TSTP Solution File: SYN461-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN461-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 23:55:36 EDT 2022
% Result : Unsatisfiable 0.49s 0.61s
% Output : Proof 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYN461-1 : TPTP v8.1.0. Released v2.1.0.
% 0.04/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 03:23:55 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.49/0.61 % SZS status Unsatisfiable
% 0.49/0.61 % SZS output start Proof
% 0.49/0.61 tff(c0_1_type, type, (
% 0.49/0.61 c0_1: $i > $o)).
% 0.49/0.61 tff(c1_1_type, type, (
% 0.49/0.61 c1_1: $i > $o)).
% 0.49/0.61 tff(c2_1_type, type, (
% 0.49/0.61 c2_1: $i > $o)).
% 0.49/0.61 tff(c3_1_type, type, (
% 0.49/0.61 c3_1: $i > $o)).
% 0.49/0.61 tff(ndr1_0_type, type, (
% 0.49/0.61 ndr1_0: $o)).
% 0.49/0.61 tff(a1200_type, type, (
% 0.49/0.61 a1200: $i)).
% 0.49/0.61 tff(hskp17_type, type, (
% 0.49/0.61 hskp17: $o)).
% 0.49/0.61 tff(a1174_type, type, (
% 0.49/0.61 a1174: $i)).
% 0.49/0.61 tff(a1194_type, type, (
% 0.49/0.61 a1194: $i)).
% 0.49/0.61 tff(hskp3_type, type, (
% 0.49/0.61 hskp3: $o)).
% 0.49/0.61 tff(a1168_type, type, (
% 0.49/0.61 a1168: $i)).
% 0.49/0.61 tff(hskp22_type, type, (
% 0.49/0.61 hskp22: $o)).
% 0.49/0.61 tff(a1211_type, type, (
% 0.49/0.61 a1211: $i)).
% 0.49/0.61 tff(hskp0_type, type, (
% 0.49/0.61 hskp0: $o)).
% 0.49/0.61 tff(hskp14_type, type, (
% 0.49/0.61 hskp14: $o)).
% 0.49/0.61 tff(hskp23_type, type, (
% 0.49/0.61 hskp23: $o)).
% 0.49/0.61 tff(hskp19_type, type, (
% 0.49/0.61 hskp19: $o)).
% 0.49/0.61 tff(a1169_type, type, (
% 0.49/0.61 a1169: $i)).
% 0.49/0.61 tff(hskp1_type, type, (
% 0.49/0.61 hskp1: $o)).
% 0.49/0.61 tff(a1204_type, type, (
% 0.49/0.61 a1204: $i)).
% 0.49/0.61 tff(hskp28_type, type, (
% 0.49/0.61 hskp28: $o)).
% 0.49/0.61 tff(hskp8_type, type, (
% 0.49/0.61 hskp8: $o)).
% 0.49/0.61 tff(a1218_type, type, (
% 0.49/0.61 a1218: $i)).
% 0.49/0.61 tff(a1199_type, type, (
% 0.49/0.61 a1199: $i)).
% 0.49/0.61 tff(hskp16_type, type, (
% 0.49/0.61 hskp16: $o)).
% 0.49/0.61 tff(a1184_type, type, (
% 0.49/0.61 a1184: $i)).
% 0.49/0.61 tff(hskp10_type, type, (
% 0.49/0.61 hskp10: $o)).
% 0.49/0.61 tff(hskp13_type, type, (
% 0.49/0.61 hskp13: $o)).
% 0.49/0.61 tff(a1192_type, type, (
% 0.49/0.61 a1192: $i)).
% 0.49/0.61 tff(hskp2_type, type, (
% 0.49/0.61 hskp2: $o)).
% 0.49/0.61 tff(a1172_type, type, (
% 0.49/0.61 a1172: $i)).
% 0.49/0.61 tff(a1236_type, type, (
% 0.49/0.61 a1236: $i)).
% 0.49/0.61 tff(a1180_type, type, (
% 0.49/0.61 a1180: $i)).
% 0.49/0.61 tff(a1190_type, type, (
% 0.49/0.61 a1190: $i)).
% 0.49/0.61 tff(hskp26_type, type, (
% 0.49/0.61 hskp26: $o)).
% 0.49/0.61 tff(a1176_type, type, (
% 0.49/0.61 a1176: $i)).
% 0.49/0.61 tff(a1178_type, type, (
% 0.49/0.61 a1178: $i)).
% 0.49/0.61 tff(hskp6_type, type, (
% 0.49/0.61 hskp6: $o)).
% 0.49/0.61 tff(a1205_type, type, (
% 0.49/0.61 a1205: $i)).
% 0.49/0.61 tff(hskp20_type, type, (
% 0.49/0.61 hskp20: $o)).
% 0.49/0.61 tff(hskp12_type, type, (
% 0.49/0.61 hskp12: $o)).
% 0.49/0.61 tff(a1207_type, type, (
% 0.49/0.61 a1207: $i)).
% 0.49/0.61 tff(hskp21_type, type, (
% 0.49/0.61 hskp21: $o)).
% 0.49/0.61 tff(a1187_type, type, (
% 0.49/0.61 a1187: $i)).
% 0.49/0.61 tff(hskp4_type, type, (
% 0.49/0.61 hskp4: $o)).
% 0.49/0.61 tff(a1175_type, type, (
% 0.49/0.61 a1175: $i)).
% 0.49/0.61 tff(hskp5_type, type, (
% 0.49/0.61 hskp5: $o)).
% 0.49/0.61 tff(a1182_type, type, (
% 0.49/0.61 a1182: $i)).
% 0.49/0.61 tff(hskp25_type, type, (
% 0.49/0.61 hskp25: $o)).
% 0.49/0.61 tff(1,plain,
% 0.49/0.61 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.49/0.61 inference(bind,[status(th)],[])).
% 0.49/0.61 tff(2,plain,
% 0.49/0.61 (![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.49/0.61 inference(quant_intro,[status(thm)],[1])).
% 0.49/0.61 tff(3,plain,
% 0.49/0.61 (![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.49/0.61 inference(rewrite,[status(thm)],[])).
% 0.49/0.61 tff(4,plain,
% 0.49/0.61 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.49/0.61 inference(bind,[status(th)],[])).
% 0.49/0.61 tff(5,plain,
% 0.49/0.61 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.49/0.61 inference(quant_intro,[status(thm)],[4])).
% 0.49/0.61 tff(6,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 0.49/0.61 tff(7,plain,
% 0.49/0.61 (![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.49/0.61 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.49/0.61 tff(8,plain,
% 0.49/0.61 (![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.49/0.61 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.49/0.61 tff(9,plain,(
% 0.49/0.61 ![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.49/0.61 inference(skolemize,[status(sab)],[8])).
% 0.49/0.61 tff(10,plain,
% 0.49/0.61 (![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.49/0.61 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.49/0.61 tff(11,assumption,(c2_1(a1174)), introduced(assumption)).
% 0.49/0.61 tff(12,plain,
% 0.49/0.61 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.49/0.61 inference(bind,[status(th)],[])).
% 0.49/0.61 tff(13,plain,
% 0.49/0.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.49/0.61 inference(quant_intro,[status(thm)],[12])).
% 0.49/0.61 tff(14,plain,
% 0.49/0.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.49/0.61 inference(rewrite,[status(thm)],[])).
% 0.49/0.61 tff(15,plain,
% 0.49/0.61 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.49/0.61 inference(bind,[status(th)],[])).
% 0.49/0.61 tff(16,plain,
% 0.49/0.61 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.49/0.61 inference(quant_intro,[status(thm)],[15])).
% 0.49/0.61 tff(17,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 0.49/0.61 tff(18,plain,
% 0.49/0.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.49/0.61 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.49/0.61 tff(19,plain,
% 0.49/0.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.49/0.62 tff(20,plain,(
% 0.49/0.62 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.49/0.62 inference(skolemize,[status(sab)],[19])).
% 0.49/0.62 tff(21,plain,
% 0.49/0.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.49/0.62 tff(22,assumption,(~hskp3), introduced(assumption)).
% 0.49/0.62 tff(23,assumption,(~hskp17), introduced(assumption)).
% 0.49/0.62 tff(24,assumption,(hskp22), introduced(assumption)).
% 0.49/0.62 tff(25,plain,
% 0.49/0.62 (((~hskp22) | (~c1_1(a1211))) <=> ((~hskp22) | (~c1_1(a1211)))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(26,plain,
% 0.49/0.62 (((~c1_1(a1211)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a1211)))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(27,axiom,((~c1_1(a1211)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 0.49/0.62 tff(28,plain,
% 0.49/0.62 ((~hskp22) | (~c1_1(a1211))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.49/0.62 tff(29,plain,
% 0.49/0.62 ((~hskp22) | (~c1_1(a1211))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.49/0.62 tff(30,plain,
% 0.49/0.62 (~c1_1(a1211)),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[29, 24])).
% 0.49/0.62 tff(31,plain,
% 0.49/0.62 (((~hskp22) | c3_1(a1211)) <=> ((~hskp22) | c3_1(a1211))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(32,axiom,((~hskp22) | c3_1(a1211)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.49/0.62 tff(33,plain,
% 0.49/0.62 ((~hskp22) | c3_1(a1211)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.49/0.62 tff(34,plain,
% 0.49/0.62 ((~hskp22) | c3_1(a1211)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[33, 31])).
% 0.49/0.62 tff(35,plain,
% 0.49/0.62 ((~hskp22) | c3_1(a1211)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.49/0.62 tff(36,plain,
% 0.49/0.62 ((~hskp22) | c3_1(a1211)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.49/0.62 tff(37,plain,
% 0.49/0.62 ((~hskp22) | c3_1(a1211)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[36, 31])).
% 0.49/0.62 tff(38,plain,
% 0.49/0.62 ((~hskp22) | c3_1(a1211)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[37, 31])).
% 0.49/0.62 tff(39,plain,
% 0.49/0.62 ((~hskp22) | c3_1(a1211)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.49/0.62 tff(40,plain,
% 0.49/0.62 ((~hskp22) | c3_1(a1211)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[39, 31])).
% 0.49/0.62 tff(41,plain,
% 0.49/0.62 (c3_1(a1211)),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[40, 24])).
% 0.49/0.62 tff(42,plain,
% 0.49/0.62 (((~hskp22) | c0_1(a1211)) <=> ((~hskp22) | c0_1(a1211))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(43,axiom,((~hskp22) | c0_1(a1211)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.49/0.62 tff(44,plain,
% 0.49/0.62 ((~hskp22) | c0_1(a1211)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.49/0.62 tff(45,plain,
% 0.49/0.62 ((~hskp22) | c0_1(a1211)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[44, 42])).
% 0.49/0.62 tff(46,plain,
% 0.49/0.62 ((~hskp22) | c0_1(a1211)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[45, 42])).
% 0.49/0.62 tff(47,plain,
% 0.49/0.62 ((~hskp22) | c0_1(a1211)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.49/0.62 tff(48,plain,
% 0.49/0.62 ((~hskp22) | c0_1(a1211)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[47, 42])).
% 0.49/0.62 tff(49,plain,
% 0.49/0.62 ((~hskp22) | c0_1(a1211)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[48, 42])).
% 0.49/0.62 tff(50,plain,
% 0.49/0.62 ((~hskp22) | c0_1(a1211)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.49/0.62 tff(51,plain,
% 0.49/0.62 ((~hskp22) | c0_1(a1211)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[50, 42])).
% 0.49/0.62 tff(52,plain,
% 0.49/0.62 (c0_1(a1211)),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[51, 24])).
% 0.49/0.62 tff(53,assumption,(~c2_1(a1211)), introduced(assumption)).
% 0.49/0.62 tff(54,plain,
% 0.49/0.62 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))))),
% 0.49/0.62 inference(bind,[status(th)],[])).
% 0.49/0.62 tff(55,plain,
% 0.49/0.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.49/0.62 inference(quant_intro,[status(thm)],[54])).
% 0.49/0.62 tff(56,plain,
% 0.49/0.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(57,plain,
% 0.49/0.62 (^[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) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))))),
% 0.49/0.62 inference(bind,[status(th)],[])).
% 0.49/0.62 tff(58,plain,
% 0.49/0.62 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.49/0.62 inference(quant_intro,[status(thm)],[57])).
% 0.49/0.62 tff(59,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 0.49/0.62 tff(60,plain,
% 0.49/0.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.49/0.62 tff(61,plain,
% 0.49/0.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.49/0.62 tff(62,plain,(
% 0.49/0.62 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.49/0.62 inference(skolemize,[status(sab)],[61])).
% 0.49/0.62 tff(63,plain,
% 0.49/0.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.49/0.62 tff(64,plain,
% 0.49/0.62 (^[U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))),
% 0.49/0.62 inference(bind,[status(th)],[])).
% 0.49/0.62 tff(65,plain,
% 0.49/0.62 (![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.49/0.62 inference(quant_intro,[status(thm)],[64])).
% 0.49/0.62 tff(66,plain,
% 0.49/0.62 (![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(67,plain,
% 0.49/0.62 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))))),
% 0.49/0.62 inference(bind,[status(th)],[])).
% 0.49/0.62 tff(68,plain,
% 0.49/0.62 (![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.49/0.62 inference(quant_intro,[status(thm)],[67])).
% 0.49/0.62 tff(69,axiom,(![U: $i] : (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 0.49/0.62 tff(70,plain,
% 0.49/0.62 (![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.49/0.62 tff(71,plain,
% 0.49/0.62 (![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.49/0.62 tff(72,plain,(
% 0.49/0.62 ![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.49/0.62 inference(skolemize,[status(sab)],[71])).
% 0.49/0.62 tff(73,plain,
% 0.49/0.62 (![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.49/0.62 tff(74,plain,
% 0.49/0.62 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 0.49/0.62 inference(bind,[status(th)],[])).
% 0.49/0.62 tff(75,plain,
% 0.49/0.62 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.49/0.62 inference(quant_intro,[status(thm)],[74])).
% 0.49/0.62 tff(76,plain,
% 0.49/0.62 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(77,plain,
% 0.49/0.62 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 0.49/0.62 inference(bind,[status(th)],[])).
% 0.49/0.62 tff(78,plain,
% 0.49/0.62 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.49/0.62 inference(quant_intro,[status(thm)],[77])).
% 0.49/0.62 tff(79,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 0.49/0.62 tff(80,plain,
% 0.49/0.62 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.49/0.62 tff(81,plain,
% 0.49/0.62 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.49/0.62 tff(82,plain,(
% 0.49/0.62 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.49/0.62 inference(skolemize,[status(sab)],[81])).
% 0.49/0.62 tff(83,plain,
% 0.49/0.62 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.49/0.62 tff(84,assumption,(~hskp0), introduced(assumption)).
% 0.49/0.62 tff(85,assumption,(~hskp14), introduced(assumption)).
% 0.49/0.62 tff(86,plain,
% 0.49/0.62 (^[U: $i] : refl((hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))),
% 0.49/0.62 inference(bind,[status(th)],[])).
% 0.49/0.62 tff(87,plain,
% 0.49/0.62 (![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.49/0.62 inference(quant_intro,[status(thm)],[86])).
% 0.49/0.62 tff(88,plain,
% 0.49/0.62 (![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(89,plain,
% 0.49/0.62 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp23) <=> ((hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp23))), rewrite(((hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp23) <=> (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp23) <=> (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))))),
% 0.49/0.62 inference(bind,[status(th)],[])).
% 0.49/0.62 tff(90,plain,
% 0.49/0.62 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp23) <=> ![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.49/0.62 inference(quant_intro,[status(thm)],[89])).
