% 1.14/1.02 (((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)))) <=> ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp0 | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)))),
% 1.14/1.02 inference(rewrite,[status(thm)],[])).
% 1.14/1.02 tff(1803,plain,
% 1.14/1.02 ((hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208))) <=> (hskp23 | hskp0 | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)))),
% 1.14/1.02 inference(rewrite,[status(thm)],[])).
% 1.14/1.02 tff(1804,plain,
% 1.14/1.02 (((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)))) <=> ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208))))),
% 1.14/1.02 inference(monotonicity,[status(thm)],[1803])).
% 1.14/1.02 tff(1805,plain,
% 1.14/1.02 (((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)))) <=> ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp0 | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)))),
% 1.14/1.02 inference(transitivity,[status(thm)],[1804, 1802])).
% 1.14/1.02 tff(1806,plain,
% 1.14/1.02 ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)))),
% 1.14/1.02 inference(quant_inst,[status(thm)],[])).
% 1.14/1.02 tff(1807,plain,
% 1.14/1.02 ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp0 | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208))),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1806, 1805])).
% 1.14/1.02 tff(1808,plain,
% 1.14/1.02 ($false),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1807, 177, 1801, 1727, 1794, 1793, 1792, 255])).
% 1.14/1.02 tff(1809,plain,(hskp28 | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c0_1(a1205) | (~c1_1(a1205))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.02 tff(1810,plain,
% 1.14/1.02 (hskp28),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1809, 1723, 1724, 1725, 22, 1627])).
% 1.14/1.02 tff(1811,plain,
% 1.14/1.02 (c3_1(a1214)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[300, 1810])).
% 1.14/1.02 tff(1812,plain,
% 1.14/1.02 (c1_1(a1214)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[311, 1810])).
% 1.14/1.02 tff(1813,plain,
% 1.14/1.02 (c0_1(a1214)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[322, 1810])).
% 1.14/1.02 tff(1814,plain,
% 1.14/1.02 (hskp10),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1285, 177, 755, 767, 778, 1464, 1463, 1461, 64])).
% 1.14/1.02 tff(1815,plain,
% 1.14/1.02 (~c3_1(a1223)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1291, 1814])).
% 1.14/1.02 tff(1816,plain,
% 1.14/1.02 (~c1_1(a1223)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1297, 1814])).
% 1.14/1.02 tff(1817,plain,
% 1.14/1.02 (c2_1(a1223)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1308, 1814])).
% 1.14/1.02 tff(1818,plain,
% 1.14/1.02 (hskp13),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1315, 177, 24, 1817, 1816, 1815, 54])).
% 1.14/1.02 tff(1819,plain,
% 1.14/1.02 (~c1_1(a1229)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1321, 1818])).
% 1.14/1.02 tff(1820,plain,
% 1.14/1.02 (c2_1(a1229)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1332, 1818])).
% 1.14/1.02 tff(1821,plain,
% 1.14/1.02 (c0_1(a1229)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1343, 1818])).
% 1.14/1.02 tff(1822,plain,
% 1.14/1.02 (~c3_1(a1233)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1350, 177, 24, 1464, 1821, 1820, 1461, 1819, 44])).
% 1.14/1.02 tff(1823,plain,
% 1.14/1.02 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.14/1.02 inference(bind,[status(th)],[])).
% 1.14/1.02 tff(1824,plain,
% 1.14/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.14/1.02 inference(quant_intro,[status(thm)],[1823])).
% 1.14/1.02 tff(1825,plain,
% 1.14/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.14/1.02 inference(rewrite,[status(thm)],[])).
% 1.14/1.02 tff(1826,plain,
% 1.14/1.02 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.14/1.02 inference(bind,[status(th)],[])).
% 1.14/1.02 tff(1827,plain,
% 1.14/1.02 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.14/1.02 inference(quant_intro,[status(thm)],[1826])).
% 1.14/1.02 tff(1828,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 1.14/1.02 tff(1829,plain,
% 1.14/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1828, 1827])).
% 1.14/1.02 tff(1830,plain,
% 1.14/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1829, 1825])).
% 1.14/1.02 tff(1831,plain,(
% 1.14/1.02 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.14/1.02 inference(skolemize,[status(sab)],[1830])).
% 1.14/1.02 tff(1832,plain,
% 1.14/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1831, 1824])).
% 1.14/1.02 tff(1833,plain,
% 1.14/1.02 (~c1_1(a1204)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1357, 177, 755, 767, 1464, 1461, 896, 1822])).
% 1.14/1.02 tff(1834,plain,
% 1.14/1.02 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.14/1.02 inference(bind,[status(th)],[])).
% 1.14/1.02 tff(1835,plain,
% 1.14/1.02 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.14/1.02 inference(quant_intro,[status(thm)],[1834])).
% 1.14/1.02 tff(1836,plain,
% 1.14/1.02 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.14/1.02 inference(rewrite,[status(thm)],[])).
% 1.14/1.02 tff(1837,plain,
% 1.14/1.02 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp18) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp18))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.14/1.02 inference(bind,[status(th)],[])).
% 1.14/1.02 tff(1838,plain,
% 1.14/1.02 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.14/1.02 inference(quant_intro,[status(thm)],[1837])).
% 1.14/1.02 tff(1839,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 1.14/1.02 tff(1840,plain,
% 1.14/1.02 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1839, 1838])).
% 1.14/1.02 tff(1841,plain,
% 1.14/1.02 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1840, 1836])).
% 1.14/1.02 tff(1842,plain,(
% 1.14/1.02 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.14/1.02 inference(skolemize,[status(sab)],[1841])).
% 1.14/1.02 tff(1843,plain,
% 1.14/1.02 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1842, 1835])).
% 1.14/1.02 tff(1844,plain,
% 1.14/1.02 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | c2_1(a1233) | (~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp18 | c2_1(a1233) | (~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))),
% 1.14/1.02 inference(rewrite,[status(thm)],[])).
% 1.14/1.02 tff(1845,plain,
% 1.14/1.02 ((hskp18 | (~ndr1_0) | c3_1(a1233) | c2_1(a1233) | (~c1_1(a1233)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204))) <=> (hskp18 | c2_1(a1233) | (~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))),
% 1.14/1.02 inference(rewrite,[status(thm)],[])).
% 1.14/1.02 tff(1846,plain,
% 1.14/1.02 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a1233) | c2_1(a1233) | (~c1_1(a1233)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | c2_1(a1233) | (~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204))))),
% 1.14/1.02 inference(monotonicity,[status(thm)],[1845])).
% 1.14/1.02 tff(1847,plain,
% 1.14/1.02 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a1233) | c2_1(a1233) | (~c1_1(a1233)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp18 | c2_1(a1233) | (~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))),
% 1.14/1.02 inference(transitivity,[status(thm)],[1846, 1844])).
% 1.14/1.02 tff(1848,plain,
% 1.14/1.02 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp18 | (~ndr1_0) | c3_1(a1233) | c2_1(a1233) | (~c1_1(a1233)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204)))),
% 1.14/1.02 inference(quant_inst,[status(thm)],[])).
% 1.14/1.02 tff(1849,plain,
% 1.14/1.02 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp18 | c2_1(a1233) | (~ndr1_0) | c3_1(a1233) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204))),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1848, 1847])).
% 1.14/1.02 tff(1850,plain,
% 1.14/1.02 (hskp18),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1849, 177, 767, 778, 1463, 1461, 1843, 1833, 1822])).
% 1.14/1.02 tff(1851,plain,
% 1.14/1.02 (((~hskp18) | (~c1_1(a1246))) <=> ((~hskp18) | (~c1_1(a1246)))),
% 1.14/1.02 inference(rewrite,[status(thm)],[])).
% 1.14/1.02 tff(1852,plain,
% 1.14/1.02 (((~c1_1(a1246)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a1246)))),
% 1.14/1.02 inference(rewrite,[status(thm)],[])).
% 1.14/1.02 tff(1853,axiom,((~c1_1(a1246)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 1.14/1.02 tff(1854,plain,
% 1.14/1.02 ((~hskp18) | (~c1_1(a1246))),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1853, 1852])).
% 1.14/1.02 tff(1855,plain,
% 1.14/1.02 ((~hskp18) | (~c1_1(a1246))),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1854, 1851])).
% 1.14/1.02 tff(1856,plain,
% 1.14/1.02 (~c1_1(a1246)),
% 1.14/1.02 inference(unit_resolution,[status(thm)],[1855, 1850])).
% 1.14/1.02 tff(1857,plain,
% 1.14/1.02 (((~hskp18) | c3_1(a1246)) <=> ((~hskp18) | c3_1(a1246))),
% 1.14/1.02 inference(rewrite,[status(thm)],[])).
% 1.14/1.02 tff(1858,axiom,((~hskp18) | c3_1(a1246)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 1.14/1.02 tff(1859,plain,
% 1.14/1.02 ((~hskp18) | c3_1(a1246)),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1858, 1857])).
% 1.14/1.02 tff(1860,plain,
% 1.14/1.02 ((~hskp18) | c3_1(a1246)),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1859, 1857])).
% 1.14/1.02 tff(1861,plain,
% 1.14/1.02 ((~hskp18) | c3_1(a1246)),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1860, 1857])).
% 1.14/1.02 tff(1862,plain,
% 1.14/1.02 ((~hskp18) | c3_1(a1246)),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1861, 1857])).
% 1.14/1.02 tff(1863,plain,
% 1.14/1.02 ((~hskp18) | c3_1(a1246)),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1862, 1857])).
% 1.14/1.02 tff(1864,plain,
% 1.14/1.02 ((~hskp18) | c3_1(a1246)),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1863, 1857])).
% 1.14/1.02 tff(1865,plain,
% 1.14/1.02 ((~hskp18) | c3_1(a1246)),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1864, 1857])).
% 1.14/1.02 tff(1866,plain,
% 1.14/1.02 ((~hskp18) | c3_1(a1246)),
% 1.14/1.02 inference(modus_ponens,[status(thm)],[1865, 1857])).
% 1.14/1.02 tff(1867,plain,
% 1.14/1.03 (c3_1(a1246)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1866, 1850])).
% 1.14/1.03 tff(1868,plain,
% 1.14/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a1246) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c3_1(a1246)) | c0_1(a1246) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a1246) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c3_1(a1246)) | c0_1(a1246) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1869,plain,
% 1.14/1.03 (((~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)) | c1_1(a1246) | c0_1(a1246) | (~c3_1(a1246))) <=> (c1_1(a1246) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c3_1(a1246)) | c0_1(a1246) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1870,plain,
% 1.14/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)) | c1_1(a1246) | c0_1(a1246) | (~c3_1(a1246)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a1246) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c3_1(a1246)) | c0_1(a1246) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))))),
% 1.14/1.03 inference(monotonicity,[status(thm)],[1869])).
% 1.14/1.03 tff(1871,plain,
% 1.14/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)) | c1_1(a1246) | c0_1(a1246) | (~c3_1(a1246)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a1246) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c3_1(a1246)) | c0_1(a1246) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.14/1.03 inference(transitivity,[status(thm)],[1870, 1868])).
% 1.14/1.03 tff(1872,plain,
% 1.14/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1233) | c2_1(a1233) | (~c0_1(a1233)) | c1_1(a1246) | c0_1(a1246) | (~c3_1(a1246)))),
% 1.14/1.03 inference(quant_inst,[status(thm)],[])).
% 1.14/1.03 tff(1873,plain,
% 1.14/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a1246) | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | c3_1(a1233) | (~c3_1(a1246)) | c0_1(a1246) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1872, 1871])).
% 1.14/1.03 tff(1874,plain,
% 1.14/1.03 (c0_1(a1246)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1873, 177, 755, 767, 778, 1867, 1464, 1856, 1461, 1832, 1822])).
% 1.14/1.03 tff(1875,plain,
% 1.14/1.03 (hskp9),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1374, 177, 755, 778, 1817, 1816, 1815, 1368, 1833])).
% 1.14/1.03 tff(1876,plain,
% 1.14/1.03 (~c0_1(a1219)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[843, 1875])).
% 1.14/1.03 tff(1877,plain,
% 1.14/1.03 (c2_1(a1219)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[819, 1875])).
% 1.14/1.03 tff(1878,plain,
% 1.14/1.03 (c1_1(a1219)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[830, 1875])).
% 1.14/1.03 tff(1879,plain,
% 1.14/1.03 (hskp1),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1394, 177, 1464, 1463, 1878, 1877, 1461, 1876, 1386])).
% 1.14/1.03 tff(1880,plain,
% 1.14/1.03 (c2_1(a1206)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1024, 1879])).
% 1.14/1.03 tff(1881,plain,
% 1.14/1.03 (c0_1(a1206)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1035, 1879])).
% 1.14/1.03 tff(1882,plain,
% 1.14/1.03 (~c1_1(a1206)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1403, 177, 1464, 1881, 1880, 1461, 896, 1822])).
% 1.14/1.03 tff(1883,plain,
% 1.14/1.03 (~c3_1(a1206)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1013, 1879])).
% 1.14/1.03 tff(1884,plain,
% 1.14/1.03 (c3_1(a1219)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1435, 177, 1464, 1878, 1881, 1461, 1876, 1883, 921, 1822, 1882])).
% 1.14/1.03 tff(1885,assumption,(c0_1(a1246)), introduced(assumption)).
% 1.14/1.03 tff(1886,assumption,(c3_1(a1219)), introduced(assumption)).
% 1.14/1.03 tff(1887,assumption,(hskp8), introduced(assumption)).
% 1.14/1.03 tff(1888,plain,
% 1.14/1.03 (~c3_1(a1217)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[584, 1887])).
% 1.14/1.03 tff(1889,plain,
% 1.14/1.03 (~c0_1(a1217)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[578, 1887])).
% 1.14/1.03 tff(1890,assumption,(c2_1(a1219)), introduced(assumption)).
% 1.14/1.03 tff(1891,plain,
% 1.14/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1892,plain,
% 1.14/1.03 (((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1217) | c3_1(a1217) | (~c2_1(a1217))) <=> (c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1893,plain,
% 1.14/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1217) | c3_1(a1217) | (~c2_1(a1217)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 1.14/1.03 inference(monotonicity,[status(thm)],[1892])).
% 1.14/1.03 tff(1894,plain,
% 1.14/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1217) | c3_1(a1217) | (~c2_1(a1217)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.03 inference(transitivity,[status(thm)],[1893, 1891])).
% 1.14/1.03 tff(1895,plain,
% 1.14/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1217) | c3_1(a1217) | (~c2_1(a1217)))),
% 1.14/1.03 inference(quant_inst,[status(thm)],[])).
% 1.14/1.03 tff(1896,plain,
% 1.14/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1895, 1894])).
% 1.14/1.03 tff(1897,plain,
% 1.14/1.03 (~c2_1(a1217)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1896, 177, 1136, 1135, 1134, 925, 1890, 1889, 1888, 10, 1886])).
% 1.14/1.03 tff(1898,plain,
% 1.14/1.03 (~c1_1(a1217)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[979, 1887])).
% 1.14/1.03 tff(1899,assumption,(~c1_1(a1246)), introduced(assumption)).
% 1.14/1.03 tff(1900,assumption,(c3_1(a1246)), introduced(assumption)).
% 1.14/1.03 tff(1901,plain,
% 1.14/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1246) | c0_1(a1219) | c0_1(a1217) | c1_1(a1217) | (~ndr1_0) | c2_1(a1217) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1246)) | (~c0_1(a1246)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1246) | c0_1(a1219) | c0_1(a1217) | c1_1(a1217) | (~ndr1_0) | c2_1(a1217) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1246)) | (~c0_1(a1246)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1902,plain,
% 1.14/1.03 (((~ndr1_0) | c1_1(a1246) | (~c3_1(a1246)) | (~c0_1(a1246)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1217) | c1_1(a1217) | c0_1(a1217)) <=> (c1_1(a1246) | c0_1(a1219) | c0_1(a1217) | c1_1(a1217) | (~ndr1_0) | c2_1(a1217) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1246)) | (~c0_1(a1246)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1903,plain,
% 1.14/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1246) | (~c3_1(a1246)) | (~c0_1(a1246)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1217) | c1_1(a1217) | c0_1(a1217))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1246) | c0_1(a1219) | c0_1(a1217) | c1_1(a1217) | (~ndr1_0) | c2_1(a1217) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1246)) | (~c0_1(a1246))))),
% 1.14/1.03 inference(monotonicity,[status(thm)],[1902])).
% 1.14/1.03 tff(1904,plain,
% 1.14/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1246) | (~c3_1(a1246)) | (~c0_1(a1246)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1217) | c1_1(a1217) | c0_1(a1217))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1246) | c0_1(a1219) | c0_1(a1217) | c1_1(a1217) | (~ndr1_0) | c2_1(a1217) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1246)) | (~c0_1(a1246)))),
% 1.14/1.03 inference(transitivity,[status(thm)],[1903, 1901])).
% 1.14/1.03 tff(1905,plain,
% 1.14/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1246) | (~c3_1(a1246)) | (~c0_1(a1246)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1217) | c1_1(a1217) | c0_1(a1217))),
% 1.14/1.03 inference(quant_inst,[status(thm)],[])).
% 1.14/1.03 tff(1906,plain,
% 1.14/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1246) | c0_1(a1219) | c0_1(a1217) | c1_1(a1217) | (~ndr1_0) | c2_1(a1217) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1246)) | (~c0_1(a1246))),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1905, 1904])).
% 1.14/1.03 tff(1907,plain,
% 1.14/1.03 ($false),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1906, 177, 1900, 925, 1890, 1899, 922, 1889, 1898, 34, 1897, 1885])).
% 1.14/1.03 tff(1908,plain,((~hskp8) | (~c3_1(a1246)) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1246) | c0_1(a1219) | (~c0_1(a1246)) | (~c0_1(a1214)) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c3_1(a1219))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.03 tff(1909,plain,
% 1.14/1.03 (~hskp8),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1908, 1867, 1878, 1877, 1856, 1876, 1874, 1136, 1135, 1134, 1884])).
% 1.14/1.03 tff(1910,plain,
% 1.14/1.03 (((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)))) <=> ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp8 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1911,plain,
% 1.14/1.03 ((hskp11 | hskp8 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233))) <=> (hskp11 | hskp8 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1912,plain,
% 1.14/1.03 (((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)))) <=> ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233))))),
% 1.14/1.03 inference(monotonicity,[status(thm)],[1911])).
% 1.14/1.03 tff(1913,plain,
% 1.14/1.03 (((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)))) <=> ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp8 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)))),
% 1.14/1.03 inference(transitivity,[status(thm)],[1912, 1910])).
% 1.14/1.03 tff(1914,plain,
% 1.14/1.03 ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp8 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)))),
% 1.14/1.03 inference(quant_inst,[status(thm)],[])).
% 1.14/1.03 tff(1915,plain,
% 1.14/1.03 ((~![U: $i] : (hskp11 | hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp8 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233))),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1914, 1913])).
% 1.14/1.03 tff(1916,plain,
% 1.14/1.03 (hskp11 | hskp8),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1915, 177, 1464, 1463, 1461, 532])).
% 1.14/1.03 tff(1917,plain,
% 1.14/1.03 (hskp11),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1916, 1909])).
% 1.14/1.03 tff(1918,plain,
% 1.14/1.03 (~c2_1(a1224)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[612, 1917])).
% 1.14/1.03 tff(1919,plain,
% 1.14/1.03 (c3_1(a1224)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[623, 1917])).
% 1.14/1.03 tff(1920,plain,
% 1.14/1.03 (c1_1(a1224)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[634, 1917])).
% 1.14/1.03 tff(1921,plain,
% 1.14/1.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a1224) | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | (~c3_1(a1224)) | (~c1_1(a1224)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1922,plain,
% 1.14/1.03 ((hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223))) <=> (hskp14 | c2_1(a1224) | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1923,plain,
% 1.14/1.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a1224) | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | (~c3_1(a1224)) | (~c1_1(a1224))))),
% 1.14/1.03 inference(monotonicity,[status(thm)],[1922])).
% 1.14/1.03 tff(1924,plain,
% 1.14/1.03 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.14/1.03 inference(transitivity,[status(thm)],[1923, 1921])).
% 1.14/1.03 tff(1925,plain,
% 1.14/1.03 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1223) | c1_1(a1223) | (~c2_1(a1223)))),
% 1.14/1.03 inference(quant_inst,[status(thm)],[])).
% 1.14/1.03 tff(1926,plain,
% 1.14/1.03 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c1_1(a1223) | c3_1(a1223) | (~ndr1_0) | (~c2_1(a1223)) | (~c3_1(a1224)) | (~c1_1(a1224))),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 1.14/1.03 tff(1927,plain,
% 1.14/1.03 (hskp14),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1926, 177, 1920, 1919, 1817, 1918, 1816, 1815, 664])).
% 1.14/1.03 tff(1928,plain,
% 1.14/1.03 (~c2_1(a1232)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[418, 1927])).
% 1.14/1.03 tff(1929,plain,
% 1.14/1.03 (~c0_1(a1232)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[453, 1927])).
% 1.14/1.03 tff(1930,plain,
% 1.14/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1246) | c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | (~c3_1(a1246)) | (~c0_1(a1246)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1246) | c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | (~c3_1(a1246)) | (~c0_1(a1246)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1931,plain,
% 1.14/1.03 (((~ndr1_0) | c1_1(a1246) | (~c3_1(a1246)) | (~c0_1(a1246)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232)) <=> (c1_1(a1246) | c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | (~c3_1(a1246)) | (~c0_1(a1246)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1932,plain,
% 1.14/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1246) | (~c3_1(a1246)) | (~c0_1(a1246)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1246) | c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | (~c3_1(a1246)) | (~c0_1(a1246))))),
% 1.14/1.03 inference(monotonicity,[status(thm)],[1931])).
% 1.14/1.03 tff(1933,plain,
% 1.14/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1246) | (~c3_1(a1246)) | (~c0_1(a1246)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1246) | c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | (~c3_1(a1246)) | (~c0_1(a1246)))),
% 1.14/1.03 inference(transitivity,[status(thm)],[1932, 1930])).
% 1.14/1.03 tff(1934,plain,
% 1.14/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1246) | (~c3_1(a1246)) | (~c0_1(a1246)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))),
% 1.14/1.03 inference(quant_inst,[status(thm)],[])).
% 1.14/1.03 tff(1935,plain,
% 1.14/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1246) | c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | (~c3_1(a1246)) | (~c0_1(a1246))),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1934, 1933])).
% 1.14/1.03 tff(1936,plain,
% 1.14/1.03 (c1_1(a1232)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1935, 177, 1867, 1878, 1877, 1856, 1929, 1928, 1876, 34, 1874])).
% 1.14/1.03 tff(1937,plain,
% 1.14/1.03 (((~hskp18) | c2_1(a1246)) <=> ((~hskp18) | c2_1(a1246))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1938,axiom,((~hskp18) | c2_1(a1246)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 1.14/1.03 tff(1939,plain,
% 1.14/1.03 ((~hskp18) | c2_1(a1246)),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1938, 1937])).
% 1.14/1.03 tff(1940,plain,
% 1.14/1.03 ((~hskp18) | c2_1(a1246)),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1939, 1937])).
% 1.14/1.03 tff(1941,plain,
% 1.14/1.03 ((~hskp18) | c2_1(a1246)),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1940, 1937])).
% 1.14/1.03 tff(1942,plain,
% 1.14/1.03 ((~hskp18) | c2_1(a1246)),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1941, 1937])).
% 1.14/1.03 tff(1943,plain,
% 1.14/1.03 ((~hskp18) | c2_1(a1246)),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1942, 1937])).
% 1.14/1.03 tff(1944,plain,
% 1.14/1.03 ((~hskp18) | c2_1(a1246)),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1943, 1937])).
% 1.14/1.03 tff(1945,plain,
% 1.14/1.03 ((~hskp18) | c2_1(a1246)),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1944, 1937])).
% 1.14/1.03 tff(1946,plain,
% 1.14/1.03 ((~hskp18) | c2_1(a1246)),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1945, 1937])).
% 1.14/1.03 tff(1947,plain,
% 1.14/1.03 (c2_1(a1246)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1946, 1850])).
% 1.14/1.03 tff(1948,assumption,(~c2_1(a1214)), introduced(assumption)).
% 1.14/1.03 tff(1949,assumption,(c2_1(a1246)), introduced(assumption)).
% 1.14/1.03 tff(1950,plain,
% 1.14/1.03 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c1_1(a1246) | (~ndr1_0) | (~c0_1(a1246)) | (~c2_1(a1246)) | c2_1(a1214) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1246) | (~ndr1_0) | (~c0_1(a1246)) | (~c2_1(a1246)) | c2_1(a1214) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1951,plain,
% 1.14/1.03 ((hskp6 | (~ndr1_0) | c2_1(a1214) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1246) | (~c2_1(a1246)) | (~c0_1(a1246))) <=> (hskp6 | c1_1(a1246) | (~ndr1_0) | (~c0_1(a1246)) | (~c2_1(a1246)) | c2_1(a1214) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1952,plain,
% 1.14/1.03 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1214) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1246) | (~c2_1(a1246)) | (~c0_1(a1246)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c1_1(a1246) | (~ndr1_0) | (~c0_1(a1246)) | (~c2_1(a1246)) | c2_1(a1214) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 1.14/1.03 inference(monotonicity,[status(thm)],[1951])).
% 1.14/1.03 tff(1953,plain,
% 1.14/1.03 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1214) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1246) | (~c2_1(a1246)) | (~c0_1(a1246)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1246) | (~ndr1_0) | (~c0_1(a1246)) | (~c2_1(a1246)) | c2_1(a1214) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.03 inference(transitivity,[status(thm)],[1952, 1950])).
% 1.14/1.03 tff(1954,plain,
% 1.14/1.03 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1214) | (~c3_1(a1214)) | (~c0_1(a1214)) | c1_1(a1246) | (~c2_1(a1246)) | (~c0_1(a1246)))),
% 1.14/1.03 inference(quant_inst,[status(thm)],[])).
% 1.14/1.03 tff(1955,plain,
% 1.14/1.03 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c1_1(a1246) | (~ndr1_0) | (~c0_1(a1246)) | (~c2_1(a1246)) | c2_1(a1214) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1954, 1953])).
% 1.14/1.03 tff(1956,plain,
% 1.14/1.03 ($false),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1955, 177, 24, 1136, 1134, 1949, 1899, 44, 1948, 1885])).
% 1.14/1.03 tff(1957,plain,(c2_1(a1214) | hskp6 | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c2_1(a1246)) | c1_1(a1246) | (~c0_1(a1246))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.03 tff(1958,plain,
% 1.14/1.03 (c2_1(a1214)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1957, 1947, 1136, 1134, 24, 1856, 1874])).