% 0.49/0.62 tff(91,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 0.49/0.62 tff(92,plain,
% 0.49/0.62 (![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.49/0.62 tff(93,plain,
% 0.49/0.62 (![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.49/0.62 tff(94,plain,(
% 0.49/0.62 ![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.49/0.62 inference(skolemize,[status(sab)],[93])).
% 0.49/0.62 tff(95,plain,
% 0.49/0.62 (![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.49/0.62 tff(96,plain,
% 0.49/0.62 ((hskp14 | hskp1 | hskp0) <=> (hskp14 | hskp1 | hskp0)),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(97,plain,
% 0.49/0.62 (((hskp0 | hskp1) | hskp14) <=> (hskp14 | hskp1 | hskp0)),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(98,axiom,((hskp0 | hskp1) | hskp14), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 0.49/0.62 tff(99,plain,
% 0.49/0.62 (hskp14 | hskp1 | hskp0),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.49/0.62 tff(100,plain,
% 0.49/0.62 (hskp14 | hskp1 | hskp0),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[99, 96])).
% 0.49/0.62 tff(101,plain,
% 0.49/0.62 (hskp14 | hskp1 | hskp0),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.49/0.62 tff(102,plain,
% 0.49/0.62 (hskp14 | hskp1 | hskp0),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[101, 96])).
% 0.49/0.62 tff(103,plain,
% 0.49/0.62 (hskp14 | hskp1 | hskp0),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[102, 96])).
% 0.49/0.62 tff(104,plain,
% 0.49/0.62 (hskp14 | hskp1 | hskp0),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.49/0.62 tff(105,plain,
% 0.49/0.62 (hskp14 | hskp1 | hskp0),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[104, 96])).
% 0.49/0.62 tff(106,plain,
% 0.49/0.62 (hskp14 | hskp1 | hskp0),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[105, 96])).
% 0.49/0.62 tff(107,plain,
% 0.49/0.62 (hskp1),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[106, 85, 84])).
% 0.49/0.62 tff(108,plain,
% 0.49/0.62 (((~hskp1) | (~c3_1(a1169))) <=> ((~hskp1) | (~c3_1(a1169)))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(109,plain,
% 0.49/0.62 (((~c3_1(a1169)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a1169)))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(110,axiom,((~c3_1(a1169)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.49/0.62 tff(111,plain,
% 0.49/0.62 ((~hskp1) | (~c3_1(a1169))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.49/0.62 tff(112,plain,
% 0.49/0.62 ((~hskp1) | (~c3_1(a1169))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[111, 108])).
% 0.49/0.62 tff(113,plain,
% 0.49/0.62 (~c3_1(a1169)),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[112, 107])).
% 0.49/0.62 tff(114,plain,
% 0.49/0.62 (((~hskp1) | (~c2_1(a1169))) <=> ((~hskp1) | (~c2_1(a1169)))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(115,plain,
% 0.49/0.62 (((~c2_1(a1169)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a1169)))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(116,axiom,((~c2_1(a1169)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.49/0.62 tff(117,plain,
% 0.49/0.62 ((~hskp1) | (~c2_1(a1169))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.49/0.62 tff(118,plain,
% 0.49/0.62 ((~hskp1) | (~c2_1(a1169))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[117, 114])).
% 0.49/0.62 tff(119,plain,
% 0.49/0.62 (~c2_1(a1169)),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[118, 107])).
% 0.49/0.62 tff(120,plain,
% 0.49/0.62 (((~hskp1) | c1_1(a1169)) <=> ((~hskp1) | c1_1(a1169))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(121,axiom,((~hskp1) | c1_1(a1169)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.49/0.62 tff(122,plain,
% 0.49/0.62 ((~hskp1) | c1_1(a1169)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.49/0.62 tff(123,plain,
% 0.49/0.62 ((~hskp1) | c1_1(a1169)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[122, 120])).
% 0.49/0.62 tff(124,plain,
% 0.49/0.62 ((~hskp1) | c1_1(a1169)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[123, 120])).
% 0.49/0.62 tff(125,plain,
% 0.49/0.62 ((~hskp1) | c1_1(a1169)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.49/0.62 tff(126,plain,
% 0.49/0.62 ((~hskp1) | c1_1(a1169)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[125, 120])).
% 0.49/0.62 tff(127,plain,
% 0.49/0.62 ((~hskp1) | c1_1(a1169)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[126, 120])).
% 0.49/0.62 tff(128,plain,
% 0.49/0.62 ((~hskp1) | c1_1(a1169)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.49/0.62 tff(129,plain,
% 0.49/0.62 ((~hskp1) | c1_1(a1169)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[128, 120])).
% 0.49/0.62 tff(130,plain,
% 0.49/0.62 (c1_1(a1169)),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[129, 107])).
% 0.49/0.62 tff(131,plain,
% 0.49/0.62 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.49/0.62 inference(bind,[status(th)],[])).
% 0.49/0.62 tff(132,plain,
% 0.49/0.62 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.49/0.62 inference(quant_intro,[status(thm)],[131])).
% 0.49/0.62 tff(133,plain,
% 0.49/0.62 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(134,plain,
% 0.49/0.62 (^[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) | c1_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_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) | c1_1(U) | c2_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)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.49/0.62 inference(bind,[status(th)],[])).
% 0.49/0.62 tff(135,plain,
% 0.49/0.62 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.49/0.62 inference(quant_intro,[status(thm)],[134])).
% 0.49/0.62 tff(136,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 0.49/0.62 tff(137,plain,
% 0.49/0.62 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.49/0.62 tff(138,plain,
% 0.49/0.62 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.49/0.62 tff(139,plain,(
% 0.49/0.62 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.49/0.62 inference(skolemize,[status(sab)],[138])).
% 0.49/0.62 tff(140,plain,
% 0.49/0.62 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.49/0.62 tff(141,assumption,(hskp19), introduced(assumption)).
% 0.49/0.62 tff(142,plain,
% 0.49/0.62 (((~hskp19) | (~c2_1(a1204))) <=> ((~hskp19) | (~c2_1(a1204)))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(143,plain,
% 0.49/0.62 (((~c2_1(a1204)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a1204)))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(144,axiom,((~c2_1(a1204)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 0.49/0.62 tff(145,plain,
% 0.49/0.62 ((~hskp19) | (~c2_1(a1204))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.49/0.62 tff(146,plain,
% 0.49/0.62 ((~hskp19) | (~c2_1(a1204))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[145, 142])).
% 0.49/0.62 tff(147,plain,
% 0.49/0.62 (~c2_1(a1204)),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[146, 141])).
% 0.49/0.62 tff(148,plain,
% 0.49/0.62 (((~hskp19) | (~c1_1(a1204))) <=> ((~hskp19) | (~c1_1(a1204)))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(149,plain,
% 0.49/0.62 (((~c1_1(a1204)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a1204)))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(150,axiom,((~c1_1(a1204)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.49/0.62 tff(151,plain,
% 0.49/0.62 ((~hskp19) | (~c1_1(a1204))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.49/0.62 tff(152,plain,
% 0.49/0.62 ((~hskp19) | (~c1_1(a1204))),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[151, 148])).
% 0.49/0.62 tff(153,plain,
% 0.49/0.62 (~c1_1(a1204)),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[152, 141])).
% 0.49/0.62 tff(154,plain,
% 0.49/0.62 (((~hskp19) | c3_1(a1204)) <=> ((~hskp19) | c3_1(a1204))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(155,axiom,((~hskp19) | c3_1(a1204)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.49/0.62 tff(156,plain,
% 0.49/0.62 ((~hskp19) | c3_1(a1204)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.49/0.62 tff(157,plain,
% 0.49/0.62 ((~hskp19) | c3_1(a1204)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[156, 154])).
% 0.49/0.62 tff(158,plain,
% 0.49/0.62 ((~hskp19) | c3_1(a1204)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[157, 154])).
% 0.49/0.62 tff(159,plain,
% 0.49/0.62 ((~hskp19) | c3_1(a1204)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[158, 154])).
% 0.49/0.62 tff(160,plain,
% 0.49/0.62 ((~hskp19) | c3_1(a1204)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[159, 154])).
% 0.49/0.62 tff(161,plain,
% 0.49/0.62 ((~hskp19) | c3_1(a1204)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[160, 154])).
% 0.49/0.62 tff(162,plain,
% 0.49/0.62 ((~hskp19) | c3_1(a1204)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[161, 154])).
% 0.49/0.62 tff(163,plain,
% 0.49/0.62 ((~hskp19) | c3_1(a1204)),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[162, 154])).
% 0.49/0.62 tff(164,plain,
% 0.49/0.62 (c3_1(a1204)),
% 0.49/0.62 inference(unit_resolution,[status(thm)],[163, 141])).
% 0.49/0.62 tff(165,assumption,(~ndr1_0), introduced(assumption)).
% 0.49/0.62 tff(166,plain,
% 0.49/0.62 (((~hskp28) | ndr1_0) <=> ((~hskp28) | ndr1_0)),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(167,axiom,((~hskp28) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.49/0.62 tff(168,plain,
% 0.49/0.62 ((~hskp28) | ndr1_0),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.49/0.62 tff(169,plain,
% 0.49/0.62 ((~hskp28) | ndr1_0),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[168, 166])).
% 0.49/0.62 tff(170,plain,
% 0.49/0.62 ((~hskp28) | ndr1_0),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[169, 166])).
% 0.49/0.62 tff(171,plain,
% 0.49/0.62 ((~hskp28) | ndr1_0),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.49/0.62 tff(172,plain,
% 0.49/0.62 ((~hskp28) | ndr1_0),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[171, 166])).
% 0.49/0.62 tff(173,plain,
% 0.49/0.62 ((~hskp28) | ndr1_0),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[172, 166])).
% 0.49/0.62 tff(174,plain,
% 0.49/0.62 ((~hskp28) | ndr1_0),
% 0.49/0.62 inference(modus_ponens,[status(thm)],[173, 166])).
% 0.49/0.63 tff(175,plain,
% 0.49/0.63 ((~hskp28) | ndr1_0),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[174, 166])).
% 0.49/0.63 tff(176,plain,
% 0.49/0.63 (~hskp28),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[175, 165])).
% 0.49/0.63 tff(177,plain,
% 0.49/0.63 ((ndr1_0 | (~hskp8)) <=> (ndr1_0 | (~hskp8))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(178,plain,
% 0.49/0.63 (((~hskp8) | ndr1_0) <=> (ndr1_0 | (~hskp8))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(179,axiom,((~hskp8) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause22')).
% 0.49/0.63 tff(180,plain,
% 0.49/0.63 (ndr1_0 | (~hskp8)),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.49/0.63 tff(181,plain,
% 0.49/0.63 (ndr1_0 | (~hskp8)),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[180, 177])).
% 0.49/0.63 tff(182,plain,
% 0.49/0.63 (~hskp8),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[181, 165])).
% 0.49/0.63 tff(183,plain,
% 0.49/0.63 ((hskp28 | hskp8) <=> (hskp28 | hskp8)),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(184,axiom,(hskp28 | hskp8), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.49/0.63 tff(185,plain,
% 0.49/0.63 (hskp28 | hskp8),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.49/0.63 tff(186,plain,
% 0.49/0.63 ($false),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[185, 182, 176])).
% 0.49/0.63 tff(187,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.49/0.63 tff(188,plain,
% 0.49/0.63 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | c0_1(a1204) | (~c3_1(a1204)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | c0_1(a1204) | (~c3_1(a1204)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(189,plain,
% 0.49/0.63 ((hskp0 | (~ndr1_0) | c1_1(a1204) | c2_1(a1204) | (~c3_1(a1204)) | c2_1(a1204) | c1_1(a1204) | c0_1(a1204)) <=> (hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | c0_1(a1204) | (~c3_1(a1204)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(190,plain,
% 0.49/0.63 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1204) | c2_1(a1204) | (~c3_1(a1204)) | c2_1(a1204) | c1_1(a1204) | c0_1(a1204))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | c0_1(a1204) | (~c3_1(a1204))))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[189])).
% 0.49/0.63 tff(191,plain,
% 0.49/0.63 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1204) | c2_1(a1204) | (~c3_1(a1204)) | c2_1(a1204) | c1_1(a1204) | c0_1(a1204))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | c0_1(a1204) | (~c3_1(a1204)))),
% 0.49/0.63 inference(transitivity,[status(thm)],[190, 188])).
% 0.49/0.63 tff(192,plain,
% 0.49/0.63 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1204) | c2_1(a1204) | (~c3_1(a1204)) | c2_1(a1204) | c1_1(a1204) | c0_1(a1204))),
% 0.49/0.63 inference(quant_inst,[status(thm)],[])).
% 0.49/0.63 tff(193,plain,
% 0.49/0.63 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | c0_1(a1204) | (~c3_1(a1204))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.49/0.63 tff(194,plain,
% 0.49/0.63 (c0_1(a1204)),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[193, 187, 84, 164, 153, 147, 140])).
% 0.49/0.63 tff(195,plain,
% 0.49/0.63 (((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | (~c0_1(a1204)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | (~c0_1(a1204)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(196,plain,
% 0.49/0.63 ((hskp0 | (~ndr1_0) | c1_1(a1204) | c2_1(a1204) | (~c0_1(a1204))) <=> (hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | (~c0_1(a1204)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(197,plain,
% 0.49/0.63 (((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | (~ndr1_0) | c1_1(a1204) | c2_1(a1204) | (~c0_1(a1204)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | (~c0_1(a1204))))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[196])).
% 0.49/0.63 tff(198,plain,
% 0.49/0.63 (((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | (~ndr1_0) | c1_1(a1204) | c2_1(a1204) | (~c0_1(a1204)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | (~c0_1(a1204)))),
% 0.49/0.63 inference(transitivity,[status(thm)],[197, 195])).
% 0.49/0.63 tff(199,plain,
% 0.49/0.63 ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | (~ndr1_0) | c1_1(a1204) | c2_1(a1204) | (~c0_1(a1204)))),
% 0.49/0.63 inference(quant_inst,[status(thm)],[])).
% 0.49/0.63 tff(200,plain,
% 0.49/0.63 ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp0 | c1_1(a1204) | c2_1(a1204) | (~ndr1_0) | (~c0_1(a1204))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.49/0.63 tff(201,plain,
% 0.49/0.63 ($false),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[200, 187, 84, 153, 147, 73, 194])).
% 0.49/0.63 tff(202,plain,((~hskp19) | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.49/0.63 tff(203,plain,
% 0.49/0.63 (~hskp19),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[202, 84])).
% 0.49/0.63 tff(204,plain,
% 0.49/0.63 (((~![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp23 | hskp19 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)))) <=> ((~![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp23 | hskp19 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(205,plain,
% 0.49/0.63 ((hskp23 | hskp19 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c1_1(a1169))) <=> (hskp23 | hskp19 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(206,plain,
% 0.49/0.63 (((~![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp23 | hskp19 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c1_1(a1169)))) <=> ((~![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp23 | hskp19 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169))))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[205])).
% 0.49/0.63 tff(207,plain,
% 0.49/0.63 (((~![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp23 | hskp19 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c1_1(a1169)))) <=> ((~![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp23 | hskp19 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)))),
% 0.49/0.63 inference(transitivity,[status(thm)],[206, 204])).
% 0.49/0.63 tff(208,plain,
% 0.49/0.63 ((~![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp23 | hskp19 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c1_1(a1169)))),
% 0.49/0.63 inference(quant_inst,[status(thm)],[])).