% 1.14/1.03 tff(1959,plain,
% 1.14/1.03 (c3_1(a1232)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[429, 1927])).
% 1.14/1.03 tff(1960,plain,
% 1.14/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c1_1(a1232)) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c1_1(a1232)) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1961,plain,
% 1.14/1.03 (((~ndr1_0) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232))) <=> (c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c1_1(a1232)) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1962,plain,
% 1.14/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c1_1(a1232)) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214))))),
% 1.14/1.03 inference(monotonicity,[status(thm)],[1961])).
% 1.14/1.03 tff(1963,plain,
% 1.14/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c1_1(a1232)) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)))),
% 1.14/1.03 inference(transitivity,[status(thm)],[1962, 1960])).
% 1.14/1.03 tff(1964,plain,
% 1.14/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))),
% 1.14/1.03 inference(quant_inst,[status(thm)],[])).
% 1.14/1.03 tff(1965,plain,
% 1.14/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c3_1(a1232)) | (~c1_1(a1232)) | (~c2_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214))),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1964, 1963])).
% 1.14/1.03 tff(1966,plain,
% 1.14/1.03 ($false),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1965, 177, 1136, 1135, 1959, 1929, 1928, 382, 1958, 1936])).
% 1.14/1.03 tff(1967,plain,((~hskp25) | (~c0_1(a1214)) | (~c1_1(a1214)) | (~c3_1(a1214)) | hskp6 | (~c0_1(a1233)) | (~c1_1(a1233)) | c2_1(a1233)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.03 tff(1968,plain,
% 1.14/1.03 (~hskp25),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1967, 1813, 1812, 1811, 1721, 1725, 1724, 1723])).
% 1.14/1.03 tff(1969,plain,
% 1.14/1.03 (hskp21),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1207, 1968])).
% 1.14/1.03 tff(1970,plain,
% 1.14/1.03 (~c1_1(a1257)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[190, 1969])).
% 1.14/1.03 tff(1971,plain,
% 1.14/1.03 (~c0_1(a1257)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[196, 1969])).
% 1.14/1.03 tff(1972,plain,
% 1.14/1.03 (c3_1(a1257)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[207, 1969])).
% 1.14/1.03 tff(1973,plain,
% 1.14/1.03 ($false),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[329, 177, 21, 1813, 1812, 1811, 1972, 1971, 1970, 20])).
% 1.14/1.03 tff(1974,plain,(c0_1(a1205) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.14/1.03 tff(1975,plain,
% 1.14/1.03 (c0_1(a1205)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1974, 21])).
% 1.14/1.03 tff(1976,plain,
% 1.14/1.03 (((~hskp0) | (~c0_1(a1205))) <=> ((~hskp0) | (~c0_1(a1205)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1977,plain,
% 1.14/1.03 (((~c0_1(a1205)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a1205)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1978,axiom,((~c0_1(a1205)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 1.14/1.03 tff(1979,plain,
% 1.14/1.03 ((~hskp0) | (~c0_1(a1205))),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1978, 1977])).
% 1.14/1.03 tff(1980,plain,
% 1.14/1.03 ((~hskp0) | (~c0_1(a1205))),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1979, 1976])).
% 1.14/1.03 tff(1981,plain,
% 1.14/1.03 (~hskp0),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1980, 1975])).
% 1.14/1.03 tff(1982,plain,
% 1.14/1.03 (~hskp6),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1720, 1981])).
% 1.14/1.03 tff(1983,plain,
% 1.14/1.03 (hskp15),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[86, 1982, 21])).
% 1.14/1.03 tff(1984,plain,
% 1.14/1.03 (~c2_1(a1233)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1256, 1983])).
% 1.14/1.03 tff(1985,plain,
% 1.14/1.03 (c1_1(a1233)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1267, 1983])).
% 1.14/1.03 tff(1986,plain,
% 1.14/1.03 (c0_1(a1233)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1278, 1983])).
% 1.14/1.03 tff(1987,plain,
% 1.14/1.03 (~hskp6),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1720, 1636])).
% 1.14/1.03 tff(1988,plain,
% 1.14/1.03 (~hskp1),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1790, 1194, 1987, 1461, 1463, 1464, 219])).
% 1.14/1.03 tff(1989,plain,
% 1.14/1.03 (hskp25),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1006, 1988, 1194])).
% 1.14/1.03 tff(1990,plain,
% 1.14/1.03 (c2_1(a1204)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[766, 1989])).
% 1.14/1.03 tff(1991,plain,
% 1.14/1.03 (c0_1(a1204)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[754, 1989])).
% 1.14/1.03 tff(1992,plain,
% 1.14/1.03 (((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))) <=> ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 1.14/1.03 inference(rewrite,[status(thm)],[])).
% 1.14/1.03 tff(1993,plain,
% 1.14/1.03 ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)))),
% 1.14/1.03 inference(quant_inst,[status(thm)],[])).
% 1.14/1.03 tff(1994,plain,
% 1.14/1.03 ((~![U: $i] : (hskp23 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp0 | (~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204))),
% 1.14/1.03 inference(modus_ponens,[status(thm)],[1993, 1992])).
% 1.14/1.03 tff(1995,plain,
% 1.14/1.03 (~c1_1(a1204)),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1994, 177, 1801, 1636, 1991, 1990, 255])).
% 1.14/1.03 tff(1996,plain,
% 1.14/1.03 ($false),
% 1.14/1.03 inference(unit_resolution,[status(thm)],[1754, 177, 1987, 1991, 1990, 1464, 1461, 44, 1995, 1730])).
% 1.14/1.04 tff(1997,plain,(hskp26 | (~c0_1(a1233)) | c2_1(a1233) | hskp0 | (~c1_1(a1233)) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.14/1.04 tff(1998,plain,
% 1.14/1.04 (hskp26),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[1997, 219, 1461, 1636, 1463, 1464])).
% 1.14/1.04 tff(1999,plain,
% 1.14/1.04 (c2_1(a1208)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[695, 1998])).
% 1.14/1.04 tff(2000,plain,
% 1.14/1.04 (c1_1(a1208)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[706, 1998])).
% 1.14/1.04 tff(2001,plain,
% 1.14/1.04 (c0_1(a1208)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[717, 1998])).
% 1.14/1.04 tff(2002,plain,
% 1.14/1.04 ($false),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[1807, 177, 1801, 1636, 2001, 2000, 1999, 255])).
% 1.14/1.04 tff(2003,plain,(hskp28 | hskp0 | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.04 tff(2004,plain,
% 1.14/1.04 (hskp28),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[2003, 1981, 1984, 1985, 1986])).
% 1.14/1.04 tff(2005,plain,
% 1.14/1.04 (c3_1(a1214)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[300, 2004])).
% 1.14/1.04 tff(2006,plain,
% 1.14/1.04 (c1_1(a1214)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[311, 2004])).
% 1.14/1.04 tff(2007,plain,
% 1.14/1.04 (c0_1(a1214)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[322, 2004])).
% 1.14/1.04 tff(2008,plain,
% 1.14/1.04 (~hskp25),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[1967, 2007, 2006, 2005, 1982, 1986, 1985, 1984])).
% 1.14/1.04 tff(2009,plain,
% 1.14/1.04 (hskp21),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[1207, 2008])).
% 1.14/1.04 tff(2010,plain,
% 1.14/1.04 (~c1_1(a1257)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[190, 2009])).
% 1.14/1.04 tff(2011,plain,
% 1.14/1.04 (~c0_1(a1257)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[196, 2009])).
% 1.14/1.04 tff(2012,plain,
% 1.14/1.04 (c3_1(a1257)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[207, 2009])).
% 1.14/1.04 tff(2013,plain,
% 1.14/1.04 ($false),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[329, 177, 21, 2007, 2006, 2005, 2012, 2011, 2010, 20])).
% 1.14/1.04 tff(2014,plain,(hskp5), inference(lemma,lemma(discharge,[]))).
% 1.14/1.04 tff(2015,plain,
% 1.14/1.04 (((~hskp5) | (~c3_1(a1212))) <=> ((~hskp5) | (~c3_1(a1212)))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2016,plain,
% 1.14/1.04 (((~c3_1(a1212)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a1212)))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2017,axiom,((~c3_1(a1212)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 1.14/1.04 tff(2018,plain,
% 1.14/1.04 ((~hskp5) | (~c3_1(a1212))),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2017, 2016])).
% 1.14/1.04 tff(2019,plain,
% 1.14/1.04 ((~hskp5) | (~c3_1(a1212))),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2018, 2015])).
% 1.14/1.04 tff(2020,plain,
% 1.14/1.04 (~c3_1(a1212)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[2019, 2014])).
% 1.14/1.04 tff(2021,plain,
% 1.14/1.04 (((~hskp5) | (~c0_1(a1212))) <=> ((~hskp5) | (~c0_1(a1212)))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2022,plain,
% 1.14/1.04 (((~c0_1(a1212)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a1212)))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2023,axiom,((~c0_1(a1212)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 1.14/1.04 tff(2024,plain,
% 1.14/1.04 ((~hskp5) | (~c0_1(a1212))),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2023, 2022])).
% 1.14/1.04 tff(2025,plain,
% 1.14/1.04 ((~hskp5) | (~c0_1(a1212))),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2024, 2021])).
% 1.14/1.04 tff(2026,plain,
% 1.14/1.04 (~c0_1(a1212)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[2025, 2014])).
% 1.14/1.04 tff(2027,plain,
% 1.14/1.04 (((~hskp5) | c2_1(a1212)) <=> ((~hskp5) | c2_1(a1212))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2028,axiom,((~hskp5) | c2_1(a1212)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 1.14/1.04 tff(2029,plain,
% 1.14/1.04 ((~hskp5) | c2_1(a1212)),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2028, 2027])).
% 1.14/1.04 tff(2030,plain,
% 1.14/1.04 ((~hskp5) | c2_1(a1212)),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2029, 2027])).
% 1.14/1.04 tff(2031,plain,
% 1.14/1.04 ((~hskp5) | c2_1(a1212)),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2030, 2027])).
% 1.14/1.04 tff(2032,plain,
% 1.14/1.04 ((~hskp5) | c2_1(a1212)),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2031, 2027])).
% 1.14/1.04 tff(2033,plain,
% 1.14/1.04 ((~hskp5) | c2_1(a1212)),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2032, 2027])).
% 1.14/1.04 tff(2034,plain,
% 1.14/1.04 ((~hskp5) | c2_1(a1212)),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2033, 2027])).
% 1.14/1.04 tff(2035,plain,
% 1.14/1.04 ((~hskp5) | c2_1(a1212)),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2034, 2027])).
% 1.14/1.04 tff(2036,plain,
% 1.14/1.04 ((~hskp5) | c2_1(a1212)),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2035, 2027])).
% 1.14/1.04 tff(2037,plain,
% 1.14/1.04 (c2_1(a1212)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[2036, 2014])).
% 1.14/1.04 tff(2038,plain,
% 1.14/1.04 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2039,plain,
% 1.14/1.04 ((hskp11 | (~ndr1_0) | c3_1(a1212) | c0_1(a1212) | (~c2_1(a1212))) <=> (hskp11 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2040,plain,
% 1.14/1.04 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1212) | c0_1(a1212) | (~c2_1(a1212)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212))))),
% 1.14/1.04 inference(monotonicity,[status(thm)],[2039])).
% 1.14/1.04 tff(2041,plain,
% 1.14/1.04 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1212) | c0_1(a1212) | (~c2_1(a1212)))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)))),
% 1.14/1.04 inference(transitivity,[status(thm)],[2040, 2038])).
% 1.14/1.04 tff(2042,plain,
% 1.14/1.04 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp11 | (~ndr1_0) | c3_1(a1212) | c0_1(a1212) | (~c2_1(a1212)))),
% 1.14/1.04 inference(quant_inst,[status(thm)],[])).
% 1.14/1.04 tff(2043,plain,
% 1.14/1.04 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp11 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212))),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2042, 2041])).
% 1.14/1.04 tff(2044,plain,
% 1.14/1.04 (hskp11),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[2043, 177, 2037, 2026, 2020, 343])).
% 1.14/1.04 tff(2045,plain,
% 1.14/1.04 (~c2_1(a1224)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[612, 2044])).
% 1.14/1.04 tff(2046,plain,
% 1.14/1.04 (c3_1(a1224)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[623, 2044])).
% 1.14/1.04 tff(2047,plain,
% 1.14/1.04 (c1_1(a1224)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[634, 2044])).
% 1.14/1.04 tff(2048,plain,
% 1.14/1.04 (c0_1(a1224)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[724, 177, 718, 707, 696, 2047, 2046, 2045, 382])).
% 1.14/1.04 tff(2049,plain,
% 1.14/1.04 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c1_1(a1224)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c1_1(a1224)))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2050,plain,
% 1.14/1.04 ((hskp8 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c1_1(a1224)) | (~c0_1(a1224))) <=> (hskp8 | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c1_1(a1224)))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2051,plain,
% 1.14/1.04 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c1_1(a1224)) | (~c0_1(a1224)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c1_1(a1224))))),
% 1.14/1.04 inference(monotonicity,[status(thm)],[2050])).
% 1.14/1.04 tff(2052,plain,
% 1.14/1.04 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c1_1(a1224)) | (~c0_1(a1224)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c1_1(a1224)))),
% 1.14/1.04 inference(transitivity,[status(thm)],[2051, 2049])).