% 0.49/0.63 tff(209,plain,
% 0.49/0.63 ((~![U: $i] : (hskp23 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp23 | hskp19 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.49/0.63 tff(210,plain,
% 0.49/0.63 (hskp23),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[209, 187, 203, 130, 119, 113, 95])).
% 0.49/0.63 tff(211,plain,
% 0.49/0.63 (^[U: $i] : refl((hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 0.49/0.63 inference(bind,[status(th)],[])).
% 0.49/0.63 tff(212,plain,
% 0.49/0.63 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.49/0.63 inference(quant_intro,[status(thm)],[211])).
% 0.49/0.63 tff(213,plain,
% 0.49/0.63 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(214,plain,
% 0.49/0.63 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | 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))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp3) <=> ((hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3))), rewrite(((hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3) <=> (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp3) <=> (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 0.49/0.63 inference(bind,[status(th)],[])).
% 0.49/0.63 tff(215,plain,
% 0.49/0.63 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp3) <=> ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.49/0.63 inference(quant_intro,[status(thm)],[214])).
% 0.49/0.63 tff(216,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.49/0.63 tff(217,plain,
% 0.49/0.63 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.49/0.63 tff(218,plain,
% 0.49/0.63 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[217, 213])).
% 0.49/0.63 tff(219,plain,(
% 0.49/0.63 ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.49/0.63 inference(skolemize,[status(sab)],[218])).
% 0.49/0.63 tff(220,plain,
% 0.49/0.63 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[219, 212])).
% 0.49/0.63 tff(221,assumption,(hskp23), introduced(assumption)).
% 0.49/0.63 tff(222,plain,
% 0.49/0.63 (((~hskp23) | (~c3_1(a1218))) <=> ((~hskp23) | (~c3_1(a1218)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(223,plain,
% 0.49/0.63 (((~c3_1(a1218)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a1218)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(224,axiom,((~c3_1(a1218)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 0.49/0.63 tff(225,plain,
% 0.49/0.63 ((~hskp23) | (~c3_1(a1218))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.49/0.63 tff(226,plain,
% 0.49/0.63 ((~hskp23) | (~c3_1(a1218))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[225, 222])).
% 0.49/0.63 tff(227,plain,
% 0.49/0.63 (~c3_1(a1218)),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[226, 221])).
% 0.49/0.63 tff(228,plain,
% 0.49/0.63 (((~hskp23) | (~c1_1(a1218))) <=> ((~hskp23) | (~c1_1(a1218)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(229,plain,
% 0.49/0.63 (((~c1_1(a1218)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a1218)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(230,axiom,((~c1_1(a1218)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 0.49/0.63 tff(231,plain,
% 0.49/0.63 ((~hskp23) | (~c1_1(a1218))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.49/0.63 tff(232,plain,
% 0.49/0.63 ((~hskp23) | (~c1_1(a1218))),
% 0.49/0.63 inference(modus_ponens,[status(thm)],[231, 228])).
% 0.49/0.63 tff(233,plain,
% 0.49/0.63 (~c1_1(a1218)),
% 0.49/0.63 inference(unit_resolution,[status(thm)],[232, 221])).
% 0.49/0.63 tff(234,plain,
% 0.49/0.63 (((~hskp23) | (~c0_1(a1218))) <=> ((~hskp23) | (~c0_1(a1218)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(235,plain,
% 0.49/0.63 (((~c0_1(a1218)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a1218)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(236,axiom,((~c0_1(a1218)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.49/0.63 tff(237,plain,
% 0.49/0.63 ((~hskp23) | (~c0_1(a1218))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.60/0.63 tff(238,plain,
% 0.60/0.63 ((~hskp23) | (~c0_1(a1218))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[237, 234])).
% 0.60/0.63 tff(239,plain,
% 0.60/0.63 (~c0_1(a1218)),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[238, 221])).
% 0.60/0.63 tff(240,plain,
% 0.60/0.63 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | c0_1(a1218) | c1_1(a1218) | c3_1(a1218) | (~ndr1_0))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp0 | c0_1(a1218) | c1_1(a1218) | c3_1(a1218) | (~ndr1_0))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(241,plain,
% 0.60/0.63 ((hskp3 | hskp0 | (~ndr1_0) | c3_1(a1218) | c1_1(a1218) | c0_1(a1218)) <=> (hskp3 | hskp0 | c0_1(a1218) | c1_1(a1218) | c3_1(a1218) | (~ndr1_0))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(242,plain,
% 0.60/0.63 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | (~ndr1_0) | c3_1(a1218) | c1_1(a1218) | c0_1(a1218))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | c0_1(a1218) | c1_1(a1218) | c3_1(a1218) | (~ndr1_0)))),
% 0.60/0.63 inference(monotonicity,[status(thm)],[241])).
% 0.60/0.63 tff(243,plain,
% 0.60/0.63 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | (~ndr1_0) | c3_1(a1218) | c1_1(a1218) | c0_1(a1218))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp0 | c0_1(a1218) | c1_1(a1218) | c3_1(a1218) | (~ndr1_0))),
% 0.60/0.63 inference(transitivity,[status(thm)],[242, 240])).
% 0.60/0.63 tff(244,plain,
% 0.60/0.63 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | (~ndr1_0) | c3_1(a1218) | c1_1(a1218) | c0_1(a1218))),
% 0.60/0.63 inference(quant_inst,[status(thm)],[])).
% 0.60/0.63 tff(245,plain,
% 0.60/0.63 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp0 | c0_1(a1218) | c1_1(a1218) | c3_1(a1218) | (~ndr1_0)),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.60/0.63 tff(246,plain,
% 0.60/0.63 ($false),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[245, 187, 22, 84, 239, 233, 227, 220])).
% 0.60/0.63 tff(247,plain,((~hskp23) | hskp3 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.60/0.63 tff(248,plain,
% 0.60/0.63 (hskp3),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[247, 210, 84])).
% 0.60/0.63 tff(249,plain,
% 0.60/0.63 (^[U: $i] : refl((hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))),
% 0.60/0.63 inference(bind,[status(th)],[])).
% 0.60/0.63 tff(250,plain,
% 0.60/0.63 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.60/0.63 inference(quant_intro,[status(thm)],[249])).
% 0.60/0.63 tff(251,plain,
% 0.60/0.63 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(252,plain,
% 0.60/0.63 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | 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)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) | hskp14) <=> ((hskp22 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp14))), rewrite(((hskp22 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp14) <=> (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) | hskp14) <=> (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))))),
% 0.60/0.63 inference(bind,[status(th)],[])).
% 0.60/0.63 tff(253,plain,
% 0.60/0.63 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) | hskp14) <=> ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.60/0.63 inference(quant_intro,[status(thm)],[252])).
% 0.60/0.63 tff(254,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.60/0.63 tff(255,plain,
% 0.60/0.63 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.60/0.63 tff(256,plain,
% 0.60/0.63 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[255, 251])).
% 0.60/0.63 tff(257,plain,(
% 0.60/0.63 ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.60/0.63 inference(skolemize,[status(sab)],[256])).
% 0.60/0.63 tff(258,plain,
% 0.60/0.63 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[257, 250])).
% 0.60/0.63 tff(259,assumption,(hskp3), introduced(assumption)).
% 0.60/0.63 tff(260,plain,
% 0.60/0.63 (((~hskp3) | (~c3_1(a1174))) <=> ((~hskp3) | (~c3_1(a1174)))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(261,plain,
% 0.60/0.63 (((~c3_1(a1174)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a1174)))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(262,axiom,((~c3_1(a1174)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.60/0.63 tff(263,plain,
% 0.60/0.63 ((~hskp3) | (~c3_1(a1174))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.60/0.63 tff(264,plain,
% 0.60/0.63 ((~hskp3) | (~c3_1(a1174))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[263, 260])).
% 0.60/0.63 tff(265,plain,
% 0.60/0.63 (~c3_1(a1174)),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[264, 259])).
% 0.60/0.63 tff(266,plain,
% 0.60/0.63 (((~hskp3) | c0_1(a1174)) <=> ((~hskp3) | c0_1(a1174))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(267,axiom,((~hskp3) | c0_1(a1174)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.60/0.63 tff(268,plain,
% 0.60/0.63 ((~hskp3) | c0_1(a1174)),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.60/0.63 tff(269,plain,
% 0.60/0.63 ((~hskp3) | c0_1(a1174)),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[268, 266])).
% 0.60/0.63 tff(270,plain,
% 0.60/0.63 ((~hskp3) | c0_1(a1174)),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[269, 266])).
% 0.60/0.63 tff(271,plain,
% 0.60/0.63 ((~hskp3) | c0_1(a1174)),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[270, 266])).
% 0.60/0.63 tff(272,plain,
% 0.60/0.63 ((~hskp3) | c0_1(a1174)),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[271, 266])).
% 0.60/0.63 tff(273,plain,
% 0.60/0.63 ((~hskp3) | c0_1(a1174)),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[272, 266])).
% 0.60/0.63 tff(274,plain,
% 0.60/0.63 ((~hskp3) | c0_1(a1174)),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[273, 266])).
% 0.60/0.63 tff(275,plain,
% 0.60/0.63 ((~hskp3) | c0_1(a1174)),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[274, 266])).
% 0.60/0.63 tff(276,plain,
% 0.60/0.63 (c0_1(a1174)),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[275, 259])).
% 0.60/0.63 tff(277,assumption,(~hskp22), introduced(assumption)).
% 0.60/0.63 tff(278,plain,
% 0.60/0.63 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | (~c2_1(a1174)) | (~c0_1(a1174)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | (~c2_1(a1174)) | (~c0_1(a1174)))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(279,plain,
% 0.60/0.63 ((hskp22 | hskp14 | (~ndr1_0) | c3_1(a1174) | (~c0_1(a1174)) | (~c2_1(a1174))) <=> (hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | (~c2_1(a1174)) | (~c0_1(a1174)))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(280,plain,
% 0.60/0.63 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1174) | (~c0_1(a1174)) | (~c2_1(a1174)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | (~c2_1(a1174)) | (~c0_1(a1174))))),
% 0.60/0.64 inference(monotonicity,[status(thm)],[279])).
% 0.60/0.64 tff(281,plain,
% 0.60/0.64 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1174) | (~c0_1(a1174)) | (~c2_1(a1174)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | (~c2_1(a1174)) | (~c0_1(a1174)))),
% 0.60/0.64 inference(transitivity,[status(thm)],[280, 278])).
% 0.60/0.64 tff(282,plain,
% 0.60/0.64 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1174) | (~c0_1(a1174)) | (~c2_1(a1174)))),
% 0.60/0.64 inference(quant_inst,[status(thm)],[])).
% 0.60/0.64 tff(283,plain,
% 0.60/0.64 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | (~c2_1(a1174)) | (~c0_1(a1174))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.60/0.64 tff(284,plain,
% 0.60/0.64 (~c2_1(a1174)),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[283, 187, 277, 85, 276, 265, 258])).
% 0.60/0.64 tff(285,plain,
% 0.60/0.64 (^[U: $i] : refl((hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 0.60/0.64 inference(bind,[status(th)],[])).
% 0.60/0.64 tff(286,plain,
% 0.60/0.64 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.64 inference(quant_intro,[status(thm)],[285])).
% 0.60/0.64 tff(287,plain,
% 0.60/0.64 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(288,plain,
% 0.60/0.64 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp14) <=> ((hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp14))), rewrite(((hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp14) <=> (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp14) <=> (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 0.60/0.64 inference(bind,[status(th)],[])).
% 0.60/0.64 tff(289,plain,
% 0.60/0.64 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp14) <=> ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.64 inference(quant_intro,[status(thm)],[288])).
% 0.60/0.64 tff(290,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.60/0.64 tff(291,plain,
% 0.60/0.64 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.60/0.64 tff(292,plain,
% 0.60/0.64 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[291, 287])).
% 0.60/0.64 tff(293,plain,(
% 0.60/0.64 ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.64 inference(skolemize,[status(sab)],[292])).
% 0.60/0.64 tff(294,plain,
% 0.60/0.64 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[293, 286])).
% 0.60/0.64 tff(295,plain,
% 0.60/0.64 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(296,plain,
% 0.60/0.64 ((hskp22 | hskp14 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174))) <=> (hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(297,plain,
% 0.60/0.64 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174))))),
% 0.60/0.64 inference(monotonicity,[status(thm)],[296])).
% 0.60/0.64 tff(298,plain,
% 0.60/0.64 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)))),
% 0.60/0.64 inference(transitivity,[status(thm)],[297, 295])).
% 0.60/0.64 tff(299,plain,
% 0.60/0.64 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)))),
% 0.60/0.64 inference(quant_inst,[status(thm)],[])).
% 0.60/0.64 tff(300,plain,
% 0.60/0.64 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.60/0.64 tff(301,plain,
% 0.60/0.64 ($false),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[300, 187, 277, 85, 276, 265, 294, 284])).
% 0.60/0.64 tff(302,plain,((~hskp3) | hskp22 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.60/0.64 tff(303,plain,
% 0.60/0.64 (hskp22),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[302, 248, 85])).
% 0.60/0.64 tff(304,plain,
% 0.60/0.64 (~c1_1(a1211)),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[29, 303])).
% 0.60/0.64 tff(305,plain,
% 0.60/0.64 (c0_1(a1211)),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[51, 303])).
% 0.60/0.64 tff(306,plain,
% 0.60/0.64 (((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | c1_1(a1211) | (~ndr1_0) | (~c0_1(a1211)) | c2_1(a1211))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp0 | c1_1(a1211) | (~ndr1_0) | (~c0_1(a1211)) | c2_1(a1211))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(307,plain,
% 0.60/0.64 ((hskp0 | (~ndr1_0) | c1_1(a1211) | c2_1(a1211) | (~c0_1(a1211))) <=> (hskp0 | c1_1(a1211) | (~ndr1_0) | (~c0_1(a1211)) | c2_1(a1211))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(308,plain,
% 0.60/0.64 (((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | (~ndr1_0) | c1_1(a1211) | c2_1(a1211) | (~c0_1(a1211)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | c1_1(a1211) | (~ndr1_0) | (~c0_1(a1211)) | c2_1(a1211)))),
% 0.60/0.64 inference(monotonicity,[status(thm)],[307])).
% 0.60/0.64 tff(309,plain,
% 0.60/0.64 (((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | (~ndr1_0) | c1_1(a1211) | c2_1(a1211) | (~c0_1(a1211)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp0 | c1_1(a1211) | (~ndr1_0) | (~c0_1(a1211)) | c2_1(a1211))),
% 0.60/0.64 inference(transitivity,[status(thm)],[308, 306])).
% 0.60/0.64 tff(310,plain,
% 0.60/0.64 ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | (~ndr1_0) | c1_1(a1211) | c2_1(a1211) | (~c0_1(a1211)))),
% 0.60/0.64 inference(quant_inst,[status(thm)],[])).
% 0.60/0.64 tff(311,plain,
% 0.60/0.64 ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp0 | c1_1(a1211) | (~ndr1_0) | (~c0_1(a1211)) | c2_1(a1211)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.60/0.64 tff(312,plain,
% 0.60/0.64 (c2_1(a1211)),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[311, 187, 84, 305, 304, 73])).
% 0.60/0.64 tff(313,plain,
% 0.60/0.64 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W))))),
% 0.60/0.64 inference(bind,[status(th)],[])).
% 0.60/0.64 tff(314,plain,
% 0.60/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 0.60/0.64 inference(quant_intro,[status(thm)],[313])).
% 0.60/0.64 tff(315,plain,
% 0.60/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(316,plain,
% 0.60/0.64 (^[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))) <=> ((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(W)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(W)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_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))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_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))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_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))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_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))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))))),
% 0.60/0.64 inference(bind,[status(th)],[])).
% 0.60/0.64 tff(317,plain,
% 0.60/0.64 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 0.60/0.64 inference(quant_intro,[status(thm)],[316])).
% 0.60/0.64 tff(318,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.60/0.64 tff(319,plain,
% 0.60/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.60/0.64 tff(320,plain,
% 0.60/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[319, 315])).
% 0.60/0.64 tff(321,plain,(
% 0.60/0.64 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 0.60/0.64 inference(skolemize,[status(sab)],[320])).
% 0.60/0.64 tff(322,plain,
% 0.60/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[321, 314])).
% 0.60/0.64 tff(323,plain,
% 0.60/0.64 (((~hskp3) | c1_1(a1174)) <=> ((~hskp3) | c1_1(a1174))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(324,axiom,((~hskp3) | c1_1(a1174)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.60/0.64 tff(325,plain,
% 0.60/0.64 ((~hskp3) | c1_1(a1174)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.60/0.64 tff(326,plain,
% 0.60/0.64 ((~hskp3) | c1_1(a1174)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[325, 323])).
% 0.60/0.64 tff(327,plain,
% 0.60/0.64 ((~hskp3) | c1_1(a1174)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[326, 323])).
% 0.60/0.64 tff(328,plain,
% 0.60/0.64 ((~hskp3) | c1_1(a1174)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[327, 323])).
% 0.60/0.64 tff(329,plain,
% 0.60/0.64 ((~hskp3) | c1_1(a1174)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[328, 323])).
% 0.60/0.64 tff(330,plain,
% 0.60/0.64 ((~hskp3) | c1_1(a1174)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[329, 323])).
% 0.60/0.64 tff(331,plain,
% 0.60/0.64 ((~hskp3) | c1_1(a1174)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[330, 323])).
% 0.60/0.64 tff(332,plain,
% 0.60/0.64 ((~hskp3) | c1_1(a1174)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[331, 323])).
% 0.60/0.64 tff(333,plain,
% 0.60/0.64 (c1_1(a1174)),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[332, 248])).
% 0.60/0.64 tff(334,plain,
% 0.60/0.64 (c0_1(a1174)),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[275, 248])).
% 0.60/0.64 tff(335,plain,
% 0.60/0.64 (c3_1(a1211)),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[40, 303])).
% 0.60/0.64 tff(336,plain,
% 0.60/0.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | (~c3_1(a1211)) | (~c0_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | (~c3_1(a1211)) | (~c0_1(a1211)))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(337,plain,
% 0.60/0.64 (((~ndr1_0) | (~c0_1(a1174)) | (~c1_1(a1174)) | (~c2_1(a1174)) | c2_1(a1169) | c3_1(a1169) | (~c1_1(a1169)) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211))) <=> (c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | (~c3_1(a1211)) | (~c0_1(a1211)))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(338,plain,
% 0.60/0.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c0_1(a1174)) | (~c1_1(a1174)) | (~c2_1(a1174)) | c2_1(a1169) | c3_1(a1169) | (~c1_1(a1169)) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | (~c3_1(a1211)) | (~c0_1(a1211))))),
% 0.60/0.64 inference(monotonicity,[status(thm)],[337])).
% 0.60/0.64 tff(339,plain,
% 0.60/0.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c0_1(a1174)) | (~c1_1(a1174)) | (~c2_1(a1174)) | c2_1(a1169) | c3_1(a1169) | (~c1_1(a1169)) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | (~c3_1(a1211)) | (~c0_1(a1211)))),
% 0.60/0.64 inference(transitivity,[status(thm)],[338, 336])).
% 0.60/0.64 tff(340,plain,
% 0.60/0.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c0_1(a1174)) | (~c1_1(a1174)) | (~c2_1(a1174)) | c2_1(a1169) | c3_1(a1169) | (~c1_1(a1169)) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)))),
% 0.60/0.64 inference(quant_inst,[status(thm)],[])).
% 0.60/0.64 tff(341,plain,
% 0.60/0.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c1_1(a1169)) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | (~c3_1(a1211)) | (~c0_1(a1211))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.60/0.64 tff(342,plain,
% 0.60/0.64 (~c2_1(a1174)),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[341, 187, 305, 335, 334, 333, 130, 304, 119, 113, 322])).
% 0.60/0.64 tff(343,plain,
% 0.60/0.64 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.60/0.64 inference(bind,[status(th)],[])).
% 0.60/0.64 tff(344,plain,
% 0.60/0.64 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.60/0.64 inference(quant_intro,[status(thm)],[343])).
% 0.60/0.64 tff(345,plain,
% 0.60/0.64 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(346,plain,
% 0.60/0.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_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)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp17) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp17))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.60/0.64 inference(bind,[status(th)],[])).
% 0.60/0.64 tff(347,plain,
% 0.60/0.64 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.60/0.64 inference(quant_intro,[status(thm)],[346])).
% 0.60/0.64 tff(348,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 0.60/0.64 tff(349,plain,
% 0.60/0.64 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.60/0.64 tff(350,plain,
% 0.60/0.64 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[349, 345])).
% 0.60/0.64 tff(351,plain,(
% 0.60/0.64 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.60/0.64 inference(skolemize,[status(sab)],[350])).
% 0.60/0.64 tff(352,plain,
% 0.60/0.64 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[351, 344])).
% 0.60/0.64 tff(353,plain,
% 0.60/0.64 (~c3_1(a1174)),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[264, 248])).
% 0.60/0.64 tff(354,assumption,(hskp17), introduced(assumption)).
% 0.60/0.64 tff(355,plain,
% 0.60/0.64 (((~hskp17) | (~c2_1(a1200))) <=> ((~hskp17) | (~c2_1(a1200)))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(356,plain,
% 0.60/0.64 (((~c2_1(a1200)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a1200)))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(357,axiom,((~c2_1(a1200)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.60/0.64 tff(358,plain,
% 0.60/0.64 ((~hskp17) | (~c2_1(a1200))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.60/0.64 tff(359,plain,
% 0.60/0.64 ((~hskp17) | (~c2_1(a1200))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[358, 355])).
% 0.60/0.64 tff(360,plain,
% 0.60/0.64 (~c2_1(a1200)),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[359, 354])).
% 0.60/0.64 tff(361,plain,
% 0.60/0.64 (((~hskp17) | (~c1_1(a1200))) <=> ((~hskp17) | (~c1_1(a1200)))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(362,plain,
% 0.60/0.64 (((~c1_1(a1200)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a1200)))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(363,axiom,((~c1_1(a1200)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 0.60/0.64 tff(364,plain,
% 0.60/0.64 ((~hskp17) | (~c1_1(a1200))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.60/0.64 tff(365,plain,
% 0.60/0.64 ((~hskp17) | (~c1_1(a1200))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[364, 361])).
% 0.60/0.64 tff(366,plain,
% 0.60/0.64 (~c1_1(a1200)),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[365, 354])).
% 0.60/0.64 tff(367,plain,
% 0.60/0.64 (((~hskp17) | c0_1(a1200)) <=> ((~hskp17) | c0_1(a1200))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(368,axiom,((~hskp17) | c0_1(a1200)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.60/0.64 tff(369,plain,
% 0.60/0.64 ((~hskp17) | c0_1(a1200)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.60/0.64 tff(370,plain,
% 0.60/0.64 ((~hskp17) | c0_1(a1200)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[369, 367])).
% 0.60/0.64 tff(371,plain,
% 0.60/0.64 ((~hskp17) | c0_1(a1200)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[370, 367])).
% 0.60/0.64 tff(372,plain,
% 0.60/0.64 ((~hskp17) | c0_1(a1200)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[371, 367])).
% 0.60/0.64 tff(373,plain,
% 0.60/0.64 ((~hskp17) | c0_1(a1200)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[372, 367])).
% 0.60/0.64 tff(374,plain,
% 0.60/0.64 ((~hskp17) | c0_1(a1200)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[373, 367])).
% 0.60/0.64 tff(375,plain,
% 0.60/0.64 ((~hskp17) | c0_1(a1200)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[374, 367])).
% 0.60/0.64 tff(376,plain,
% 0.60/0.64 ((~hskp17) | c0_1(a1200)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[375, 367])).
% 0.60/0.64 tff(377,plain,
% 0.60/0.64 (c0_1(a1200)),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[376, 354])).
% 0.60/0.64 tff(378,plain,
% 0.60/0.64 (((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c0_1(a1200)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp0 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c0_1(a1200)))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(379,plain,
% 0.60/0.64 ((hskp0 | (~ndr1_0) | c1_1(a1200) | c2_1(a1200) | (~c0_1(a1200))) <=> (hskp0 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c0_1(a1200)))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(380,plain,
% 0.60/0.64 (((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | (~ndr1_0) | c1_1(a1200) | c2_1(a1200) | (~c0_1(a1200)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c0_1(a1200))))),
% 0.60/0.64 inference(monotonicity,[status(thm)],[379])).
% 0.60/0.64 tff(381,plain,
% 0.60/0.64 (((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | (~ndr1_0) | c1_1(a1200) | c2_1(a1200) | (~c0_1(a1200)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp0 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c0_1(a1200)))),
% 0.60/0.64 inference(transitivity,[status(thm)],[380, 378])).
% 0.60/0.65 tff(382,plain,
% 0.60/0.65 ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp0 | (~ndr1_0) | c1_1(a1200) | c2_1(a1200) | (~c0_1(a1200)))),
% 0.60/0.65 inference(quant_inst,[status(thm)],[])).
% 0.60/0.65 tff(383,plain,
% 0.60/0.65 ((~![U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp0 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c0_1(a1200))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.60/0.65 tff(384,plain,
% 0.60/0.65 ($false),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[383, 187, 84, 377, 366, 360, 73])).
% 0.60/0.65 tff(385,plain,((~hskp17) | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.60/0.65 tff(386,plain,
% 0.60/0.65 (~hskp17),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[385, 84])).
% 0.60/0.65 tff(387,plain,
% 0.60/0.65 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | c1_1(a1211) | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c0_1(a1211)) | (~c2_1(a1211)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a1211) | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(388,plain,
% 0.60/0.65 ((hskp17 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211))) <=> (hskp17 | c1_1(a1211) | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(389,plain,
% 0.60/0.65 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | c1_1(a1211) | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c0_1(a1211)) | (~c2_1(a1211))))),
% 0.60/0.65 inference(monotonicity,[status(thm)],[388])).
% 0.60/0.65 tff(390,plain,
% 0.60/0.65 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a1211) | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.60/0.65 inference(transitivity,[status(thm)],[389, 387])).
% 0.60/0.65 tff(391,plain,
% 0.60/0.65 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)))),
% 0.60/0.65 inference(quant_inst,[status(thm)],[])).
% 0.60/0.65 tff(392,plain,
% 0.60/0.65 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a1211) | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c0_1(a1211)) | (~c2_1(a1211))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.60/0.65 tff(393,plain,
% 0.60/0.65 ($false),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[392, 187, 386, 305, 334, 304, 353, 352, 342, 312])).
% 0.60/0.65 tff(394,plain,(hskp14 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.60/0.65 tff(395,plain,
% 0.60/0.65 (hskp14),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[394, 84])).
% 0.60/0.65 tff(396,plain,
% 0.60/0.65 (((~hskp14) | (~c1_1(a1194))) <=> ((~hskp14) | (~c1_1(a1194)))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(397,plain,
% 0.60/0.65 (((~c1_1(a1194)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a1194)))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(398,axiom,((~c1_1(a1194)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.60/0.65 tff(399,plain,
% 0.60/0.65 ((~hskp14) | (~c1_1(a1194))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.60/0.65 tff(400,plain,
% 0.60/0.65 ((~hskp14) | (~c1_1(a1194))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[399, 396])).
% 0.60/0.65 tff(401,plain,
% 0.60/0.65 (~c1_1(a1194)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[400, 395])).
% 0.60/0.65 tff(402,plain,
% 0.60/0.65 (((~hskp14) | (~c0_1(a1194))) <=> ((~hskp14) | (~c0_1(a1194)))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(403,plain,
% 0.60/0.65 (((~c0_1(a1194)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a1194)))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(404,axiom,((~c0_1(a1194)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 0.60/0.65 tff(405,plain,
% 0.60/0.65 ((~hskp14) | (~c0_1(a1194))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.60/0.65 tff(406,plain,
% 0.60/0.65 ((~hskp14) | (~c0_1(a1194))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[405, 402])).
% 0.60/0.65 tff(407,plain,
% 0.60/0.65 (~c0_1(a1194)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[406, 395])).
% 0.60/0.65 tff(408,plain,
% 0.60/0.65 (((~hskp14) | c2_1(a1194)) <=> ((~hskp14) | c2_1(a1194))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(409,axiom,((~hskp14) | c2_1(a1194)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.60/0.65 tff(410,plain,
% 0.60/0.65 ((~hskp14) | c2_1(a1194)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.60/0.65 tff(411,plain,
% 0.60/0.65 ((~hskp14) | c2_1(a1194)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[410, 408])).
% 0.60/0.65 tff(412,plain,
% 0.60/0.65 ((~hskp14) | c2_1(a1194)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[411, 408])).
% 0.60/0.65 tff(413,plain,
% 0.60/0.65 ((~hskp14) | c2_1(a1194)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[412, 408])).
% 0.60/0.65 tff(414,plain,
% 0.60/0.65 ((~hskp14) | c2_1(a1194)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[413, 408])).
% 0.60/0.65 tff(415,plain,
% 0.60/0.65 ((~hskp14) | c2_1(a1194)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[414, 408])).
% 0.60/0.65 tff(416,plain,
% 0.60/0.65 ((~hskp14) | c2_1(a1194)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[415, 408])).
% 0.60/0.65 tff(417,plain,
% 0.60/0.65 ((~hskp14) | c2_1(a1194)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[416, 408])).
% 0.60/0.65 tff(418,plain,
% 0.60/0.65 (c2_1(a1194)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[417, 395])).
% 0.60/0.65 tff(419,plain,
% 0.60/0.65 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp0 | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | c3_1(a1194) | (~c2_1(a1194)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp0 | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | c3_1(a1194) | (~c2_1(a1194)))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(420,plain,
% 0.60/0.65 ((hskp0 | (~ndr1_0) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)) | c1_1(a1194) | c0_1(a1194) | c3_1(a1194)) <=> (hskp0 | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | c3_1(a1194) | (~c2_1(a1194)))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(421,plain,
% 0.60/0.65 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)) | c1_1(a1194) | c0_1(a1194) | c3_1(a1194))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp0 | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | c3_1(a1194) | (~c2_1(a1194))))),
% 0.60/0.65 inference(monotonicity,[status(thm)],[420])).
% 0.60/0.65 tff(422,plain,
% 0.60/0.65 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)) | c1_1(a1194) | c0_1(a1194) | c3_1(a1194))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp0 | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | c3_1(a1194) | (~c2_1(a1194)))),
% 0.60/0.65 inference(transitivity,[status(thm)],[421, 419])).
% 0.60/0.65 tff(423,plain,
% 0.60/0.65 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)) | c1_1(a1194) | c0_1(a1194) | c3_1(a1194))),
% 0.60/0.65 inference(quant_inst,[status(thm)],[])).
% 0.60/0.65 tff(424,plain,
% 0.60/0.65 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp0 | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | c3_1(a1194) | (~c2_1(a1194))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[423, 422])).
% 0.60/0.65 tff(425,plain,
% 0.60/0.65 (c3_1(a1194)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[424, 187, 84, 418, 407, 401, 83])).
% 0.60/0.65 tff(426,plain,
% 0.60/0.65 (~hskp23),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[247, 22, 84])).