% 1.14/1.04 tff(2053,plain,
% 1.14/1.04 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c0_1(a1208)) | c2_1(a1224) | (~c1_1(a1224)) | (~c0_1(a1224)))),
% 1.14/1.04 inference(quant_inst,[status(thm)],[])).
% 1.14/1.04 tff(2054,plain,
% 1.14/1.04 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a1224) | (~ndr1_0) | (~c1_1(a1208)) | (~c0_1(a1208)) | (~c2_1(a1208)) | (~c0_1(a1224)) | (~c1_1(a1224))),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2053, 2052])).
% 1.14/1.04 tff(2055,plain,
% 1.14/1.04 (hskp8),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[2054, 177, 718, 707, 696, 2047, 2045, 1556, 2048])).
% 1.14/1.04 tff(2056,plain,
% 1.14/1.04 (~c3_1(a1217)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[584, 2055])).
% 1.14/1.04 tff(2057,plain,
% 1.14/1.04 (~c0_1(a1217)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[578, 2055])).
% 1.14/1.04 tff(2058,plain,
% 1.14/1.04 (c2_1(a1217)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[601, 219, 177, 2057, 2056, 218])).
% 1.14/1.04 tff(2059,plain,
% 1.14/1.04 (~c1_1(a1217)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[979, 2055])).
% 1.14/1.04 tff(2060,plain,
% 1.14/1.04 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a1224) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c3_1(a1224)) | (~c1_1(a1224)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2061,plain,
% 1.14/1.04 ((hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1217) | c1_1(a1217) | (~c2_1(a1217))) <=> (hskp14 | c2_1(a1224) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2062,plain,
% 1.14/1.04 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1217) | c1_1(a1217) | (~c2_1(a1217)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a1224) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c3_1(a1224)) | (~c1_1(a1224))))),
% 1.14/1.04 inference(monotonicity,[status(thm)],[2061])).
% 1.14/1.04 tff(2063,plain,
% 1.14/1.04 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1217) | c1_1(a1217) | (~c2_1(a1217)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.14/1.04 inference(transitivity,[status(thm)],[2062, 2060])).
% 1.14/1.04 tff(2064,plain,
% 1.14/1.04 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1217) | c1_1(a1217) | (~c2_1(a1217)))),
% 1.14/1.04 inference(quant_inst,[status(thm)],[])).
% 1.14/1.04 tff(2065,plain,
% 1.14/1.04 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c1_1(a1217) | c3_1(a1217) | (~ndr1_0) | (~c2_1(a1217)) | (~c3_1(a1224)) | (~c1_1(a1224))),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2064, 2063])).
% 1.14/1.04 tff(2066,plain,
% 1.14/1.04 (hskp14),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[2065, 177, 2047, 2046, 2045, 2059, 2056, 664, 2058])).
% 1.14/1.04 tff(2067,plain,
% 1.14/1.04 (~c2_1(a1232)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[418, 2066])).
% 1.14/1.04 tff(2068,plain,
% 1.14/1.04 (~c0_1(a1232)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[453, 2066])).
% 1.14/1.04 tff(2069,plain,
% 1.14/1.04 (c3_1(a1232)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[429, 2066])).
% 1.14/1.04 tff(2070,plain,
% 1.14/1.04 ($false),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[736, 177, 718, 707, 696, 2069, 2047, 2046, 2068, 2067, 2045, 382])).
% 1.14/1.04 tff(2071,plain,((~hskp26) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.14/1.04 tff(2072,plain,
% 1.14/1.04 (~hskp26),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[2071, 219])).
% 1.14/1.04 tff(2073,plain,
% 1.14/1.04 (hskp24),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[175, 2072, 219])).
% 1.14/1.04 tff(2074,plain,
% 1.14/1.04 (~c2_1(a1267)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[479, 2073])).
% 1.14/1.04 tff(2075,plain,
% 1.14/1.04 (~c1_1(a1267)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[485, 2073])).
% 1.14/1.04 tff(2076,plain,
% 1.14/1.04 (c0_1(a1267)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[496, 2073])).
% 1.14/1.04 tff(2077,plain,
% 1.14/1.04 (hskp14),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[1044, 1196, 926, 924, 923])).
% 1.14/1.04 tff(2078,plain,
% 1.14/1.04 (~c2_1(a1232)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[418, 2077])).
% 1.14/1.04 tff(2079,plain,
% 1.14/1.04 (~c0_1(a1232)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[453, 2077])).
% 1.14/1.04 tff(2080,plain,
% 1.14/1.04 (c3_1(a1232)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[429, 2077])).
% 1.14/1.04 tff(2081,plain,
% 1.14/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2082,plain,
% 1.14/1.04 (((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232))) <=> (c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2083,plain,
% 1.14/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232))))),
% 1.14/1.04 inference(monotonicity,[status(thm)],[2082])).
% 1.14/1.04 tff(2084,plain,
% 1.14/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232)))),
% 1.14/1.04 inference(transitivity,[status(thm)],[2083, 2081])).
% 1.14/1.04 tff(2085,plain,
% 1.14/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | c2_1(a1224) | (~c3_1(a1224)) | (~c1_1(a1224)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))),
% 1.14/1.04 inference(quant_inst,[status(thm)],[])).
% 1.14/1.04 tff(2086,plain,
% 1.14/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | c2_1(a1224) | (~ndr1_0) | (~c2_1(a1206)) | (~c1_1(a1206)) | (~c0_1(a1206)) | (~c3_1(a1224)) | (~c1_1(a1224)) | (~c3_1(a1232))),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2085, 2084])).
% 1.14/1.04 tff(2087,plain,
% 1.14/1.04 (~c1_1(a1206)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[2086, 177, 2080, 2047, 2046, 1212, 1211, 2079, 2078, 2045, 382])).
% 1.14/1.04 tff(2088,plain,
% 1.14/1.04 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.14/1.04 inference(bind,[status(th)],[])).
% 1.14/1.04 tff(2089,plain,
% 1.14/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.14/1.04 inference(quant_intro,[status(thm)],[2088])).
% 1.14/1.04 tff(2090,plain,
% 1.14/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2091,plain,
% 1.14/1.04 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.14/1.04 inference(bind,[status(th)],[])).
% 1.14/1.04 tff(2092,plain,
% 1.14/1.04 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.14/1.04 inference(quant_intro,[status(thm)],[2091])).
% 1.14/1.04 tff(2093,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 1.14/1.04 tff(2094,plain,
% 1.14/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2093, 2092])).
% 1.14/1.04 tff(2095,plain,
% 1.14/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2094, 2090])).
% 1.14/1.04 tff(2096,plain,(
% 1.14/1.04 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.14/1.04 inference(skolemize,[status(sab)],[2095])).
% 1.14/1.04 tff(2097,plain,
% 1.14/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2096, 2089])).
% 1.14/1.04 tff(2098,plain,
% 1.14/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1267) | c2_1(a1267) | c0_1(a1232) | c2_1(a1232) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | c1_1(a1232) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1267) | c2_1(a1267) | c0_1(a1232) | c2_1(a1232) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | c1_1(a1232) | (~c0_1(a1267)))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2099,plain,
% 1.14/1.04 (((~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c3_1(a1212) | c0_1(a1212) | (~c2_1(a1212)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232)) <=> (c1_1(a1267) | c2_1(a1267) | c0_1(a1232) | c2_1(a1232) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | c1_1(a1232) | (~c0_1(a1267)))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2100,plain,
% 1.14/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c3_1(a1212) | c0_1(a1212) | (~c2_1(a1212)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1267) | c2_1(a1267) | c0_1(a1232) | c2_1(a1232) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | c1_1(a1232) | (~c0_1(a1267))))),
% 1.14/1.04 inference(monotonicity,[status(thm)],[2099])).
% 1.14/1.04 tff(2101,plain,
% 1.14/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c3_1(a1212) | c0_1(a1212) | (~c2_1(a1212)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1267) | c2_1(a1267) | c0_1(a1232) | c2_1(a1232) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | c1_1(a1232) | (~c0_1(a1267)))),
% 1.14/1.04 inference(transitivity,[status(thm)],[2100, 2098])).
% 1.14/1.04 tff(2102,plain,
% 1.14/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c3_1(a1212) | c0_1(a1212) | (~c2_1(a1212)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))),
% 1.14/1.04 inference(quant_inst,[status(thm)],[])).
% 1.14/1.04 tff(2103,plain,
% 1.14/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1267) | c2_1(a1267) | c0_1(a1232) | c2_1(a1232) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | c1_1(a1232) | (~c0_1(a1267))),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2102, 2101])).
% 1.14/1.04 tff(2104,plain,
% 1.14/1.04 (c1_1(a1232)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[2103, 177, 926, 2037, 924, 923, 2079, 2078, 2026, 2020, 2097])).
% 1.14/1.04 tff(2105,plain,
% 1.14/1.04 (c1_1(a1206) | (~c1_1(a1232))),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[1081, 1195, 177, 1212, 2079, 2078, 1197, 1074])).
% 1.14/1.04 tff(2106,plain,
% 1.14/1.04 ($false),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[2105, 2104, 2087])).
% 1.14/1.04 tff(2107,plain,(hskp25 | (~c0_1(a1267)) | c1_1(a1267) | c2_1(a1267) | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.14/1.04 tff(2108,plain,
% 1.14/1.04 (hskp25),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[2107, 2076, 2075, 2074, 2072])).
% 1.14/1.04 tff(2109,plain,
% 1.14/1.04 (c3_1(a1204)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[777, 2108])).
% 1.14/1.04 tff(2110,plain,
% 1.14/1.04 (c2_1(a1204)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[766, 2108])).
% 1.14/1.04 tff(2111,plain,
% 1.14/1.04 (c0_1(a1204)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[754, 2108])).
% 1.14/1.04 tff(2112,plain,
% 1.14/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2113,plain,
% 1.14/1.04 (((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | (~c3_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212))) <=> (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2114,plain,
% 1.14/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | (~c3_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))))),
% 1.14/1.04 inference(monotonicity,[status(thm)],[2113])).
% 1.14/1.04 tff(2115,plain,
% 1.14/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | (~c3_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.14/1.04 inference(transitivity,[status(thm)],[2114, 2112])).
% 1.14/1.04 tff(2116,plain,
% 1.14/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | (~c3_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))),
% 1.14/1.04 inference(quant_inst,[status(thm)],[])).
% 1.14/1.04 tff(2117,plain,
% 1.14/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))),
% 1.14/1.04 inference(modus_ponens,[status(thm)],[2116, 2115])).
% 1.14/1.04 tff(2118,plain,
% 1.14/1.04 (~c1_1(a1204)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[2117, 177, 2111, 2110, 2109, 2037, 2026, 2020, 10])).
% 1.14/1.04 tff(2119,plain,
% 1.14/1.04 (hskp25),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[2107, 1574, 1561, 1560, 1194])).
% 1.14/1.04 tff(2120,plain,
% 1.14/1.04 (c3_1(a1204)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[777, 2119])).
% 1.14/1.04 tff(2121,plain,
% 1.14/1.04 (c2_1(a1204)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[766, 2119])).
% 1.14/1.04 tff(2122,plain,
% 1.14/1.04 (c0_1(a1204)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[754, 2119])).
% 1.14/1.04 tff(2123,plain,
% 1.14/1.04 (~c1_1(a1204)),
% 1.14/1.04 inference(unit_resolution,[status(thm)],[2117, 177, 2122, 2121, 2120, 2037, 2026, 2020, 10])).
% 1.14/1.04 tff(2124,plain,
% 1.14/1.04 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c2_1(a1267) | (~ndr1_0) | (~c0_1(a1267)) | (~c3_1(a1267)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c2_1(a1267) | (~ndr1_0) | (~c0_1(a1267)) | (~c3_1(a1267)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204)))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2125,plain,
% 1.14/1.04 ((hskp6 | (~ndr1_0) | c2_1(a1267) | (~c3_1(a1267)) | (~c0_1(a1267)) | c1_1(a1204) | (~c2_1(a1204)) | (~c0_1(a1204))) <=> (hskp6 | c2_1(a1267) | (~ndr1_0) | (~c0_1(a1267)) | (~c3_1(a1267)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204)))),
% 1.14/1.04 inference(rewrite,[status(thm)],[])).
% 1.14/1.04 tff(2126,plain,
% 1.14/1.04 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1267) | (~c3_1(a1267)) | (~c0_1(a1267)) | c1_1(a1204) | (~c2_1(a1204)) | (~c0_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c2_1(a1267) | (~ndr1_0) | (~c0_1(a1267)) | (~c3_1(a1267)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204))))),
% 1.14/1.04 inference(monotonicity,[status(thm)],[2125])).
% 1.14/1.04 tff(2127,plain,
% 1.14/1.05 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1267) | (~c3_1(a1267)) | (~c0_1(a1267)) | c1_1(a1204) | (~c2_1(a1204)) | (~c0_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c2_1(a1267) | (~ndr1_0) | (~c0_1(a1267)) | (~c3_1(a1267)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204)))),
% 1.14/1.05 inference(transitivity,[status(thm)],[2126, 2124])).
% 1.14/1.05 tff(2128,plain,
% 1.14/1.05 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a1267) | (~c3_1(a1267)) | (~c0_1(a1267)) | c1_1(a1204) | (~c2_1(a1204)) | (~c0_1(a1204)))),
% 1.14/1.05 inference(quant_inst,[status(thm)],[])).
% 1.14/1.05 tff(2129,plain,
% 1.14/1.05 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c2_1(a1267) | (~ndr1_0) | (~c0_1(a1267)) | (~c3_1(a1267)) | (~c2_1(a1204)) | c1_1(a1204) | (~c0_1(a1204))),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 1.14/1.05 tff(2130,plain,
% 1.14/1.05 (~c3_1(a1267)),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[2129, 177, 24, 2122, 2121, 1574, 1560, 44, 2123])).
% 1.14/1.05 tff(2131,plain,
% 1.14/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c0_1(a1267)) | c3_1(a1267))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1267) | c2_1(a1267) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c0_1(a1267)) | c3_1(a1267))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2132,plain,
% 1.14/1.05 (((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1212) | c3_1(a1212) | (~c1_1(a1212))) <=> (c1_1(a1267) | c2_1(a1267) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c0_1(a1267)) | c3_1(a1267))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2133,plain,
% 1.14/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1212) | c3_1(a1212) | (~c1_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c0_1(a1267)) | c3_1(a1267)))),
% 1.14/1.05 inference(monotonicity,[status(thm)],[2132])).
% 1.14/1.05 tff(2134,plain,
% 1.14/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1212) | c3_1(a1212) | (~c1_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1267) | c2_1(a1267) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c0_1(a1267)) | c3_1(a1267))),
% 1.14/1.05 inference(transitivity,[status(thm)],[2133, 2131])).
% 1.14/1.05 tff(2135,plain,
% 1.14/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)) | c3_1(a1267) | c1_1(a1267) | (~c0_1(a1267)) | c0_1(a1212) | c3_1(a1212) | (~c1_1(a1212)))),
% 1.14/1.05 inference(quant_inst,[status(thm)],[])).
% 1.14/1.05 tff(2136,plain,
% 1.14/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a1267) | c2_1(a1267) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c0_1(a1267)) | c3_1(a1267)),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2135, 2134])).
% 1.14/1.05 tff(2137,plain,
% 1.14/1.05 (~c1_1(a1212)),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[2136, 177, 1574, 1561, 1560, 2026, 2020, 921, 2130])).
% 1.14/1.05 tff(2138,plain,
% 1.14/1.05 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2139,plain,
% 1.14/1.05 ((hskp9 | (~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1212) | c1_1(a1212) | (~c2_1(a1212))) <=> (hskp9 | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2140,plain,
% 1.14/1.05 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1212) | c1_1(a1212) | (~c2_1(a1212)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204))))),
% 1.14/1.05 inference(monotonicity,[status(thm)],[2139])).
% 1.14/1.05 tff(2141,plain,
% 1.14/1.05 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1212) | c1_1(a1212) | (~c2_1(a1212)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.14/1.05 inference(transitivity,[status(thm)],[2140, 2138])).
% 1.14/1.05 tff(2142,plain,
% 1.14/1.05 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1212) | c1_1(a1212) | (~c2_1(a1212)))),
% 1.14/1.05 inference(quant_inst,[status(thm)],[])).
% 1.14/1.05 tff(2143,plain,
% 1.14/1.05 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204))),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2142, 2141])).
% 1.14/1.05 tff(2144,plain,
% 1.14/1.05 (hskp9 | c1_1(a1212)),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[2143, 177, 2122, 2120, 2037, 2020, 1368, 2123])).
% 1.14/1.05 tff(2145,plain,
% 1.14/1.05 (hskp9),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[2144, 2137])).
% 1.14/1.05 tff(2146,plain,
% 1.14/1.05 (~c0_1(a1219)),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[843, 2145])).
% 1.14/1.05 tff(2147,plain,
% 1.14/1.05 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a1224) | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | (~c3_1(a1224)) | (~c1_1(a1224)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2148,plain,
% 1.14/1.05 ((hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1212) | c1_1(a1212) | (~c2_1(a1212))) <=> (hskp14 | c2_1(a1224) | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2149,plain,
% 1.14/1.05 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1212) | c1_1(a1212) | (~c2_1(a1212)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c2_1(a1224) | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | (~c3_1(a1224)) | (~c1_1(a1224))))),
% 1.14/1.05 inference(monotonicity,[status(thm)],[2148])).
% 1.14/1.05 tff(2150,plain,
% 1.14/1.05 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1212) | c1_1(a1212) | (~c2_1(a1212)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | (~c3_1(a1224)) | (~c1_1(a1224)))),
% 1.14/1.05 inference(transitivity,[status(thm)],[2149, 2147])).
% 1.14/1.05 tff(2151,plain,
% 1.14/1.05 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a1224) | (~c1_1(a1224)) | (~c3_1(a1224)) | c3_1(a1212) | c1_1(a1212) | (~c2_1(a1212)))),
% 1.14/1.05 inference(quant_inst,[status(thm)],[])).
% 1.14/1.05 tff(2152,plain,
% 1.14/1.05 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c2_1(a1224) | c3_1(a1212) | (~ndr1_0) | c1_1(a1212) | (~c2_1(a1212)) | (~c3_1(a1224)) | (~c1_1(a1224))),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2151, 2150])).
% 1.14/1.05 tff(2153,plain,
% 1.14/1.05 (hskp14 | c1_1(a1212)),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[2152, 177, 2047, 2046, 2037, 2045, 2020, 664])).
% 1.14/1.05 tff(2154,plain,
% 1.14/1.05 (hskp14),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[2153, 2137])).
% 1.14/1.05 tff(2155,plain,
% 1.14/1.05 (~c2_1(a1232)),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[418, 2154])).
% 1.14/1.05 tff(2156,plain,
% 1.14/1.05 (~c0_1(a1232)),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[453, 2154])).
% 1.14/1.05 tff(2157,plain,
% 1.14/1.05 (c2_1(a1219)),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[819, 2145])).
% 1.14/1.05 tff(2158,plain,
% 1.14/1.05 (c1_1(a1219)),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[830, 2145])).
% 1.14/1.05 tff(2159,plain,
% 1.14/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2160,plain,
% 1.14/1.05 (((~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232)) <=> (c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2161,plain,
% 1.14/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204))))),
% 1.14/1.05 inference(monotonicity,[status(thm)],[2160])).
% 1.14/1.05 tff(2162,plain,
% 1.14/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.14/1.05 inference(transitivity,[status(thm)],[2161, 2159])).
% 1.14/1.05 tff(2163,plain,
% 1.14/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1204) | (~c3_1(a1204)) | (~c0_1(a1204)) | c0_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1232) | c1_1(a1232) | c0_1(a1232))),
% 1.14/1.05 inference(quant_inst,[status(thm)],[])).
% 1.14/1.05 tff(2164,plain,
% 1.14/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1232) | c2_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c1_1(a1219)) | (~c2_1(a1219)) | c1_1(a1232) | c1_1(a1204) | (~c0_1(a1204)) | (~c3_1(a1204))),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2163, 2162])).
% 1.14/1.05 tff(2165,plain,
% 1.14/1.05 (c1_1(a1232)),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[2164, 177, 2122, 2120, 2158, 2157, 2156, 2155, 2146, 34, 2123])).
% 1.14/1.05 tff(2166,plain,
% 1.14/1.05 (c3_1(a1219)),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[934, 2158, 2130, 1561, 1560, 2146, 1574])).
% 1.14/1.05 tff(2167,plain,
% 1.14/1.05 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.14/1.05 inference(bind,[status(th)],[])).
% 1.14/1.05 tff(2168,plain,
% 1.14/1.05 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.14/1.05 inference(quant_intro,[status(thm)],[2167])).
% 1.14/1.05 tff(2169,plain,
% 1.14/1.05 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2170,plain,
% 1.14/1.05 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp3) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp3))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.14/1.05 inference(bind,[status(th)],[])).
% 1.14/1.05 tff(2171,plain,
% 1.14/1.05 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.14/1.05 inference(quant_intro,[status(thm)],[2170])).
% 1.14/1.05 tff(2172,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 1.14/1.05 tff(2173,plain,
% 1.14/1.05 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2172, 2171])).
% 1.14/1.05 tff(2174,plain,
% 1.14/1.05 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2173, 2169])).
% 1.14/1.05 tff(2175,plain,(
% 1.14/1.05 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.14/1.05 inference(skolemize,[status(sab)],[2174])).
% 1.14/1.05 tff(2176,plain,
% 1.14/1.05 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2175, 2168])).
% 1.14/1.05 tff(2177,plain,
% 1.14/1.05 (c3_1(a1232)),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[429, 2154])).
% 1.14/1.05 tff(2178,plain,
% 1.14/1.05 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1232)) | (~c1_1(a1232)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2179,plain,
% 1.14/1.05 ((hskp3 | (~ndr1_0) | c0_1(a1219) | (~c2_1(a1219)) | (~c3_1(a1219)) | c0_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232))) <=> (hskp3 | c0_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2180,plain,
% 1.14/1.05 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1219) | (~c2_1(a1219)) | (~c3_1(a1219)) | c0_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1232)) | (~c1_1(a1232))))),
% 1.14/1.05 inference(monotonicity,[status(thm)],[2179])).
% 1.14/1.05 tff(2181,plain,
% 1.14/1.05 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1219) | (~c2_1(a1219)) | (~c3_1(a1219)) | c0_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 1.14/1.05 inference(transitivity,[status(thm)],[2180, 2178])).
% 1.14/1.05 tff(2182,plain,
% 1.14/1.05 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c0_1(a1219) | (~c2_1(a1219)) | (~c3_1(a1219)) | c0_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 1.14/1.05 inference(quant_inst,[status(thm)],[])).
% 1.14/1.05 tff(2183,plain,
% 1.14/1.05 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1232) | c0_1(a1219) | (~ndr1_0) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c3_1(a1232)) | (~c1_1(a1232))),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2182, 2181])).
% 1.14/1.05 tff(2184,plain,
% 1.14/1.05 (hskp3),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[2183, 177, 2177, 2157, 2156, 2146, 2176, 2166, 2165])).
% 1.14/1.05 tff(2185,plain,
% 1.14/1.05 (((~hskp3) | (~c3_1(a1210))) <=> ((~hskp3) | (~c3_1(a1210)))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2186,plain,
% 1.14/1.05 (((~c3_1(a1210)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a1210)))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2187,axiom,((~c3_1(a1210)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 1.14/1.05 tff(2188,plain,
% 1.14/1.05 ((~hskp3) | (~c3_1(a1210))),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2187, 2186])).
% 1.14/1.05 tff(2189,plain,
% 1.14/1.05 ((~hskp3) | (~c3_1(a1210))),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2188, 2185])).
% 1.14/1.05 tff(2190,plain,
% 1.14/1.05 (~c3_1(a1210)),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[2189, 2184])).
% 1.14/1.05 tff(2191,plain,
% 1.14/1.05 (((~hskp3) | c1_1(a1210)) <=> ((~hskp3) | c1_1(a1210))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2192,axiom,((~hskp3) | c1_1(a1210)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 1.14/1.05 tff(2193,plain,
% 1.14/1.05 ((~hskp3) | c1_1(a1210)),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2192, 2191])).
% 1.14/1.05 tff(2194,plain,
% 1.14/1.05 ((~hskp3) | c1_1(a1210)),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2193, 2191])).
% 1.14/1.05 tff(2195,plain,
% 1.14/1.05 ((~hskp3) | c1_1(a1210)),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2194, 2191])).
% 1.14/1.05 tff(2196,plain,
% 1.14/1.05 ((~hskp3) | c1_1(a1210)),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2195, 2191])).
% 1.14/1.05 tff(2197,plain,
% 1.14/1.05 ((~hskp3) | c1_1(a1210)),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2196, 2191])).
% 1.14/1.05 tff(2198,plain,
% 1.14/1.05 ((~hskp3) | c1_1(a1210)),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2197, 2191])).
% 1.14/1.05 tff(2199,plain,
% 1.14/1.05 ((~hskp3) | c1_1(a1210)),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2198, 2191])).
% 1.14/1.05 tff(2200,plain,
% 1.14/1.05 ((~hskp3) | c1_1(a1210)),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2199, 2191])).
% 1.14/1.05 tff(2201,plain,
% 1.14/1.05 (c1_1(a1210)),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[2200, 2184])).
% 1.14/1.05 tff(2202,plain,
% 1.14/1.05 (((~hskp3) | c0_1(a1210)) <=> ((~hskp3) | c0_1(a1210))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2203,axiom,((~hskp3) | c0_1(a1210)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 1.14/1.05 tff(2204,plain,
% 1.14/1.05 ((~hskp3) | c0_1(a1210)),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2203, 2202])).
% 1.14/1.05 tff(2205,plain,
% 1.14/1.05 ((~hskp3) | c0_1(a1210)),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2204, 2202])).
% 1.14/1.05 tff(2206,plain,
% 1.14/1.05 ((~hskp3) | c0_1(a1210)),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2205, 2202])).
% 1.14/1.05 tff(2207,plain,
% 1.14/1.05 ((~hskp3) | c0_1(a1210)),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2206, 2202])).
% 1.14/1.05 tff(2208,plain,
% 1.14/1.05 ((~hskp3) | c0_1(a1210)),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2207, 2202])).
% 1.14/1.05 tff(2209,plain,
% 1.14/1.05 ((~hskp3) | c0_1(a1210)),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2208, 2202])).