% 0.60/0.65 tff(427,assumption,(hskp1), introduced(assumption)).
% 0.60/0.65 tff(428,plain,
% 0.60/0.65 (~c3_1(a1169)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[112, 427])).
% 0.60/0.65 tff(429,plain,
% 0.60/0.65 (~c2_1(a1169)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[118, 427])).
% 0.60/0.65 tff(430,plain,
% 0.60/0.65 (c1_1(a1169)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[129, 427])).
% 0.60/0.65 tff(431,assumption,(~hskp19), introduced(assumption)).
% 0.60/0.65 tff(432,assumption,(~hskp23), introduced(assumption)).
% 0.60/0.65 tff(433,plain,
% 0.60/0.65 ($false),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[209, 187, 432, 431, 430, 429, 428, 95])).
% 0.60/0.65 tff(434,plain,((~hskp1) | hskp23 | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.60/0.65 tff(435,plain,
% 0.60/0.65 (~hskp1),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[434, 426, 203])).
% 0.60/0.65 tff(436,plain,
% 0.60/0.65 ((hskp17 | hskp16 | hskp1) <=> (hskp17 | hskp16 | hskp1)),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(437,plain,
% 0.60/0.65 (((hskp17 | hskp1) | hskp16) <=> (hskp17 | hskp16 | hskp1)),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(438,plain,
% 0.60/0.65 ((hskp17 | hskp1) <=> (hskp17 | hskp1)),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(439,plain,
% 0.60/0.65 (((hskp17 | hskp1) | hskp16) <=> ((hskp17 | hskp1) | hskp16)),
% 0.60/0.65 inference(monotonicity,[status(thm)],[438])).
% 0.60/0.65 tff(440,plain,
% 0.60/0.65 (((hskp17 | hskp1) | hskp16) <=> (hskp17 | hskp16 | hskp1)),
% 0.60/0.65 inference(transitivity,[status(thm)],[439, 437])).
% 0.60/0.65 tff(441,axiom,((hskp17 | hskp1) | hskp16), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 0.60/0.65 tff(442,plain,
% 0.60/0.65 (hskp17 | hskp16 | hskp1),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.60/0.65 tff(443,plain,
% 0.60/0.65 (hskp17 | hskp16 | hskp1),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[442, 436])).
% 0.60/0.65 tff(444,plain,
% 0.60/0.65 (hskp17 | hskp16 | hskp1),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[443, 436])).
% 0.60/0.65 tff(445,plain,
% 0.60/0.65 (hskp17 | hskp16 | hskp1),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[444, 436])).
% 0.60/0.65 tff(446,plain,
% 0.60/0.65 (hskp17 | hskp16 | hskp1),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[445, 436])).
% 0.60/0.65 tff(447,plain,
% 0.60/0.65 (hskp17 | hskp16 | hskp1),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[446, 436])).
% 0.60/0.65 tff(448,plain,
% 0.60/0.65 (hskp17 | hskp16 | hskp1),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[447, 436])).
% 0.60/0.65 tff(449,plain,
% 0.60/0.65 (hskp17 | hskp16 | hskp1),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[448, 436])).
% 0.60/0.65 tff(450,plain,
% 0.60/0.65 (hskp16),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[449, 435, 386])).
% 0.60/0.65 tff(451,plain,
% 0.60/0.65 (((~hskp16) | (~c3_1(a1199))) <=> ((~hskp16) | (~c3_1(a1199)))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(452,plain,
% 0.60/0.65 (((~c3_1(a1199)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a1199)))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(453,axiom,((~c3_1(a1199)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 0.60/0.65 tff(454,plain,
% 0.60/0.65 ((~hskp16) | (~c3_1(a1199))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.60/0.65 tff(455,plain,
% 0.60/0.65 ((~hskp16) | (~c3_1(a1199))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[454, 451])).
% 0.60/0.65 tff(456,plain,
% 0.60/0.65 (~c3_1(a1199)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[455, 450])).
% 0.60/0.65 tff(457,plain,
% 0.60/0.65 (((~hskp16) | (~c0_1(a1199))) <=> ((~hskp16) | (~c0_1(a1199)))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(458,plain,
% 0.60/0.65 (((~c0_1(a1199)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a1199)))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(459,axiom,((~c0_1(a1199)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.60/0.65 tff(460,plain,
% 0.60/0.65 ((~hskp16) | (~c0_1(a1199))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.60/0.65 tff(461,plain,
% 0.60/0.65 ((~hskp16) | (~c0_1(a1199))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[460, 457])).
% 0.60/0.65 tff(462,plain,
% 0.60/0.65 (~c0_1(a1199)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[461, 450])).
% 0.60/0.65 tff(463,plain,
% 0.60/0.65 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | c1_1(a1199))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp0 | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | c1_1(a1199))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(464,plain,
% 0.60/0.65 ((hskp3 | hskp0 | (~ndr1_0) | c3_1(a1199) | c1_1(a1199) | c0_1(a1199)) <=> (hskp3 | hskp0 | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | c1_1(a1199))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(465,plain,
% 0.60/0.65 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | (~ndr1_0) | c3_1(a1199) | c1_1(a1199) | c0_1(a1199))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | c1_1(a1199)))),
% 0.60/0.65 inference(monotonicity,[status(thm)],[464])).
% 0.60/0.65 tff(466,plain,
% 0.60/0.65 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | (~ndr1_0) | c3_1(a1199) | c1_1(a1199) | c0_1(a1199))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp0 | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | c1_1(a1199))),
% 0.60/0.65 inference(transitivity,[status(thm)],[465, 463])).
% 0.60/0.65 tff(467,plain,
% 0.60/0.65 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | hskp0 | (~ndr1_0) | c3_1(a1199) | c1_1(a1199) | c0_1(a1199))),
% 0.60/0.65 inference(quant_inst,[status(thm)],[])).
% 0.60/0.65 tff(468,plain,
% 0.60/0.65 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | hskp0 | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | c1_1(a1199)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.60/0.65 tff(469,plain,
% 0.60/0.65 (c1_1(a1199)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[468, 187, 22, 84, 462, 456, 220])).
% 0.60/0.65 tff(470,plain,
% 0.60/0.65 (((~hskp16) | c2_1(a1199)) <=> ((~hskp16) | c2_1(a1199))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(471,axiom,((~hskp16) | c2_1(a1199)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.60/0.65 tff(472,plain,
% 0.60/0.65 ((~hskp16) | c2_1(a1199)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[471, 470])).
% 0.60/0.65 tff(473,plain,
% 0.60/0.65 ((~hskp16) | c2_1(a1199)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[472, 470])).
% 0.60/0.65 tff(474,plain,
% 0.60/0.65 ((~hskp16) | c2_1(a1199)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[473, 470])).
% 0.60/0.65 tff(475,plain,
% 0.60/0.65 ((~hskp16) | c2_1(a1199)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[474, 470])).
% 0.60/0.65 tff(476,plain,
% 0.60/0.65 ((~hskp16) | c2_1(a1199)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[475, 470])).
% 0.60/0.65 tff(477,plain,
% 0.60/0.65 ((~hskp16) | c2_1(a1199)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[476, 470])).
% 0.60/0.65 tff(478,plain,
% 0.60/0.65 ((~hskp16) | c2_1(a1199)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[477, 470])).
% 0.60/0.65 tff(479,plain,
% 0.60/0.65 ((~hskp16) | c2_1(a1199)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[478, 470])).
% 0.60/0.65 tff(480,plain,
% 0.60/0.65 (c2_1(a1199)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[479, 450])).
% 0.60/0.65 tff(481,plain,
% 0.60/0.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1199) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c3_1(a1194)) | (~c2_1(a1194)) | (~c1_1(a1199)) | (~c2_1(a1199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1199) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c3_1(a1194)) | (~c2_1(a1194)) | (~c1_1(a1199)) | (~c2_1(a1199)))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(482,plain,
% 0.60/0.65 (((~ndr1_0) | c3_1(a1199) | (~c1_1(a1199)) | (~c2_1(a1199)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194))) <=> (c3_1(a1199) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c3_1(a1194)) | (~c2_1(a1194)) | (~c1_1(a1199)) | (~c2_1(a1199)))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(483,plain,
% 0.60/0.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a1199) | (~c1_1(a1199)) | (~c2_1(a1199)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1199) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c3_1(a1194)) | (~c2_1(a1194)) | (~c1_1(a1199)) | (~c2_1(a1199))))),
% 0.60/0.65 inference(monotonicity,[status(thm)],[482])).
% 0.60/0.65 tff(484,plain,
% 0.60/0.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a1199) | (~c1_1(a1199)) | (~c2_1(a1199)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1199) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c3_1(a1194)) | (~c2_1(a1194)) | (~c1_1(a1199)) | (~c2_1(a1199)))),
% 0.60/0.65 inference(transitivity,[status(thm)],[483, 481])).
% 0.60/0.65 tff(485,plain,
% 0.60/0.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a1199) | (~c1_1(a1199)) | (~c2_1(a1199)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)))),
% 0.60/0.65 inference(quant_inst,[status(thm)],[])).
% 0.60/0.65 tff(486,plain,
% 0.60/0.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1199) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c3_1(a1194)) | (~c2_1(a1194)) | (~c1_1(a1199)) | (~c2_1(a1199))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[485, 484])).
% 0.60/0.65 tff(487,plain,
% 0.60/0.65 ($false),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[486, 187, 480, 418, 456, 407, 401, 21, 425, 469])).
% 0.60/0.65 tff(488,plain,(hskp3 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.60/0.65 tff(489,plain,
% 0.60/0.65 (hskp3),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[488, 84])).
% 0.60/0.65 tff(490,plain,
% 0.60/0.65 (~c3_1(a1174)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[264, 489])).
% 0.60/0.65 tff(491,plain,
% 0.60/0.65 (c1_1(a1174)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[332, 489])).
% 0.60/0.65 tff(492,plain,
% 0.60/0.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1194) | c1_1(a1194) | c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c3_1(a1194)) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1194) | c1_1(a1194) | c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c3_1(a1194)) | (~c2_1(a1194)))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(493,plain,
% 0.60/0.65 (((~ndr1_0) | c3_1(a1174) | (~c1_1(a1174)) | (~c2_1(a1174)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194))) <=> (c0_1(a1194) | c1_1(a1194) | c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c3_1(a1194)) | (~c2_1(a1194)))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(494,plain,
% 0.60/0.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a1174) | (~c1_1(a1174)) | (~c2_1(a1174)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1194) | c1_1(a1194) | c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c3_1(a1194)) | (~c2_1(a1194))))),
% 0.60/0.65 inference(monotonicity,[status(thm)],[493])).
% 0.60/0.65 tff(495,plain,
% 0.60/0.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a1174) | (~c1_1(a1174)) | (~c2_1(a1174)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1194) | c1_1(a1194) | c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c3_1(a1194)) | (~c2_1(a1194)))),
% 0.60/0.65 inference(transitivity,[status(thm)],[494, 492])).
% 0.60/0.65 tff(496,plain,
% 0.60/0.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a1174) | (~c1_1(a1174)) | (~c2_1(a1174)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)))),
% 0.60/0.65 inference(quant_inst,[status(thm)],[])).
% 0.60/0.65 tff(497,plain,
% 0.60/0.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1194) | c1_1(a1194) | c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c3_1(a1194)) | (~c2_1(a1194))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[496, 495])).
% 0.60/0.65 tff(498,plain,
% 0.60/0.65 (~c2_1(a1174)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[497, 187, 418, 491, 407, 401, 490, 21, 425])).
% 0.60/0.65 tff(499,plain,
% 0.60/0.65 (^[U: $i] : refl((hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(500,plain,
% 0.60/0.66 (![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[499])).
% 0.60/0.66 tff(501,plain,
% 0.60/0.66 (![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(502,plain,
% 0.60/0.66 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp17) <=> ((hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp17))), rewrite(((hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp17) <=> (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp17) <=> (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(503,plain,
% 0.60/0.66 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp17) <=> ![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[502])).
% 0.60/0.66 tff(504,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.60/0.66 tff(505,plain,
% 0.60/0.66 (![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[504, 503])).
% 0.60/0.66 tff(506,plain,
% 0.60/0.66 (![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[505, 501])).
% 0.60/0.66 tff(507,plain,(
% 0.60/0.66 ![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.66 inference(skolemize,[status(sab)],[506])).
% 0.60/0.66 tff(508,plain,
% 0.60/0.66 (![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[507, 500])).
% 0.60/0.66 tff(509,plain,
% 0.60/0.66 (c0_1(a1174)),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[275, 489])).
% 0.60/0.66 tff(510,plain,
% 0.60/0.66 (((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)))) <=> ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp17 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(511,plain,
% 0.60/0.66 ((hskp22 | hskp17 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174))) <=> (hskp22 | hskp17 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(512,plain,
% 0.60/0.66 (((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)))) <=> ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174))))),
% 0.60/0.66 inference(monotonicity,[status(thm)],[511])).
% 0.60/0.66 tff(513,plain,
% 0.60/0.66 (((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)))) <=> ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp17 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)))),
% 0.60/0.66 inference(transitivity,[status(thm)],[512, 510])).
% 0.60/0.66 tff(514,plain,
% 0.60/0.66 ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | (~ndr1_0) | c3_1(a1174) | c2_1(a1174) | (~c0_1(a1174)))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(515,plain,
% 0.60/0.66 ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp17 | c3_1(a1174) | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.60/0.66 tff(516,plain,
% 0.60/0.66 (hskp22 | c2_1(a1174)),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[515, 187, 386, 509, 490, 508])).
% 0.60/0.66 tff(517,plain,
% 0.60/0.66 (hskp22),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[516, 498])).
% 0.60/0.66 tff(518,plain,
% 0.60/0.66 (~c1_1(a1211)),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[29, 517])).
% 0.60/0.66 tff(519,plain,
% 0.60/0.66 (c0_1(a1211)),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[51, 517])).
% 0.60/0.66 tff(520,plain,
% 0.60/0.66 (c2_1(a1211)),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[311, 187, 84, 519, 518, 73])).
% 0.60/0.66 tff(521,plain,
% 0.60/0.66 ($false),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[392, 187, 386, 519, 509, 518, 490, 352, 498, 520])).
% 0.60/0.66 tff(522,plain,(hskp0), inference(lemma,lemma(discharge,[]))).
% 0.60/0.66 tff(523,plain,
% 0.60/0.66 (((~hskp0) | (~c2_1(a1168))) <=> ((~hskp0) | (~c2_1(a1168)))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(524,plain,
% 0.60/0.66 (((~c2_1(a1168)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a1168)))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(525,axiom,((~c2_1(a1168)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.60/0.66 tff(526,plain,
% 0.60/0.66 ((~hskp0) | (~c2_1(a1168))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[525, 524])).
% 0.60/0.66 tff(527,plain,
% 0.60/0.66 ((~hskp0) | (~c2_1(a1168))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[526, 523])).
% 0.60/0.66 tff(528,plain,
% 0.60/0.66 (~c2_1(a1168)),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[527, 522])).
% 0.60/0.66 tff(529,assumption,(~c1_1(a1211)), introduced(assumption)).
% 0.60/0.66 tff(530,plain,
% 0.60/0.66 (((~hskp0) | c1_1(a1168)) <=> ((~hskp0) | c1_1(a1168))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(531,axiom,((~hskp0) | c1_1(a1168)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.60/0.66 tff(532,plain,
% 0.60/0.66 ((~hskp0) | c1_1(a1168)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.60/0.66 tff(533,plain,
% 0.60/0.66 ((~hskp0) | c1_1(a1168)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[532, 530])).