% 1.14/1.05 tff(2210,plain,
% 1.14/1.05 ((~hskp3) | c0_1(a1210)),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2209, 2202])).
% 1.14/1.05 tff(2211,plain,
% 1.14/1.05 ((~hskp3) | c0_1(a1210)),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2210, 2202])).
% 1.14/1.05 tff(2212,plain,
% 1.14/1.05 (c0_1(a1210)),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[2211, 2184])).
% 1.14/1.05 tff(2213,plain,
% 1.14/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c3_1(a1210) | (~ndr1_0) | (~c1_1(a1210)) | c2_1(a1210) | (~c0_1(a1210)) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1267) | c2_1(a1267) | c3_1(a1210) | (~ndr1_0) | (~c1_1(a1210)) | c2_1(a1210) | (~c0_1(a1210)) | (~c0_1(a1267)))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2214,plain,
% 1.14/1.05 (((~ndr1_0) | c3_1(a1210) | (~c1_1(a1210)) | (~c0_1(a1210)) | c3_1(a1210) | c2_1(a1210) | (~c1_1(a1210)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267))) <=> (c1_1(a1267) | c2_1(a1267) | c3_1(a1210) | (~ndr1_0) | (~c1_1(a1210)) | c2_1(a1210) | (~c0_1(a1210)) | (~c0_1(a1267)))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2215,plain,
% 1.14/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1210) | (~c1_1(a1210)) | (~c0_1(a1210)) | c3_1(a1210) | c2_1(a1210) | (~c1_1(a1210)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c3_1(a1210) | (~ndr1_0) | (~c1_1(a1210)) | c2_1(a1210) | (~c0_1(a1210)) | (~c0_1(a1267))))),
% 1.14/1.05 inference(monotonicity,[status(thm)],[2214])).
% 1.14/1.05 tff(2216,plain,
% 1.14/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1210) | (~c1_1(a1210)) | (~c0_1(a1210)) | c3_1(a1210) | c2_1(a1210) | (~c1_1(a1210)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1267) | c2_1(a1267) | c3_1(a1210) | (~ndr1_0) | (~c1_1(a1210)) | c2_1(a1210) | (~c0_1(a1210)) | (~c0_1(a1267)))),
% 1.14/1.05 inference(transitivity,[status(thm)],[2215, 2213])).
% 1.14/1.05 tff(2217,plain,
% 1.14/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1210) | (~c1_1(a1210)) | (~c0_1(a1210)) | c3_1(a1210) | c2_1(a1210) | (~c1_1(a1210)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)))),
% 1.14/1.05 inference(quant_inst,[status(thm)],[])).
% 1.14/1.05 tff(2218,plain,
% 1.14/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1267) | c2_1(a1267) | c3_1(a1210) | (~ndr1_0) | (~c1_1(a1210)) | c2_1(a1210) | (~c0_1(a1210)) | (~c0_1(a1267))),
% 1.14/1.05 inference(modus_ponens,[status(thm)],[2217, 2216])).
% 1.14/1.05 tff(2219,plain,
% 1.14/1.05 (c2_1(a1210)),
% 1.14/1.05 inference(unit_resolution,[status(thm)],[2218, 177, 1574, 2212, 2201, 1561, 1560, 2190, 1474])).
% 1.14/1.05 tff(2220,plain,
% 1.14/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c1_1(a1210)) | (~c2_1(a1210)) | (~c0_1(a1210)) | (~c3_1(a1232)) | (~c1_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c1_1(a1210)) | (~c2_1(a1210)) | (~c0_1(a1210)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2221,plain,
% 1.14/1.05 (((~ndr1_0) | (~c2_1(a1210)) | (~c1_1(a1210)) | (~c0_1(a1210)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232))) <=> (c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c1_1(a1210)) | (~c2_1(a1210)) | (~c0_1(a1210)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 1.14/1.05 inference(rewrite,[status(thm)],[])).
% 1.14/1.05 tff(2222,plain,
% 1.14/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1210)) | (~c1_1(a1210)) | (~c0_1(a1210)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c1_1(a1210)) | (~c2_1(a1210)) | (~c0_1(a1210)) | (~c3_1(a1232)) | (~c1_1(a1232))))),
% 1.14/1.06 inference(monotonicity,[status(thm)],[2221])).
% 1.14/1.06 tff(2223,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1210)) | (~c1_1(a1210)) | (~c0_1(a1210)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c1_1(a1210)) | (~c2_1(a1210)) | (~c0_1(a1210)) | (~c3_1(a1232)) | (~c1_1(a1232)))),
% 1.14/1.06 inference(transitivity,[status(thm)],[2222, 2220])).
% 1.14/1.06 tff(2224,plain,
% 1.14/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1210)) | (~c1_1(a1210)) | (~c0_1(a1210)) | c2_1(a1232) | (~c3_1(a1232)) | (~c1_1(a1232)) | c2_1(a1232) | c0_1(a1232) | (~c3_1(a1232)))),
% 1.14/1.06 inference(quant_inst,[status(thm)],[])).
% 1.14/1.06 tff(2225,plain,
% 1.14/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1232) | c2_1(a1232) | (~ndr1_0) | (~c1_1(a1210)) | (~c2_1(a1210)) | (~c0_1(a1210)) | (~c3_1(a1232)) | (~c1_1(a1232))),
% 1.14/1.06 inference(modus_ponens,[status(thm)],[2224, 2223])).
% 1.14/1.06 tff(2226,plain,
% 1.14/1.06 ($false),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[2225, 177, 2177, 2212, 2201, 2156, 2155, 382, 2165, 2219])).
% 1.14/1.06 tff(2227,plain,(hskp26 | hskp6 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.14/1.06 tff(2228,plain,
% 1.14/1.06 (hskp6),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[2227, 2072, 219])).
% 1.14/1.06 tff(2229,plain,
% 1.14/1.06 (c1_1(a1215)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[103, 2228])).
% 1.14/1.06 tff(2230,plain,
% 1.14/1.06 (c2_1(a1215)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[114, 2228])).
% 1.14/1.06 tff(2231,plain,
% 1.14/1.06 (~c3_1(a1215)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[92, 2228])).
% 1.14/1.06 tff(2232,plain,
% 1.14/1.06 ((~hskp25) | c3_1(a1215) | hskp15 | hskp28 | (~c1_1(a1215)) | c0_1(a1215)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[991, 2047, 2046, 2045])).
% 1.14/1.06 tff(2233,plain,
% 1.14/1.06 (c0_1(a1215)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[2232, 75, 219, 2229, 2108, 2231])).
% 1.14/1.06 tff(2234,plain,
% 1.14/1.06 (~hskp4),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[401, 2233, 219, 2230, 2229])).
% 1.14/1.06 tff(2235,plain,
% 1.14/1.06 (hskp15 | hskp4 | (~c3_1(a1267))),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[961, 177, 2075, 2074, 412])).
% 1.14/1.06 tff(2236,plain,
% 1.14/1.06 (~c3_1(a1267)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[2235, 2234, 75])).
% 1.14/1.06 tff(2237,plain,
% 1.14/1.06 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1267) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1267) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267))),
% 1.14/1.06 inference(rewrite,[status(thm)],[])).
% 1.14/1.06 tff(2238,plain,
% 1.14/1.06 (((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267))) <=> (c2_1(a1267) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267))),
% 1.14/1.06 inference(rewrite,[status(thm)],[])).
% 1.14/1.06 tff(2239,plain,
% 1.14/1.06 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a1267) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267)))),
% 1.14/1.06 inference(monotonicity,[status(thm)],[2238])).
% 1.14/1.06 tff(2240,plain,
% 1.14/1.06 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1267) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267))),
% 1.14/1.06 inference(transitivity,[status(thm)],[2239, 2237])).
% 1.14/1.06 tff(2241,plain,
% 1.14/1.06 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a1215)) | (~c1_1(a1215)) | (~c0_1(a1215)) | c3_1(a1267) | c2_1(a1267) | (~c0_1(a1267)))),
% 1.14/1.06 inference(quant_inst,[status(thm)],[])).
% 1.14/1.06 tff(2242,plain,
% 1.14/1.06 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a1267) | (~ndr1_0) | (~c0_1(a1215)) | (~c1_1(a1215)) | (~c2_1(a1215)) | (~c0_1(a1267)) | c3_1(a1267)),
% 1.14/1.06 inference(modus_ponens,[status(thm)],[2241, 2240])).
% 1.14/1.06 tff(2243,plain,
% 1.14/1.06 ($false),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[2242, 177, 2076, 2229, 2230, 2074, 896, 2233, 2236])).
% 1.14/1.06 tff(2244,plain,(hskp15 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.14/1.06 tff(2245,plain,
% 1.14/1.06 (hskp15),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[2244, 219])).
% 1.14/1.06 tff(2246,plain,
% 1.14/1.06 (~c2_1(a1233)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[1256, 2245])).
% 1.14/1.06 tff(2247,plain,
% 1.14/1.06 (c1_1(a1233)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[1267, 2245])).
% 1.14/1.06 tff(2248,plain,
% 1.14/1.06 (c0_1(a1233)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[1278, 2245])).
% 1.14/1.06 tff(2249,plain,
% 1.14/1.06 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))),
% 1.14/1.06 inference(rewrite,[status(thm)],[])).
% 1.14/1.06 tff(2250,plain,
% 1.14/1.06 ((hskp19 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204))) <=> (hskp19 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))),
% 1.14/1.06 inference(rewrite,[status(thm)],[])).
% 1.14/1.06 tff(2251,plain,
% 1.14/1.06 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204))))),
% 1.14/1.06 inference(monotonicity,[status(thm)],[2250])).
% 1.14/1.06 tff(2252,plain,
% 1.14/1.06 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204)))),
% 1.14/1.06 inference(transitivity,[status(thm)],[2251, 2249])).
% 1.14/1.06 tff(2253,plain,
% 1.14/1.06 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c2_1(a1233) | (~c1_1(a1233)) | (~c0_1(a1233)) | c1_1(a1204) | (~c3_1(a1204)) | (~c2_1(a1204)))),
% 1.14/1.06 inference(quant_inst,[status(thm)],[])).
% 1.14/1.06 tff(2254,plain,
% 1.14/1.06 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c2_1(a1233) | (~ndr1_0) | (~c0_1(a1233)) | (~c1_1(a1233)) | (~c2_1(a1204)) | c1_1(a1204) | (~c3_1(a1204))),
% 1.14/1.06 inference(modus_ponens,[status(thm)],[2253, 2252])).
% 1.14/1.06 tff(2255,plain,
% 1.14/1.06 (hskp19),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[2254, 177, 2110, 2109, 2248, 2247, 2246, 869, 2118])).
% 1.14/1.06 tff(2256,plain,
% 1.14/1.06 (~c3_1(a1247)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[563, 2255])).
% 1.14/1.06 tff(2257,plain,
% 1.14/1.06 (~c2_1(a1247)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[538, 2255])).
% 1.14/1.06 tff(2258,plain,
% 1.14/1.06 (c1_1(a1247)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[549, 2255])).
% 1.14/1.06 tff(2259,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1267) | c2_1(a1267) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)) | (~c0_1(a1267)))),
% 1.14/1.06 inference(rewrite,[status(thm)],[])).
% 1.14/1.06 tff(2260,plain,
% 1.14/1.06 (((~ndr1_0) | c3_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)) | c3_1(a1247) | c2_1(a1247) | (~c1_1(a1247)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267))) <=> (c1_1(a1267) | c2_1(a1267) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)) | (~c0_1(a1267)))),
% 1.14/1.06 inference(rewrite,[status(thm)],[])).
% 1.14/1.06 tff(2261,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)) | c3_1(a1247) | c2_1(a1247) | (~c1_1(a1247)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1267) | c2_1(a1267) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)) | (~c0_1(a1267))))),
% 1.14/1.06 inference(monotonicity,[status(thm)],[2260])).
% 1.14/1.06 tff(2262,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)) | c3_1(a1247) | c2_1(a1247) | (~c1_1(a1247)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1267) | c2_1(a1267) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)) | (~c0_1(a1267)))),
% 1.14/1.06 inference(transitivity,[status(thm)],[2261, 2259])).
% 1.14/1.06 tff(2263,plain,
% 1.14/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)) | c3_1(a1247) | c2_1(a1247) | (~c1_1(a1247)) | c2_1(a1267) | c1_1(a1267) | (~c0_1(a1267)))),
% 1.14/1.06 inference(quant_inst,[status(thm)],[])).
% 1.14/1.06 tff(2264,plain,
% 1.14/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1267) | c2_1(a1267) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | (~c1_1(a1247)) | (~c0_1(a1247)) | (~c0_1(a1267))),
% 1.14/1.06 inference(modus_ponens,[status(thm)],[2263, 2262])).
% 1.14/1.06 tff(2265,plain,
% 1.14/1.06 (~c0_1(a1247)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[2264, 177, 2076, 2258, 2075, 2074, 2257, 2256, 1474])).
% 1.14/1.06 tff(2266,plain,
% 1.14/1.06 ($false),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[570, 219, 177, 2257, 2256, 218, 2265])).
% 1.14/1.06 tff(2267,plain,(hskp28), inference(lemma,lemma(discharge,[]))).
% 1.14/1.06 tff(2268,plain,
% 1.14/1.06 (c1_1(a1214)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[311, 2267])).
% 1.14/1.06 tff(2269,plain,
% 1.14/1.06 (c3_1(a1214)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[300, 2267])).