% 0.60/0.66 tff(534,plain,
% 0.60/0.66 ((~hskp0) | c1_1(a1168)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[533, 530])).
% 0.60/0.66 tff(535,plain,
% 0.60/0.66 ((~hskp0) | c1_1(a1168)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[534, 530])).
% 0.60/0.66 tff(536,plain,
% 0.60/0.66 ((~hskp0) | c1_1(a1168)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[535, 530])).
% 0.60/0.66 tff(537,plain,
% 0.60/0.66 ((~hskp0) | c1_1(a1168)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[536, 530])).
% 0.60/0.66 tff(538,plain,
% 0.60/0.66 ((~hskp0) | c1_1(a1168)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[537, 530])).
% 0.60/0.66 tff(539,plain,
% 0.60/0.66 ((~hskp0) | c1_1(a1168)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[538, 530])).
% 0.60/0.66 tff(540,plain,
% 0.60/0.66 (c1_1(a1168)),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[539, 522])).
% 0.60/0.66 tff(541,plain,
% 0.60/0.66 (((~hskp0) | c0_1(a1168)) <=> ((~hskp0) | c0_1(a1168))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(542,axiom,((~hskp0) | c0_1(a1168)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 0.60/0.66 tff(543,plain,
% 0.60/0.66 ((~hskp0) | c0_1(a1168)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[542, 541])).
% 0.60/0.66 tff(544,plain,
% 0.60/0.66 ((~hskp0) | c0_1(a1168)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[543, 541])).
% 0.60/0.66 tff(545,plain,
% 0.60/0.66 ((~hskp0) | c0_1(a1168)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[544, 541])).
% 0.60/0.66 tff(546,plain,
% 0.60/0.66 ((~hskp0) | c0_1(a1168)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[545, 541])).
% 0.60/0.66 tff(547,plain,
% 0.60/0.66 ((~hskp0) | c0_1(a1168)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[546, 541])).
% 0.60/0.66 tff(548,plain,
% 0.60/0.66 ((~hskp0) | c0_1(a1168)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[547, 541])).
% 0.60/0.66 tff(549,plain,
% 0.60/0.66 ((~hskp0) | c0_1(a1168)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[548, 541])).
% 0.60/0.66 tff(550,plain,
% 0.60/0.66 ((~hskp0) | c0_1(a1168)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[549, 541])).
% 0.60/0.66 tff(551,plain,
% 0.60/0.66 (c0_1(a1168)),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[550, 522])).
% 0.60/0.66 tff(552,assumption,(c3_1(a1211)), introduced(assumption)).
% 0.60/0.66 tff(553,assumption,(c0_1(a1211)), introduced(assumption)).
% 0.60/0.66 tff(554,plain,
% 0.60/0.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1211) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1211) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(555,plain,
% 0.60/0.66 (((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1211) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211) | c1_1(a1211) | (~c0_1(a1211))) <=> (c1_1(a1211) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(556,plain,
% 0.60/0.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1211) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211) | c1_1(a1211) | (~c0_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1211) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211)))),
% 0.60/0.66 inference(monotonicity,[status(thm)],[555])).
% 0.60/0.66 tff(557,plain,
% 0.60/0.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1211) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211) | c1_1(a1211) | (~c0_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1211) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211))),
% 0.60/0.66 inference(transitivity,[status(thm)],[556, 554])).
% 0.60/0.66 tff(558,plain,
% 0.60/0.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1211) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211) | c1_1(a1211) | (~c0_1(a1211)))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(559,plain,
% 0.60/0.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1211) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1211)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[558, 557])).
% 0.60/0.66 tff(560,plain,
% 0.60/0.66 ($false),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[559, 187, 553, 552, 551, 540, 529, 528, 63, 53])).
% 0.60/0.66 tff(561,plain,(c2_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.66 tff(562,plain,
% 0.60/0.66 (c2_1(a1211)),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[561, 52, 41, 30])).
% 0.60/0.66 tff(563,plain,
% 0.60/0.66 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(564,plain,
% 0.60/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[563])).
% 0.60/0.66 tff(565,plain,
% 0.60/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(566,plain,
% 0.60/0.66 (^[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) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_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))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_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))) | c1_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(567,plain,
% 0.60/0.66 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[566])).
% 0.60/0.66 tff(568,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 0.60/0.66 tff(569,plain,
% 0.60/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.60/0.66 tff(570,plain,
% 0.60/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[569, 565])).
% 0.60/0.66 tff(571,plain,(
% 0.60/0.66 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.60/0.66 inference(skolemize,[status(sab)],[570])).
% 0.60/0.66 tff(572,plain,
% 0.60/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[571, 564])).
% 0.60/0.66 tff(573,plain,
% 0.60/0.66 (c2_1(a1211)),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[561, 553, 552, 529])).
% 0.60/0.66 tff(574,assumption,(~hskp1), introduced(assumption)).
% 0.60/0.66 tff(575,assumption,(hskp13), introduced(assumption)).
% 0.60/0.66 tff(576,plain,
% 0.60/0.66 (((~hskp13) | (~c2_1(a1192))) <=> ((~hskp13) | (~c2_1(a1192)))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(577,plain,
% 0.60/0.66 (((~c2_1(a1192)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a1192)))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(578,axiom,((~c2_1(a1192)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.60/0.66 tff(579,plain,
% 0.60/0.66 ((~hskp13) | (~c2_1(a1192))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[578, 577])).
% 0.60/0.66 tff(580,plain,
% 0.60/0.66 ((~hskp13) | (~c2_1(a1192))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[579, 576])).
% 0.60/0.66 tff(581,plain,
% 0.60/0.66 (~c2_1(a1192)),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[580, 575])).
% 0.60/0.66 tff(582,plain,
% 0.60/0.66 (((~hskp13) | (~c0_1(a1192))) <=> ((~hskp13) | (~c0_1(a1192)))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(583,plain,
% 0.60/0.66 (((~c0_1(a1192)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a1192)))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(584,axiom,((~c0_1(a1192)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.60/0.66 tff(585,plain,
% 0.60/0.66 ((~hskp13) | (~c0_1(a1192))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[584, 583])).
% 0.60/0.66 tff(586,plain,
% 0.60/0.66 ((~hskp13) | (~c0_1(a1192))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[585, 582])).
% 0.60/0.66 tff(587,plain,
% 0.60/0.66 (~c0_1(a1192)),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[586, 575])).
% 0.60/0.66 tff(588,plain,
% 0.60/0.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | c3_1(a1192) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | c3_1(a1192) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(589,plain,
% 0.60/0.66 (((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1192) | c0_1(a1192) | c3_1(a1192)) <=> (c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | c3_1(a1192) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(590,plain,
% 0.60/0.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1192) | c0_1(a1192) | c3_1(a1192))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | c3_1(a1192) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211))))),
% 0.60/0.66 inference(monotonicity,[status(thm)],[589])).
% 0.60/0.66 tff(591,plain,
% 0.60/0.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1192) | c0_1(a1192) | c3_1(a1192))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | c3_1(a1192) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.60/0.66 inference(transitivity,[status(thm)],[590, 588])).
% 0.60/0.66 tff(592,plain,
% 0.60/0.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1192) | c0_1(a1192) | c3_1(a1192))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(593,plain,
% 0.60/0.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | c3_1(a1192) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[592, 591])).
% 0.60/0.66 tff(594,plain,
% 0.60/0.66 (c3_1(a1192)),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[593, 187, 553, 552, 529, 587, 581, 572, 573])).
% 0.60/0.66 tff(595,plain,
% 0.60/0.66 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(596,plain,
% 0.60/0.66 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[595])).
% 0.60/0.66 tff(597,plain,
% 0.60/0.66 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(598,plain,
% 0.60/0.66 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(599,plain,
% 0.60/0.66 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[598])).
% 0.60/0.66 tff(600,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 0.60/0.66 tff(601,plain,
% 0.60/0.66 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[600, 599])).
% 0.60/0.66 tff(602,plain,
% 0.60/0.66 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[601, 597])).
% 0.60/0.67 tff(603,plain,(
% 0.60/0.67 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.60/0.67 inference(skolemize,[status(sab)],[602])).
% 0.60/0.67 tff(604,plain,
% 0.60/0.67 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[603, 596])).
% 0.60/0.67 tff(605,plain,
% 0.60/0.67 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | (~c3_1(a1192)) | (~c3_1(a1211)) | (~c2_1(a1211)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | (~c3_1(a1192)) | (~c3_1(a1211)) | (~c2_1(a1211)))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(606,plain,
% 0.60/0.67 ((hskp1 | (~ndr1_0) | c1_1(a1211) | (~c3_1(a1211)) | (~c2_1(a1211)) | c2_1(a1192) | c0_1(a1192) | (~c3_1(a1192))) <=> (hskp1 | c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | (~c3_1(a1192)) | (~c3_1(a1211)) | (~c2_1(a1211)))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(607,plain,
% 0.60/0.67 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a1211) | (~c3_1(a1211)) | (~c2_1(a1211)) | c2_1(a1192) | c0_1(a1192) | (~c3_1(a1192)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | (~c3_1(a1192)) | (~c3_1(a1211)) | (~c2_1(a1211))))),
% 0.60/0.67 inference(monotonicity,[status(thm)],[606])).
% 0.60/0.67 tff(608,plain,
% 0.60/0.67 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a1211) | (~c3_1(a1211)) | (~c2_1(a1211)) | c2_1(a1192) | c0_1(a1192) | (~c3_1(a1192)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | (~c3_1(a1192)) | (~c3_1(a1211)) | (~c2_1(a1211)))),
% 0.60/0.67 inference(transitivity,[status(thm)],[607, 605])).
% 0.60/0.67 tff(609,plain,
% 0.60/0.67 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a1211) | (~c3_1(a1211)) | (~c2_1(a1211)) | c2_1(a1192) | c0_1(a1192) | (~c3_1(a1192)))),
% 0.60/0.67 inference(quant_inst,[status(thm)],[])).
% 0.60/0.67 tff(610,plain,
% 0.60/0.67 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1211) | c0_1(a1192) | c2_1(a1192) | (~ndr1_0) | (~c3_1(a1192)) | (~c3_1(a1211)) | (~c2_1(a1211))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[609, 608])).
% 0.60/0.67 tff(611,plain,
% 0.60/0.67 ($false),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[610, 187, 574, 552, 529, 587, 581, 604, 573, 594])).
% 0.60/0.67 tff(612,plain,((~hskp13) | hskp1 | (~c3_1(a1211)) | c1_1(a1211) | (~c0_1(a1211))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.67 tff(613,plain,
% 0.60/0.67 (~hskp13),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[612, 574, 552, 529, 553])).
% 0.60/0.67 tff(614,plain,
% 0.60/0.67 (^[U: $i] : refl((hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))))),
% 0.60/0.67 inference(bind,[status(th)],[])).
% 0.60/0.67 tff(615,plain,
% 0.60/0.67 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.60/0.67 inference(quant_intro,[status(thm)],[614])).
% 0.60/0.67 tff(616,plain,
% 0.60/0.67 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(617,plain,
% 0.60/0.67 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp13))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp10) <=> ((hskp13 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp10))), rewrite(((hskp13 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp10) <=> (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp10) <=> (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.60/0.67 inference(bind,[status(th)],[])).
% 0.60/0.67 tff(618,plain,
% 0.60/0.67 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp10) <=> ![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.60/0.67 inference(quant_intro,[status(thm)],[617])).
% 0.60/0.67 tff(619,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp13) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.60/0.67 tff(620,plain,
% 0.60/0.67 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[619, 618])).
% 0.60/0.67 tff(621,plain,
% 0.60/0.67 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[620, 616])).
% 0.60/0.67 tff(622,plain,(
% 0.60/0.67 ![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.60/0.67 inference(skolemize,[status(sab)],[621])).
% 0.60/0.67 tff(623,plain,
% 0.60/0.67 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[622, 615])).
% 0.60/0.67 tff(624,plain,
% 0.60/0.67 (((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))) <=> ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(625,plain,
% 0.60/0.67 ((hskp13 | hskp10 | (~ndr1_0) | (~c0_1(a1211)) | (~c3_1(a1211)) | (~c2_1(a1211))) <=> (hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(626,plain,
% 0.60/0.67 (((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(a1211)) | (~c3_1(a1211)) | (~c2_1(a1211)))) <=> ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211))))),
% 0.60/0.67 inference(monotonicity,[status(thm)],[625])).
% 0.60/0.67 tff(627,plain,
% 0.60/0.67 (((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(a1211)) | (~c3_1(a1211)) | (~c2_1(a1211)))) <=> ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.60/0.67 inference(transitivity,[status(thm)],[626, 624])).
% 0.60/0.67 tff(628,plain,
% 0.60/0.67 ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(a1211)) | (~c3_1(a1211)) | (~c2_1(a1211)))),
% 0.60/0.67 inference(quant_inst,[status(thm)],[])).
% 0.60/0.67 tff(629,plain,
% 0.60/0.67 ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[628, 627])).
% 0.60/0.67 tff(630,plain,
% 0.60/0.67 (hskp13 | hskp10 | (~c2_1(a1211))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[629, 187, 553, 552, 623])).
% 0.60/0.67 tff(631,plain,
% 0.60/0.67 (hskp10),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[630, 613, 573])).
% 0.60/0.67 tff(632,plain,
% 0.60/0.67 (((~hskp10) | (~c2_1(a1184))) <=> ((~hskp10) | (~c2_1(a1184)))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(633,plain,
% 0.60/0.67 (((~c2_1(a1184)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a1184)))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(634,axiom,((~c2_1(a1184)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 0.60/0.67 tff(635,plain,
% 0.60/0.67 ((~hskp10) | (~c2_1(a1184))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[634, 633])).
% 0.60/0.67 tff(636,plain,
% 0.60/0.67 ((~hskp10) | (~c2_1(a1184))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[635, 632])).
% 0.60/0.67 tff(637,plain,
% 0.60/0.67 (~c2_1(a1184)),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[636, 631])).
% 0.60/0.67 tff(638,plain,
% 0.60/0.67 (((~hskp10) | (~c0_1(a1184))) <=> ((~hskp10) | (~c0_1(a1184)))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(639,plain,
% 0.60/0.67 (((~c0_1(a1184)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a1184)))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(640,axiom,((~c0_1(a1184)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.60/0.67 tff(641,plain,
% 0.60/0.67 ((~hskp10) | (~c0_1(a1184))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[640, 639])).
% 0.60/0.67 tff(642,plain,
% 0.60/0.67 ((~hskp10) | (~c0_1(a1184))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[641, 638])).
% 0.60/0.67 tff(643,plain,
% 0.60/0.67 (~c0_1(a1184)),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[642, 631])).
% 0.60/0.67 tff(644,plain,
% 0.60/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1211) | c0_1(a1184) | c2_1(a1184) | (~ndr1_0) | c3_1(a1184) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1211) | c0_1(a1184) | c2_1(a1184) | (~ndr1_0) | c3_1(a1184) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(645,plain,
% 0.60/0.67 (((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1184) | c0_1(a1184) | c3_1(a1184)) <=> (c1_1(a1211) | c0_1(a1184) | c2_1(a1184) | (~ndr1_0) | c3_1(a1184) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(646,plain,
% 0.60/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1184) | c0_1(a1184) | c3_1(a1184))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1211) | c0_1(a1184) | c2_1(a1184) | (~ndr1_0) | c3_1(a1184) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211))))),
% 0.60/0.67 inference(monotonicity,[status(thm)],[645])).