% 1.14/1.06 tff(2270,plain,
% 1.14/1.06 (c0_1(a1214)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[322, 2267])).
% 1.14/1.06 tff(2271,plain,
% 1.14/1.06 (hskp26),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[1221, 1195, 2270, 2269, 2268])).
% 1.14/1.06 tff(2272,plain,
% 1.14/1.06 (c2_1(a1208)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[695, 2271])).
% 1.14/1.06 tff(2273,plain,
% 1.14/1.06 (c1_1(a1208)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[706, 2271])).
% 1.14/1.06 tff(2274,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | (~c2_1(a1212)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | (~c2_1(a1212)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.06 inference(rewrite,[status(thm)],[])).
% 1.14/1.06 tff(2275,plain,
% 1.14/1.06 (((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212))) <=> (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | (~c2_1(a1212)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.06 inference(rewrite,[status(thm)],[])).
% 1.14/1.06 tff(2276,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | (~c2_1(a1212)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 1.14/1.06 inference(monotonicity,[status(thm)],[2275])).
% 1.14/1.06 tff(2277,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | (~c2_1(a1212)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.06 inference(transitivity,[status(thm)],[2276, 2274])).
% 1.14/1.06 tff(2278,plain,
% 1.14/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1208)) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))),
% 1.14/1.06 inference(quant_inst,[status(thm)],[])).
% 1.14/1.06 tff(2279,plain,
% 1.14/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1208)) | (~c3_1(a1208)) | (~c2_1(a1208)) | (~c2_1(a1212)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 1.14/1.06 inference(modus_ponens,[status(thm)],[2278, 2277])).
% 1.14/1.06 tff(2280,plain,
% 1.14/1.06 (~c3_1(a1208)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[2279, 177, 2270, 2268, 2269, 2273, 2272, 2037, 2026, 2020, 10])).
% 1.14/1.06 tff(2281,plain,
% 1.14/1.06 (c0_1(a1208)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[717, 2271])).
% 1.14/1.06 tff(2282,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c0_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c0_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.06 inference(rewrite,[status(thm)],[])).
% 1.14/1.06 tff(2283,plain,
% 1.14/1.06 (((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1208)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257))) <=> (c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c0_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.06 inference(rewrite,[status(thm)],[])).
% 1.14/1.06 tff(2284,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1208)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c0_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 1.14/1.06 inference(monotonicity,[status(thm)],[2283])).
% 1.14/1.06 tff(2285,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1208)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c0_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.06 inference(transitivity,[status(thm)],[2284, 2282])).
% 1.14/1.06 tff(2286,plain,
% 1.14/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1208) | (~c2_1(a1208)) | (~c0_1(a1208)) | c1_1(a1257) | c0_1(a1257) | (~c3_1(a1257)))),
% 1.14/1.06 inference(quant_inst,[status(thm)],[])).
% 1.14/1.06 tff(2287,plain,
% 1.14/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a1257) | c1_1(a1257) | (~ndr1_0) | (~c0_1(a1208)) | c3_1(a1208) | (~c2_1(a1208)) | (~c3_1(a1257)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 1.14/1.06 inference(modus_ponens,[status(thm)],[2286, 2285])).
% 1.14/1.06 tff(2288,plain,
% 1.14/1.06 ($false),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[2287, 177, 2270, 2268, 2269, 2281, 2272, 1213, 1210, 1209, 1193, 2280])).
% 1.14/1.06 tff(2289,plain,(hskp25), inference(lemma,lemma(discharge,[]))).
% 1.14/1.06 tff(2290,plain,
% 1.14/1.06 (c2_1(a1204)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[766, 2289])).
% 1.14/1.06 tff(2291,assumption,(hskp9), introduced(assumption)).
% 1.14/1.06 tff(2292,plain,
% 1.14/1.06 (c2_1(a1219)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[819, 2291])).
% 1.14/1.06 tff(2293,plain,
% 1.14/1.06 (c1_1(a1219)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[830, 2291])).
% 1.14/1.06 tff(2294,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.06 inference(rewrite,[status(thm)],[])).
% 1.14/1.06 tff(2295,plain,
% 1.14/1.06 (((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212))) <=> (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.06 inference(rewrite,[status(thm)],[])).
% 1.14/1.06 tff(2296,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 1.14/1.06 inference(monotonicity,[status(thm)],[2295])).
% 1.14/1.06 tff(2297,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.06 inference(transitivity,[status(thm)],[2296, 2294])).
% 1.14/1.06 tff(2298,plain,
% 1.14/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1219)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))),
% 1.14/1.06 inference(quant_inst,[status(thm)],[])).
% 1.14/1.06 tff(2299,plain,
% 1.14/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c1_1(a1219)) | (~c3_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 1.14/1.06 inference(modus_ponens,[status(thm)],[2298, 2297])).
% 1.14/1.06 tff(2300,plain,
% 1.14/1.06 (~c3_1(a1219)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[2299, 177, 2270, 2268, 2269, 2293, 2292, 2037, 2026, 2020, 10])).
% 1.14/1.06 tff(2301,plain,
% 1.14/1.06 (~c0_1(a1219)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[843, 2291])).
% 1.14/1.06 tff(2302,plain,
% 1.14/1.06 (~c3_1(a1219)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[2299, 177, 2270, 2268, 2269, 925, 1890, 2037, 2026, 2020, 10])).
% 1.14/1.06 tff(2303,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1219) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c3_1(a1219) | (~c1_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1219) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c3_1(a1219) | (~c1_1(a1219)))),
% 1.14/1.06 inference(rewrite,[status(thm)],[])).
% 1.14/1.06 tff(2304,plain,
% 1.14/1.06 (((~ndr1_0) | c3_1(a1219) | c0_1(a1219) | (~c1_1(a1219)) | c0_1(a1207) | c2_1(a1207) | (~c3_1(a1207)) | c2_1(a1207) | c1_1(a1207) | c0_1(a1207)) <=> (c0_1(a1219) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c3_1(a1219) | (~c1_1(a1219)))),
% 1.14/1.06 inference(rewrite,[status(thm)],[])).
% 1.14/1.06 tff(2305,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1219) | c0_1(a1219) | (~c1_1(a1219)) | c0_1(a1207) | c2_1(a1207) | (~c3_1(a1207)) | c2_1(a1207) | c1_1(a1207) | c0_1(a1207))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a1219) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c3_1(a1219) | (~c1_1(a1219))))),
% 1.14/1.06 inference(monotonicity,[status(thm)],[2304])).
% 1.14/1.06 tff(2306,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1219) | c0_1(a1219) | (~c1_1(a1219)) | c0_1(a1207) | c2_1(a1207) | (~c3_1(a1207)) | c2_1(a1207) | c1_1(a1207) | c0_1(a1207))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1219) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c3_1(a1219) | (~c1_1(a1219)))),
% 1.14/1.06 inference(transitivity,[status(thm)],[2305, 2303])).
% 1.14/1.06 tff(2307,plain,
% 1.14/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1219) | c0_1(a1219) | (~c1_1(a1219)) | c0_1(a1207) | c2_1(a1207) | (~c3_1(a1207)) | c2_1(a1207) | c1_1(a1207) | c0_1(a1207))),
% 1.14/1.06 inference(quant_inst,[status(thm)],[])).
% 1.14/1.06 tff(2308,plain,
% 1.14/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a1219) | c0_1(a1207) | c1_1(a1207) | c2_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c3_1(a1219) | (~c1_1(a1219))),
% 1.14/1.06 inference(modus_ponens,[status(thm)],[2307, 2306])).
% 1.14/1.06 tff(2309,plain,
% 1.14/1.06 (~c3_1(a1207)),
% 1.14/1.06 inference(unit_resolution,[status(thm)],[2308, 177, 925, 922, 1126, 1120, 1114, 237, 2302])).
% 1.14/1.06 tff(2310,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.06 inference(rewrite,[status(thm)],[])).
% 1.14/1.06 tff(2311,plain,
% 1.14/1.06 (((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1207) | c0_1(a1207) | c3_1(a1207)) <=> (c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.06 inference(rewrite,[status(thm)],[])).
% 1.14/1.06 tff(2312,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1207) | c0_1(a1207) | c3_1(a1207))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 1.14/1.06 inference(monotonicity,[status(thm)],[2311])).
% 1.14/1.06 tff(2313,plain,
% 1.14/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1207) | c0_1(a1207) | c3_1(a1207))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.07 inference(transitivity,[status(thm)],[2312, 2310])).
% 1.14/1.07 tff(2314,plain,
% 1.14/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1207) | c0_1(a1207) | c3_1(a1207))),
% 1.14/1.07 inference(quant_inst,[status(thm)],[])).
% 1.14/1.07 tff(2315,plain,
% 1.14/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1207) | c2_1(a1207) | (~ndr1_0) | c3_1(a1207) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 1.14/1.07 inference(modus_ponens,[status(thm)],[2314, 2313])).
% 1.14/1.07 tff(2316,plain,
% 1.14/1.07 ($false),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[2315, 177, 2270, 2268, 2269, 925, 1890, 1126, 1114, 74, 2302, 2309])).
% 1.14/1.07 tff(2317,plain,((~hskp2) | (~c1_1(a1219)) | (~c2_1(a1219)) | c0_1(a1219)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.07 tff(2318,plain,
% 1.14/1.07 (~hskp2),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[2317, 2293, 2292, 2301])).
% 1.14/1.07 tff(2319,plain,
% 1.14/1.07 (hskp7 | hskp2),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[1161, 177, 2270, 2268, 2269, 1155])).
% 1.14/1.07 tff(2320,plain,
% 1.14/1.07 (hskp7),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[2319, 2318])).
% 1.14/1.07 tff(2321,plain,
% 1.14/1.07 (~c3_1(a1216)),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[1168, 2320])).
% 1.14/1.07 tff(2322,plain,
% 1.14/1.07 (~c2_1(a1216)),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[1174, 2320])).
% 1.14/1.07 tff(2323,plain,
% 1.14/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | c0_1(a1216) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | c0_1(a1216) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.07 inference(rewrite,[status(thm)],[])).
% 1.14/1.07 tff(2324,plain,
% 1.14/1.07 (((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1216) | c0_1(a1216) | c3_1(a1216)) <=> (c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | c0_1(a1216) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.07 inference(rewrite,[status(thm)],[])).
% 1.14/1.07 tff(2325,plain,
% 1.14/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1216) | c0_1(a1216) | c3_1(a1216))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | c0_1(a1216) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 1.14/1.07 inference(monotonicity,[status(thm)],[2324])).
% 1.14/1.07 tff(2326,plain,
% 1.14/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1216) | c0_1(a1216) | c3_1(a1216))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | c0_1(a1216) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.07 inference(transitivity,[status(thm)],[2325, 2323])).
% 1.14/1.07 tff(2327,plain,
% 1.14/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1216) | c0_1(a1216) | c3_1(a1216))),
% 1.14/1.07 inference(quant_inst,[status(thm)],[])).
% 1.14/1.07 tff(2328,plain,
% 1.14/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1216) | c3_1(a1216) | (~ndr1_0) | c0_1(a1216) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 1.14/1.07 inference(modus_ponens,[status(thm)],[2327, 2326])).
% 1.14/1.07 tff(2329,plain,
% 1.14/1.07 (c0_1(a1216)),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[2328, 177, 2270, 2268, 2269, 2293, 2292, 2322, 2321, 74, 2300])).
% 1.14/1.07 tff(2330,plain,
% 1.14/1.07 (~c1_1(a1216)),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[1240, 2320])).
% 1.14/1.07 tff(2331,assumption,(hskp27), introduced(assumption)).
% 1.14/1.07 tff(2332,plain,
% 1.14/1.07 (c3_1(a1213)),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[1666, 2331])).
% 1.14/1.07 tff(2333,plain,
% 1.14/1.07 (c2_1(a1213)),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[1677, 2331])).
% 1.14/1.07 tff(2334,plain,
% 1.14/1.07 (c1_1(a1213)),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[1688, 2331])).
% 1.14/1.07 tff(2335,plain,
% 1.14/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213)))),
% 1.14/1.07 inference(rewrite,[status(thm)],[])).
% 1.14/1.07 tff(2336,plain,
% 1.14/1.07 (((~ndr1_0) | (~c2_1(a1213)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1219) | c3_1(a1219) | (~c2_1(a1219))) <=> (c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213)))),
% 1.14/1.07 inference(rewrite,[status(thm)],[])).
% 1.14/1.07 tff(2337,plain,
% 1.14/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1213)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1219) | c3_1(a1219) | (~c2_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213))))),
% 1.14/1.07 inference(monotonicity,[status(thm)],[2336])).
% 1.14/1.07 tff(2338,plain,
% 1.14/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1213)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1219) | c3_1(a1219) | (~c2_1(a1219)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213)))),
% 1.14/1.07 inference(transitivity,[status(thm)],[2337, 2335])).
% 1.14/1.07 tff(2339,plain,
% 1.14/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1213)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1219) | c3_1(a1219) | (~c2_1(a1219)))),
% 1.14/1.07 inference(quant_inst,[status(thm)],[])).
% 1.14/1.07 tff(2340,plain,
% 1.14/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1219) | (~ndr1_0) | c3_1(a1219) | (~c2_1(a1219)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c1_1(a1213)) | (~c3_1(a1213)) | (~c2_1(a1213))),
% 1.14/1.07 inference(modus_ponens,[status(thm)],[2339, 2338])).
% 1.14/1.07 tff(2341,plain,
% 1.14/1.07 ($false),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[2340, 177, 2270, 2268, 2269, 2334, 2333, 2332, 1890, 922, 10, 911])).
% 1.14/1.07 tff(2342,plain,((~hskp27) | (~c2_1(a1219)) | c0_1(a1219) | c3_1(a1219)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.07 tff(2343,plain,
% 1.14/1.07 (~hskp27),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[2342, 2292, 2301, 2300])).
% 1.14/1.07 tff(2344,plain,
% 1.14/1.07 ((hskp27 | hskp19 | hskp2) <=> (hskp27 | hskp19 | hskp2)),
% 1.14/1.07 inference(rewrite,[status(thm)],[])).
% 1.14/1.07 tff(2345,plain,
% 1.14/1.07 (((hskp27 | hskp19) | hskp2) <=> (hskp27 | hskp19 | hskp2)),
% 1.14/1.07 inference(rewrite,[status(thm)],[])).
% 1.14/1.07 tff(2346,plain,
% 1.14/1.07 ((hskp27 | hskp19) <=> (hskp27 | hskp19)),
% 1.14/1.07 inference(rewrite,[status(thm)],[])).
% 1.14/1.07 tff(2347,plain,
% 1.14/1.07 (((hskp27 | hskp19) | hskp2) <=> ((hskp27 | hskp19) | hskp2)),
% 1.14/1.07 inference(monotonicity,[status(thm)],[2346])).
% 1.14/1.07 tff(2348,plain,
% 1.14/1.07 (((hskp27 | hskp19) | hskp2) <=> (hskp27 | hskp19 | hskp2)),
% 1.14/1.07 inference(transitivity,[status(thm)],[2347, 2345])).
% 1.14/1.07 tff(2349,axiom,((hskp27 | hskp19) | hskp2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 1.14/1.07 tff(2350,plain,
% 1.14/1.07 (hskp27 | hskp19 | hskp2),
% 1.14/1.07 inference(modus_ponens,[status(thm)],[2349, 2348])).
% 1.14/1.07 tff(2351,plain,
% 1.14/1.07 (hskp27 | hskp19 | hskp2),
% 1.14/1.07 inference(modus_ponens,[status(thm)],[2350, 2344])).
% 1.14/1.07 tff(2352,plain,
% 1.14/1.07 (hskp27 | hskp19 | hskp2),
% 1.14/1.07 inference(modus_ponens,[status(thm)],[2351, 2344])).
% 1.14/1.07 tff(2353,plain,
% 1.14/1.07 (hskp27 | hskp19 | hskp2),
% 1.14/1.07 inference(modus_ponens,[status(thm)],[2352, 2344])).
% 1.14/1.07 tff(2354,plain,
% 1.14/1.07 (hskp27 | hskp19 | hskp2),
% 1.14/1.07 inference(modus_ponens,[status(thm)],[2353, 2344])).
% 1.14/1.07 tff(2355,plain,
% 1.14/1.07 (hskp27 | hskp19 | hskp2),
% 1.14/1.07 inference(modus_ponens,[status(thm)],[2354, 2344])).
% 1.14/1.07 tff(2356,plain,
% 1.14/1.07 (hskp27 | hskp19 | hskp2),
% 1.14/1.07 inference(modus_ponens,[status(thm)],[2355, 2344])).
% 1.14/1.07 tff(2357,plain,
% 1.14/1.07 (hskp27 | hskp19 | hskp2),
% 1.14/1.07 inference(modus_ponens,[status(thm)],[2356, 2344])).
% 1.14/1.07 tff(2358,plain,
% 1.14/1.07 (hskp19),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[2357, 2318, 2343])).
% 1.14/1.07 tff(2359,plain,
% 1.14/1.07 (~c3_1(a1247)),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[563, 2358])).
% 1.14/1.07 tff(2360,plain,
% 1.14/1.07 (~c2_1(a1247)),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[538, 2358])).
% 1.14/1.07 tff(2361,plain,
% 1.14/1.07 (c1_1(a1247)),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[549, 2358])).
% 1.14/1.07 tff(2362,plain,
% 1.14/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1247) | c3_1(a1247) | c1_1(a1216) | c2_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | (~c1_1(a1247)) | (~c0_1(a1247)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1247) | c3_1(a1247) | c1_1(a1216) | c2_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | (~c1_1(a1247)) | (~c0_1(a1247)))),
% 1.14/1.07 inference(rewrite,[status(thm)],[])).
% 1.14/1.07 tff(2363,plain,
% 1.14/1.07 (((~ndr1_0) | c3_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)) | c3_1(a1247) | c2_1(a1247) | (~c1_1(a1247)) | c2_1(a1216) | c1_1(a1216) | (~c0_1(a1216))) <=> (c2_1(a1247) | c3_1(a1247) | c1_1(a1216) | c2_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | (~c1_1(a1247)) | (~c0_1(a1247)))),
% 1.14/1.07 inference(rewrite,[status(thm)],[])).
% 1.14/1.07 tff(2364,plain,
% 1.14/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)) | c3_1(a1247) | c2_1(a1247) | (~c1_1(a1247)) | c2_1(a1216) | c1_1(a1216) | (~c0_1(a1216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a1247) | c3_1(a1247) | c1_1(a1216) | c2_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | (~c1_1(a1247)) | (~c0_1(a1247))))),
% 1.14/1.07 inference(monotonicity,[status(thm)],[2363])).
% 1.14/1.07 tff(2365,plain,
% 1.14/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)) | c3_1(a1247) | c2_1(a1247) | (~c1_1(a1247)) | c2_1(a1216) | c1_1(a1216) | (~c0_1(a1216)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1247) | c3_1(a1247) | c1_1(a1216) | c2_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | (~c1_1(a1247)) | (~c0_1(a1247)))),
% 1.14/1.07 inference(transitivity,[status(thm)],[2364, 2362])).
% 1.14/1.07 tff(2366,plain,
% 1.14/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1247) | (~c1_1(a1247)) | (~c0_1(a1247)) | c3_1(a1247) | c2_1(a1247) | (~c1_1(a1247)) | c2_1(a1216) | c1_1(a1216) | (~c0_1(a1216)))),
% 1.14/1.07 inference(quant_inst,[status(thm)],[])).
% 1.14/1.07 tff(2367,plain,
% 1.14/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a1247) | c3_1(a1247) | c1_1(a1216) | c2_1(a1216) | (~ndr1_0) | (~c0_1(a1216)) | (~c1_1(a1247)) | (~c0_1(a1247))),
% 1.14/1.07 inference(modus_ponens,[status(thm)],[2366, 2365])).
% 1.14/1.07 tff(2368,plain,
% 1.14/1.07 (~c0_1(a1247)),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[2367, 177, 2361, 2360, 2359, 2330, 2322, 1474, 2329])).
% 1.14/1.07 tff(2369,plain,
% 1.14/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c0_1(a1247) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c0_1(a1247) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.07 inference(rewrite,[status(thm)],[])).
% 1.14/1.07 tff(2370,plain,
% 1.14/1.07 (((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1247) | c0_1(a1247) | c3_1(a1247)) <=> (c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c0_1(a1247) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.07 inference(rewrite,[status(thm)],[])).
% 1.14/1.07 tff(2371,plain,
% 1.14/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1247) | c0_1(a1247) | c3_1(a1247))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c0_1(a1247) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))))),
% 1.14/1.07 inference(monotonicity,[status(thm)],[2370])).
% 1.14/1.07 tff(2372,plain,
% 1.14/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1247) | c0_1(a1247) | c3_1(a1247))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c0_1(a1247) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)))),
% 1.14/1.07 inference(transitivity,[status(thm)],[2371, 2369])).
% 1.14/1.07 tff(2373,plain,
% 1.14/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c1_1(a1214)) | (~c3_1(a1214)) | (~c0_1(a1214)) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c2_1(a1247) | c0_1(a1247) | c3_1(a1247))),
% 1.14/1.07 inference(quant_inst,[status(thm)],[])).
% 1.14/1.07 tff(2374,plain,
% 1.14/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a1247) | c3_1(a1247) | (~ndr1_0) | c3_1(a1219) | (~c1_1(a1219)) | (~c2_1(a1219)) | c0_1(a1247) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214))),
% 1.14/1.07 inference(modus_ponens,[status(thm)],[2373, 2372])).
% 1.14/1.07 tff(2375,plain,
% 1.14/1.07 ($false),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[2374, 177, 2270, 2268, 2269, 2293, 2292, 2360, 2359, 74, 2300, 2368])).
% 1.14/1.07 tff(2376,plain,(~hskp9), inference(lemma,lemma(discharge,[]))).
% 1.14/1.07 tff(2377,plain,
% 1.14/1.07 (c0_1(a1204)),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[754, 2289])).
% 1.14/1.07 tff(2378,plain,
% 1.14/1.07 (c3_1(a1204)),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[777, 2289])).
% 1.14/1.07 tff(2379,assumption,(~hskp9), introduced(assumption)).
% 1.14/1.07 tff(2380,plain,
% 1.14/1.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.14/1.07 inference(rewrite,[status(thm)],[])).
% 1.14/1.07 tff(2381,plain,
% 1.14/1.07 ((hskp9 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1212) | c0_1(a1212) | (~c1_1(a1212))) <=> (hskp9 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.14/1.07 inference(rewrite,[status(thm)],[])).
% 1.14/1.07 tff(2382,plain,
% 1.14/1.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1212) | c0_1(a1212) | (~c1_1(a1212)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))))),
% 1.14/1.07 inference(monotonicity,[status(thm)],[2381])).
% 1.14/1.07 tff(2383,plain,
% 1.14/1.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1212) | c0_1(a1212) | (~c1_1(a1212)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204)))),
% 1.14/1.07 inference(transitivity,[status(thm)],[2382, 2380])).
% 1.14/1.07 tff(2384,plain,
% 1.14/1.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1204)) | (~c3_1(a1204)) | (~c0_1(a1204)) | c3_1(a1212) | c0_1(a1212) | (~c1_1(a1212)))),
% 1.14/1.07 inference(quant_inst,[status(thm)],[])).
% 1.14/1.07 tff(2385,plain,
% 1.14/1.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c1_1(a1212)) | (~c2_1(a1204)) | (~c0_1(a1204)) | (~c3_1(a1204))),
% 1.14/1.07 inference(modus_ponens,[status(thm)],[2384, 2383])).
% 1.14/1.07 tff(2386,plain,
% 1.14/1.07 (hskp9 | (~c1_1(a1212))),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[2385, 177, 801, 800, 799, 2026, 2020, 798])).
% 1.14/1.07 tff(2387,plain,
% 1.14/1.07 (~c1_1(a1212)),
% 1.14/1.07 inference(unit_resolution,[status(thm)],[2386, 2379])).
% 1.14/1.07 tff(2388,plain,
% 1.14/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c3_1(a1204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c3_1(a1204)))),
% 1.22/1.08 inference(rewrite,[status(thm)],[])).
% 1.22/1.08 tff(2389,plain,
% 1.22/1.08 (((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212))) <=> (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c3_1(a1204)))),
% 1.22/1.08 inference(rewrite,[status(thm)],[])).
% 1.22/1.08 tff(2390,plain,
% 1.22/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c3_1(a1204))))),
% 1.22/1.08 inference(monotonicity,[status(thm)],[2389])).
% 1.22/1.08 tff(2391,plain,
% 1.22/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c3_1(a1204)))),
% 1.22/1.08 inference(transitivity,[status(thm)],[2390, 2388])).
% 1.22/1.08 tff(2392,plain,
% 1.22/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c3_1(a1204)) | (~c3_1(a1214)) | (~c1_1(a1214)) | (~c0_1(a1214)) | c0_1(a1212) | c3_1(a1212) | (~c2_1(a1212)))),
% 1.22/1.08 inference(quant_inst,[status(thm)],[])).
% 1.22/1.08 tff(2393,plain,
% 1.22/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a1212) | c3_1(a1212) | (~ndr1_0) | (~c2_1(a1212)) | (~c2_1(a1204)) | (~c1_1(a1204)) | (~c1_1(a1214)) | (~c0_1(a1214)) | (~c3_1(a1214)) | (~c3_1(a1204))),
% 1.22/1.08 inference(modus_ponens,[status(thm)],[2392, 2391])).
% 1.22/1.08 tff(2394,plain,
% 1.22/1.08 (~c1_1(a1204)),
% 1.22/1.08 inference(unit_resolution,[status(thm)],[2393, 177, 2270, 2268, 2269, 800, 799, 2037, 2026, 2020, 10])).
% 1.22/1.08 tff(2395,plain,
% 1.22/1.08 (hskp9 | c1_1(a1212)),
% 1.22/1.08 inference(unit_resolution,[status(thm)],[2143, 177, 801, 799, 2037, 2020, 1368, 2394])).
% 1.22/1.08 tff(2396,plain,
% 1.22/1.08 ($false),
% 1.22/1.08 inference(unit_resolution,[status(thm)],[2395, 2387, 2379])).
% 1.22/1.08 tff(2397,plain,(hskp9 | (~c0_1(a1204)) | (~c3_1(a1204)) | (~c2_1(a1204))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.08 tff(2398,plain,
% 1.22/1.08 ($false),
% 1.22/1.08 inference(unit_resolution,[status(thm)],[2397, 2378, 2377, 2376, 2290])).
% 1.22/1.08 % SZS output end Proof
%------------------------------------------------------------------------------