% 0.60/0.67 tff(647,plain,
% 0.60/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1184) | c0_1(a1184) | c3_1(a1184))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1211) | c0_1(a1184) | c2_1(a1184) | (~ndr1_0) | c3_1(a1184) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.60/0.67 inference(transitivity,[status(thm)],[646, 644])).
% 0.60/0.67 tff(648,plain,
% 0.60/0.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1184) | c0_1(a1184) | c3_1(a1184))),
% 0.60/0.67 inference(quant_inst,[status(thm)],[])).
% 0.60/0.67 tff(649,plain,
% 0.60/0.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1211) | c0_1(a1184) | c2_1(a1184) | (~ndr1_0) | c3_1(a1184) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[648, 647])).
% 0.60/0.67 tff(650,plain,
% 0.60/0.67 (c3_1(a1184)),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[649, 187, 553, 552, 529, 643, 637, 572, 573])).
% 0.60/0.67 tff(651,plain,
% 0.60/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1211) | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c0_1(a1200)) | (~c3_1(a1211)) | (~c0_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1211) | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c0_1(a1200)) | (~c3_1(a1211)) | (~c0_1(a1211)))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(652,plain,
% 0.60/0.67 (((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1211) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200))) <=> (c1_1(a1211) | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c0_1(a1200)) | (~c3_1(a1211)) | (~c0_1(a1211)))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(653,plain,
% 0.60/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1211) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1211) | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c0_1(a1200)) | (~c3_1(a1211)) | (~c0_1(a1211))))),
% 0.60/0.67 inference(monotonicity,[status(thm)],[652])).
% 0.60/0.67 tff(654,plain,
% 0.60/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1211) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1211) | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c0_1(a1200)) | (~c3_1(a1211)) | (~c0_1(a1211)))),
% 0.60/0.67 inference(transitivity,[status(thm)],[653, 651])).
% 0.60/0.67 tff(655,plain,
% 0.60/0.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1211) | (~c3_1(a1211)) | (~c0_1(a1211)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))),
% 0.60/0.67 inference(quant_inst,[status(thm)],[])).
% 0.60/0.67 tff(656,plain,
% 0.60/0.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1211) | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c0_1(a1200)) | (~c3_1(a1211)) | (~c0_1(a1211))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[655, 654])).
% 0.60/0.67 tff(657,plain,
% 0.60/0.67 ($false),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[656, 187, 553, 552, 377, 551, 540, 529, 366, 360, 528, 63])).
% 0.60/0.67 tff(658,plain,((~hskp17) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.67 tff(659,plain,
% 0.60/0.67 (~hskp17),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[658, 553, 552, 529])).
% 0.60/0.67 tff(660,plain,
% 0.60/0.67 (hskp16),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[449, 574, 659])).
% 0.60/0.67 tff(661,plain,
% 0.60/0.67 (c2_1(a1199)),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[479, 660])).
% 0.60/0.67 tff(662,plain,
% 0.60/0.67 (~c3_1(a1199)),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[455, 660])).
% 0.60/0.67 tff(663,plain,
% 0.60/0.67 (~c0_1(a1199)),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[461, 660])).
% 0.60/0.67 tff(664,plain,
% 0.60/0.67 ((hskp17 | hskp13 | hskp2) <=> (hskp17 | hskp13 | hskp2)),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(665,plain,
% 0.60/0.67 (((hskp17 | hskp13) | hskp2) <=> (hskp17 | hskp13 | hskp2)),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(666,plain,
% 0.60/0.67 ((hskp17 | hskp13) <=> (hskp17 | hskp13)),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(667,plain,
% 0.60/0.67 (((hskp17 | hskp13) | hskp2) <=> ((hskp17 | hskp13) | hskp2)),
% 0.60/0.67 inference(monotonicity,[status(thm)],[666])).
% 0.60/0.67 tff(668,plain,
% 0.60/0.67 (((hskp17 | hskp13) | hskp2) <=> (hskp17 | hskp13 | hskp2)),
% 0.60/0.67 inference(transitivity,[status(thm)],[667, 665])).
% 0.60/0.67 tff(669,axiom,((hskp17 | hskp13) | hskp2), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 0.60/0.67 tff(670,plain,
% 0.60/0.67 (hskp17 | hskp13 | hskp2),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[669, 668])).
% 0.60/0.67 tff(671,plain,
% 0.60/0.67 (hskp17 | hskp13 | hskp2),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[670, 664])).
% 0.60/0.67 tff(672,plain,
% 0.60/0.67 (hskp17 | hskp13 | hskp2),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[671, 664])).
% 0.60/0.67 tff(673,plain,
% 0.60/0.67 (hskp17 | hskp13 | hskp2),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[672, 664])).
% 0.60/0.67 tff(674,plain,
% 0.60/0.67 (hskp17 | hskp13 | hskp2),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[673, 664])).
% 0.60/0.67 tff(675,plain,
% 0.60/0.67 (hskp17 | hskp13 | hskp2),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[674, 664])).
% 0.60/0.67 tff(676,plain,
% 0.60/0.67 (hskp17 | hskp13 | hskp2),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[675, 664])).
% 0.60/0.67 tff(677,plain,
% 0.60/0.67 (hskp17 | hskp13 | hskp2),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[676, 664])).
% 0.60/0.67 tff(678,plain,
% 0.60/0.67 (hskp2),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[677, 613, 659])).
% 0.60/0.67 tff(679,assumption,(~c1_1(a1199)), introduced(assumption)).
% 0.60/0.67 tff(680,plain,
% 0.60/0.67 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 0.60/0.67 inference(bind,[status(th)],[])).
% 0.60/0.67 tff(681,plain,
% 0.60/0.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.60/0.67 inference(quant_intro,[status(thm)],[680])).
% 0.60/0.67 tff(682,plain,
% 0.60/0.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(683,plain,
% 0.60/0.67 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 0.60/0.67 inference(bind,[status(th)],[])).
% 0.60/0.67 tff(684,plain,
% 0.60/0.67 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.60/0.67 inference(quant_intro,[status(thm)],[683])).
% 0.60/0.67 tff(685,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 0.60/0.67 tff(686,plain,
% 0.60/0.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[685, 684])).
% 0.60/0.67 tff(687,plain,
% 0.60/0.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[686, 682])).
% 0.60/0.68 tff(688,plain,(
% 0.60/0.68 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.60/0.68 inference(skolemize,[status(sab)],[687])).
% 0.60/0.68 tff(689,plain,
% 0.60/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[688, 681])).
% 0.60/0.68 tff(690,assumption,(hskp2), introduced(assumption)).
% 0.60/0.68 tff(691,plain,
% 0.60/0.68 (((~hskp2) | (~c0_1(a1172))) <=> ((~hskp2) | (~c0_1(a1172)))),
% 0.60/0.68 inference(rewrite,[status(thm)],[])).
% 0.60/0.68 tff(692,plain,
% 0.60/0.68 (((~c0_1(a1172)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a1172)))),
% 0.60/0.68 inference(rewrite,[status(thm)],[])).
% 0.60/0.68 tff(693,axiom,((~c0_1(a1172)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.60/0.68 tff(694,plain,
% 0.60/0.68 ((~hskp2) | (~c0_1(a1172))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[693, 692])).
% 0.60/0.68 tff(695,plain,
% 0.60/0.68 ((~hskp2) | (~c0_1(a1172))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[694, 691])).
% 0.60/0.68 tff(696,plain,
% 0.60/0.68 (~c0_1(a1172)),
% 0.60/0.68 inference(unit_resolution,[status(thm)],[695, 690])).
% 0.60/0.68 tff(697,assumption,(~c3_1(a1199)), introduced(assumption)).
% 0.60/0.68 tff(698,assumption,(~c0_1(a1199)), introduced(assumption)).
% 0.60/0.68 tff(699,plain,
% 0.60/0.68 (((~hskp2) | c3_1(a1172)) <=> ((~hskp2) | c3_1(a1172))),
% 0.60/0.68 inference(rewrite,[status(thm)],[])).
% 0.60/0.68 tff(700,axiom,((~hskp2) | c3_1(a1172)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 0.60/0.68 tff(701,plain,
% 0.60/0.68 ((~hskp2) | c3_1(a1172)),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[700, 699])).
% 0.60/0.68 tff(702,plain,
% 0.60/0.68 ((~hskp2) | c3_1(a1172)),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[701, 699])).
% 0.60/0.68 tff(703,plain,
% 0.60/0.68 ((~hskp2) | c3_1(a1172)),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[702, 699])).
% 0.60/0.68 tff(704,plain,
% 0.60/0.68 ((~hskp2) | c3_1(a1172)),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[703, 699])).
% 0.60/0.68 tff(705,plain,
% 0.60/0.68 ((~hskp2) | c3_1(a1172)),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[704, 699])).
% 0.60/0.68 tff(706,plain,
% 0.60/0.68 ((~hskp2) | c3_1(a1172)),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[705, 699])).
% 0.60/0.68 tff(707,plain,
% 0.60/0.68 ((~hskp2) | c3_1(a1172)),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[706, 699])).
% 0.60/0.68 tff(708,plain,
% 0.60/0.68 ((~hskp2) | c3_1(a1172)),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[707, 699])).
% 0.60/0.68 tff(709,plain,
% 0.60/0.68 (c3_1(a1172)),
% 0.60/0.68 inference(unit_resolution,[status(thm)],[708, 690])).
% 0.60/0.68 tff(710,plain,
% 0.60/0.68 (((~hskp2) | c2_1(a1172)) <=> ((~hskp2) | c2_1(a1172))),
% 0.60/0.68 inference(rewrite,[status(thm)],[])).
% 0.60/0.68 tff(711,axiom,((~hskp2) | c2_1(a1172)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.60/0.68 tff(712,plain,
% 0.60/0.68 ((~hskp2) | c2_1(a1172)),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[711, 710])).
% 0.60/0.68 tff(713,plain,
% 0.60/0.68 ((~hskp2) | c2_1(a1172)),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[712, 710])).
% 0.60/0.68 tff(714,plain,
% 0.60/0.68 ((~hskp2) | c2_1(a1172)),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[713, 710])).
% 0.60/0.68 tff(715,plain,
% 0.60/0.68 ((~hskp2) | c2_1(a1172)),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[714, 710])).
% 0.60/0.68 tff(716,plain,
% 0.60/0.68 ((~hskp2) | c2_1(a1172)),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[715, 710])).
% 0.60/0.68 tff(717,plain,
% 0.60/0.68 ((~hskp2) | c2_1(a1172)),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[716, 710])).
% 0.60/0.68 tff(718,plain,
% 0.60/0.68 ((~hskp2) | c2_1(a1172)),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[717, 710])).
% 0.60/0.68 tff(719,plain,
% 0.60/0.68 ((~hskp2) | c2_1(a1172)),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[718, 710])).
% 0.60/0.68 tff(720,plain,
% 0.60/0.68 (c2_1(a1172)),
% 0.60/0.68 inference(unit_resolution,[status(thm)],[719, 690])).
% 0.60/0.68 tff(721,assumption,(c2_1(a1199)), introduced(assumption)).
% 0.60/0.68 tff(722,plain,
% 0.60/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1199) | c3_1(a1199) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c1_1(a1199) | (~c2_1(a1199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1199) | c3_1(a1199) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c1_1(a1199) | (~c2_1(a1199)))),
% 0.65/0.68 inference(rewrite,[status(thm)],[])).
% 0.65/0.68 tff(723,plain,
% 0.65/0.68 (((~ndr1_0) | c0_1(a1172) | (~c3_1(a1172)) | (~c2_1(a1172)) | c0_1(a1199) | c3_1(a1199) | (~c2_1(a1199)) | c1_1(a1199) | c0_1(a1199) | c3_1(a1199)) <=> (c0_1(a1199) | c3_1(a1199) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c1_1(a1199) | (~c2_1(a1199)))),
% 0.65/0.68 inference(rewrite,[status(thm)],[])).
% 0.65/0.68 tff(724,plain,
% 0.65/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1172) | (~c3_1(a1172)) | (~c2_1(a1172)) | c0_1(a1199) | c3_1(a1199) | (~c2_1(a1199)) | c1_1(a1199) | c0_1(a1199) | c3_1(a1199))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1199) | c3_1(a1199) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c1_1(a1199) | (~c2_1(a1199))))),
% 0.65/0.68 inference(monotonicity,[status(thm)],[723])).
% 0.65/0.68 tff(725,plain,
% 0.65/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1172) | (~c3_1(a1172)) | (~c2_1(a1172)) | c0_1(a1199) | c3_1(a1199) | (~c2_1(a1199)) | c1_1(a1199) | c0_1(a1199) | c3_1(a1199))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1199) | c3_1(a1199) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c1_1(a1199) | (~c2_1(a1199)))),
% 0.65/0.68 inference(transitivity,[status(thm)],[724, 722])).
% 0.65/0.68 tff(726,plain,
% 0.65/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1172) | (~c3_1(a1172)) | (~c2_1(a1172)) | c0_1(a1199) | c3_1(a1199) | (~c2_1(a1199)) | c1_1(a1199) | c0_1(a1199) | c3_1(a1199))),
% 0.65/0.68 inference(quant_inst,[status(thm)],[])).
% 0.65/0.68 tff(727,plain,
% 0.65/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1199) | c3_1(a1199) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c1_1(a1199) | (~c2_1(a1199))),
% 0.65/0.68 inference(modus_ponens,[status(thm)],[726, 725])).
% 0.65/0.68 tff(728,plain,
% 0.65/0.68 ($false),
% 0.65/0.68 inference(unit_resolution,[status(thm)],[727, 187, 721, 720, 709, 698, 697, 696, 689, 679])).
% 0.65/0.68 tff(729,plain,((~hskp2) | (~c2_1(a1199)) | c0_1(a1199) | c3_1(a1199) | c1_1(a1199)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.68 tff(730,plain,
% 0.65/0.68 (c1_1(a1199)),
% 0.65/0.68 inference(unit_resolution,[status(thm)],[729, 678, 663, 662, 661])).
% 0.65/0.68 tff(731,plain,
% 0.65/0.68 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.65/0.68 inference(bind,[status(th)],[])).
% 0.65/0.68 tff(732,plain,
% 0.65/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_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) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.65/0.68 inference(quant_intro,[status(thm)],[731])).
% 0.65/0.68 tff(733,plain,
% 0.65/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_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) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.65/0.68 inference(rewrite,[status(thm)],[])).
% 0.65/0.68 tff(734,plain,
% 0.65/0.68 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.65/0.68 inference(bind,[status(th)],[])).
% 0.65/0.68 tff(735,plain,
% 0.65/0.68 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | 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) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.65/0.68 inference(quant_intro,[status(thm)],[734])).
% 0.65/0.68 tff(736,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 0.65/0.68 tff(737,plain,
% 0.65/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.65/0.68 inference(modus_ponens,[status(thm)],[736, 735])).
% 0.65/0.68 tff(738,plain,
% 0.65/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.65/0.68 inference(modus_ponens,[status(thm)],[737, 733])).
% 0.65/0.68 tff(739,plain,(
% 0.65/0.68 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.65/0.68 inference(skolemize,[status(sab)],[738])).
% 0.65/0.68 tff(740,plain,
% 0.65/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.65/0.68 inference(modus_ponens,[status(thm)],[739, 732])).
% 0.65/0.68 tff(741,plain,
% 0.65/0.68 (((~hskp10) | (~c1_1(a1184))) <=> ((~hskp10) | (~c1_1(a1184)))),
% 0.65/0.68 inference(rewrite,[status(thm)],[])).
% 0.65/0.68 tff(742,plain,
% 0.65/0.68 (((~c1_1(a1184)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a1184)))),
% 0.65/0.68 inference(rewrite,[status(thm)],[])).
% 0.65/0.68 tff(743,axiom,((~c1_1(a1184)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.65/0.68 tff(744,plain,
% 0.65/0.68 ((~hskp10) | (~c1_1(a1184))),
% 0.65/0.68 inference(modus_ponens,[status(thm)],[743, 742])).
% 0.65/0.68 tff(745,plain,
% 0.65/0.68 ((~hskp10) | (~c1_1(a1184))),
% 0.65/0.68 inference(modus_ponens,[status(thm)],[744, 741])).
% 0.65/0.68 tff(746,plain,
% 0.65/0.68 (~c1_1(a1184)),
% 0.65/0.68 inference(unit_resolution,[status(thm)],[745, 631])).
% 0.65/0.68 tff(747,plain,
% 0.65/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a1199) | c0_1(a1184) | c1_1(a1184) | c2_1(a1184) | (~ndr1_0) | (~c3_1(a1184)) | (~c1_1(a1199)) | (~c2_1(a1199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1199) | c0_1(a1184) | c1_1(a1184) | c2_1(a1184) | (~ndr1_0) | (~c3_1(a1184)) | (~c1_1(a1199)) | (~c2_1(a1199)))),
% 0.65/0.68 inference(rewrite,[status(thm)],[])).
% 0.65/0.68 tff(748,plain,
% 0.65/0.68 (((~ndr1_0) | c3_1(a1199) | (~c1_1(a1199)) | (~c2_1(a1199)) | c2_1(a1184) | c0_1(a1184) | (~c3_1(a1184)) | c2_1(a1184) | c1_1(a1184) | c0_1(a1184)) <=> (c3_1(a1199) | c0_1(a1184) | c1_1(a1184) | c2_1(a1184) | (~ndr1_0) | (~c3_1(a1184)) | (~c1_1(a1199)) | (~c2_1(a1199)))),
% 0.65/0.68 inference(rewrite,[status(thm)],[])).
% 0.65/0.68 tff(749,plain,
% 0.65/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1199) | (~c1_1(a1199)) | (~c2_1(a1199)) | c2_1(a1184) | c0_1(a1184) | (~c3_1(a1184)) | c2_1(a1184) | c1_1(a1184) | c0_1(a1184))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a1199) | c0_1(a1184) | c1_1(a1184) | c2_1(a1184) | (~ndr1_0) | (~c3_1(a1184)) | (~c1_1(a1199)) | (~c2_1(a1199))))),
% 0.65/0.68 inference(monotonicity,[status(thm)],[748])).
% 0.65/0.68 tff(750,plain,
% 0.65/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1199) | (~c1_1(a1199)) | (~c2_1(a1199)) | c2_1(a1184) | c0_1(a1184) | (~c3_1(a1184)) | c2_1(a1184) | c1_1(a1184) | c0_1(a1184))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1199) | c0_1(a1184) | c1_1(a1184) | c2_1(a1184) | (~ndr1_0) | (~c3_1(a1184)) | (~c1_1(a1199)) | (~c2_1(a1199)))),
% 0.65/0.68 inference(transitivity,[status(thm)],[749, 747])).
% 0.65/0.68 tff(751,plain,
% 0.65/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a1199) | (~c1_1(a1199)) | (~c2_1(a1199)) | c2_1(a1184) | c0_1(a1184) | (~c3_1(a1184)) | c2_1(a1184) | c1_1(a1184) | c0_1(a1184))),
% 0.65/0.68 inference(quant_inst,[status(thm)],[])).
% 0.65/0.68 tff(752,plain,
% 0.65/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a1199) | c0_1(a1184) | c1_1(a1184) | c2_1(a1184) | (~ndr1_0) | (~c3_1(a1184)) | (~c1_1(a1199)) | (~c2_1(a1199))),
% 0.65/0.68 inference(modus_ponens,[status(thm)],[751, 750])).
% 0.65/0.68 tff(753,plain,
% 0.65/0.68 ($false),
% 0.65/0.68 inference(unit_resolution,[status(thm)],[752, 187, 661, 662, 643, 746, 637, 740, 730, 650])).
% 0.65/0.68 tff(754,plain,(hskp1 | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.68 tff(755,plain,
% 0.65/0.68 (hskp1),
% 0.65/0.68 inference(unit_resolution,[status(thm)],[754, 52, 41, 30])).
% 0.65/0.68 tff(756,plain,
% 0.65/0.68 (~c3_1(a1169)),
% 0.65/0.68 inference(unit_resolution,[status(thm)],[112, 755])).
% 0.65/0.68 tff(757,plain,
% 0.65/0.68 (~c2_1(a1169)),
% 0.65/0.68 inference(unit_resolution,[status(thm)],[118, 755])).
% 0.65/0.68 tff(758,plain,
% 0.65/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.65/0.68 inference(rewrite,[status(thm)],[])).
% 0.65/0.68 tff(759,plain,
% 0.65/0.68 (((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1169) | c0_1(a1169) | c3_1(a1169)) <=> (c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.65/0.68 inference(rewrite,[status(thm)],[])).
% 0.65/0.68 tff(760,plain,
% 0.65/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1169) | c0_1(a1169) | c3_1(a1169))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211))))),
% 0.65/0.68 inference(monotonicity,[status(thm)],[759])).
% 0.65/0.68 tff(761,plain,
% 0.65/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1169) | c0_1(a1169) | c3_1(a1169))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.65/0.68 inference(transitivity,[status(thm)],[760, 758])).
% 0.65/0.68 tff(762,plain,
% 0.65/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a1211) | (~c0_1(a1211)) | (~c3_1(a1211)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)) | c2_1(a1169) | c0_1(a1169) | c3_1(a1169))),
% 0.65/0.68 inference(quant_inst,[status(thm)],[])).
% 0.65/0.68 tff(763,plain,
% 0.65/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169) | (~c3_1(a1211)) | (~c0_1(a1211)) | (~c2_1(a1211))),
% 0.65/0.68 inference(modus_ponens,[status(thm)],[762, 761])).
% 0.65/0.68 tff(764,plain,
% 0.65/0.68 (c0_1(a1169)),
% 0.65/0.68 inference(unit_resolution,[status(thm)],[763, 187, 52, 41, 30, 757, 756, 572, 562])).
% 0.65/0.68 tff(765,plain,
% 0.65/0.68 (~hskp17),
% 0.65/0.68 inference(unit_resolution,[status(thm)],[658, 52, 41, 30])).
% 0.65/0.68 tff(766,plain,
% 0.65/0.68 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)) | (~c0_1(a1211)) | (~c2_1(a1211)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.65/0.68 inference(rewrite,[status(thm)],[])).
% 0.65/0.68 tff(767,plain,
% 0.65/0.68 ((hskp17 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211))) <=> (hskp17 | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.65/0.68 inference(rewrite,[status(thm)],[])).
% 0.65/0.68 tff(768,plain,
% 0.65/0.68 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)) | (~c0_1(a1211)) | (~c2_1(a1211))))),
% 0.65/0.68 inference(monotonicity,[status(thm)],[767])).
% 0.65/0.68 tff(769,plain,
% 0.65/0.68 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)) | (~c0_1(a1211)) | (~c2_1(a1211)))),
% 0.65/0.68 inference(transitivity,[status(thm)],[768, 766])).
% 0.65/0.68 tff(770,plain,
% 0.65/0.68 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)) | c1_1(a1211) | (~c2_1(a1211)) | (~c0_1(a1211)))),
% 0.65/0.68 inference(quant_inst,[status(thm)],[])).
% 0.65/0.68 tff(771,plain,
% 0.65/0.68 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a1211) | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)) | (~c0_1(a1211)) | (~c2_1(a1211))),
% 0.65/0.68 inference(modus_ponens,[status(thm)],[770, 769])).
% 0.65/0.68 tff(772,plain,
% 0.65/0.68 ($false),
% 0.65/0.68 inference(unit_resolution,[status(thm)],[771, 187, 765, 52, 30, 757, 756, 352, 764, 562])).
% 0.65/0.68 tff(773,plain,(~hskp22), inference(lemma,lemma(discharge,[]))).
% 0.65/0.68 tff(774,plain,
% 0.65/0.68 (((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168)))) <=> ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp17 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168)))),
% 0.65/0.68 inference(rewrite,[status(thm)],[])).
% 0.65/0.68 tff(775,plain,
% 0.65/0.68 ((hskp22 | hskp17 | (~ndr1_0) | c3_1(a1168) | c2_1(a1168) | (~c0_1(a1168))) <=> (hskp22 | hskp17 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168)))),
% 0.65/0.68 inference(rewrite,[status(thm)],[])).
% 0.65/0.68 tff(776,plain,
% 0.65/0.68 (((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | (~ndr1_0) | c3_1(a1168) | c2_1(a1168) | (~c0_1(a1168)))) <=> ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168))))),
% 0.65/0.68 inference(monotonicity,[status(thm)],[775])).
% 0.65/0.68 tff(777,plain,
% 0.65/0.68 (((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | (~ndr1_0) | c3_1(a1168) | c2_1(a1168) | (~c0_1(a1168)))) <=> ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp17 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168)))),
% 0.65/0.69 inference(transitivity,[status(thm)],[776, 774])).
% 0.65/0.69 tff(778,plain,
% 0.65/0.69 ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | (~ndr1_0) | c3_1(a1168) | c2_1(a1168) | (~c0_1(a1168)))),
% 0.65/0.69 inference(quant_inst,[status(thm)],[])).
% 0.65/0.69 tff(779,plain,
% 0.65/0.69 ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp17 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168))),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[778, 777])).
% 0.65/0.69 tff(780,plain,
% 0.65/0.69 (hskp22 | hskp17 | c3_1(a1168)),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[779, 187, 551, 528, 508])).
% 0.65/0.69 tff(781,plain,
% 0.65/0.69 (hskp17 | c3_1(a1168)),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[780, 773])).
% 0.65/0.69 tff(782,plain,
% 0.65/0.69 (c3_1(a1168)),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[781, 23])).
% 0.65/0.69 tff(783,plain,
% 0.65/0.69 (^[U: $i] : refl((hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))))),
% 0.65/0.69 inference(bind,[status(th)],[])).
% 0.65/0.69 tff(784,plain,
% 0.65/0.69 (![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.65/0.69 inference(quant_intro,[status(thm)],[783])).
% 0.65/0.69 tff(785,plain,
% 0.65/0.69 (![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.65/0.69 inference(rewrite,[status(thm)],[])).
% 0.65/0.69 tff(786,plain,
% 0.65/0.69 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp22))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp2) <=> ((hskp22 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp2))), rewrite(((hskp22 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp2) <=> (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp2) <=> (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.65/0.69 inference(bind,[status(th)],[])).
% 0.65/0.69 tff(787,plain,
% 0.65/0.69 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp2) <=> ![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.65/0.69 inference(quant_intro,[status(thm)],[786])).
% 0.65/0.69 tff(788,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 0.65/0.69 tff(789,plain,
% 0.65/0.69 (![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[788, 787])).
% 0.65/0.69 tff(790,plain,
% 0.65/0.69 (![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[789, 785])).
% 0.65/0.69 tff(791,plain,(
% 0.65/0.69 ![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.65/0.69 inference(skolemize,[status(sab)],[790])).
% 0.65/0.69 tff(792,plain,
% 0.65/0.69 (![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[791, 784])).
% 0.65/0.69 tff(793,plain,
% 0.65/0.69 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 0.65/0.69 inference(bind,[status(th)],[])).
% 0.65/0.69 tff(794,plain,
% 0.65/0.69 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.65/0.69 inference(quant_intro,[status(thm)],[793])).
% 0.65/0.69 tff(795,plain,
% 0.65/0.69 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.65/0.69 inference(rewrite,[status(thm)],[])).
% 0.65/0.69 tff(796,plain,
% 0.65/0.69 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~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)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 0.65/0.69 inference(bind,[status(th)],[])).
% 0.65/0.69 tff(797,plain,
% 0.65/0.69 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.65/0.69 inference(quant_intro,[status(thm)],[796])).
% 0.65/0.69 tff(798,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 0.65/0.69 tff(799,plain,
% 0.65/0.69 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[798, 797])).
% 0.65/0.69 tff(800,plain,
% 0.65/0.69 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[799, 795])).
% 0.65/0.69 tff(801,plain,(
% 0.65/0.69 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.65/0.69 inference(skolemize,[status(sab)],[800])).
% 0.65/0.69 tff(802,plain,
% 0.65/0.69 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[801, 794])).
% 0.65/0.69 tff(803,assumption,(~hskp2), introduced(assumption)).
% 0.65/0.69 tff(804,plain,
% 0.65/0.69 (hskp13),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[677, 803, 23])).
% 0.65/0.69 tff(805,plain,
% 0.65/0.69 (~c0_1(a1192)),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[586, 804])).
% 0.65/0.69 tff(806,plain,
% 0.65/0.69 (((~hskp13) | c1_1(a1192)) <=> ((~hskp13) | c1_1(a1192))),
% 0.65/0.69 inference(rewrite,[status(thm)],[])).
% 0.65/0.69 tff(807,axiom,((~hskp13) | c1_1(a1192)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.65/0.69 tff(808,plain,
% 0.65/0.69 ((~hskp13) | c1_1(a1192)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[807, 806])).
% 0.65/0.69 tff(809,plain,
% 0.65/0.69 ((~hskp13) | c1_1(a1192)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[808, 806])).
% 0.65/0.69 tff(810,plain,
% 0.65/0.69 ((~hskp13) | c1_1(a1192)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[809, 806])).
% 0.65/0.69 tff(811,plain,
% 0.65/0.69 ((~hskp13) | c1_1(a1192)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[810, 806])).
% 0.65/0.69 tff(812,plain,
% 0.65/0.69 ((~hskp13) | c1_1(a1192)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[811, 806])).
% 0.65/0.69 tff(813,plain,
% 0.65/0.69 ((~hskp13) | c1_1(a1192)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[812, 806])).
% 0.65/0.69 tff(814,plain,
% 0.65/0.69 ((~hskp13) | c1_1(a1192)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[813, 806])).
% 0.65/0.69 tff(815,plain,
% 0.65/0.69 ((~hskp13) | c1_1(a1192)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[814, 806])).
% 0.65/0.69 tff(816,plain,
% 0.65/0.69 (c1_1(a1192)),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[815, 804])).
% 0.65/0.69 tff(817,plain,
% 0.65/0.69 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1192) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c3_1(a1192) | (~c1_1(a1192)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1192) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c3_1(a1192) | (~c1_1(a1192)))),
% 0.65/0.69 inference(rewrite,[status(thm)],[])).
% 0.65/0.69 tff(818,plain,
% 0.65/0.69 ((hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1192) | c3_1(a1192) | (~c1_1(a1192))) <=> (hskp3 | c0_1(a1192) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c3_1(a1192) | (~c1_1(a1192)))),
% 0.65/0.69 inference(rewrite,[status(thm)],[])).
% 0.65/0.69 tff(819,plain,
% 0.65/0.69 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1192) | c3_1(a1192) | (~c1_1(a1192)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1192) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c3_1(a1192) | (~c1_1(a1192))))),
% 0.65/0.69 inference(monotonicity,[status(thm)],[818])).
% 0.65/0.69 tff(820,plain,
% 0.65/0.69 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1192) | c3_1(a1192) | (~c1_1(a1192)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1192) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c3_1(a1192) | (~c1_1(a1192)))),
% 0.65/0.69 inference(transitivity,[status(thm)],[819, 817])).
% 0.65/0.69 tff(821,plain,
% 0.65/0.69 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1192) | c3_1(a1192) | (~c1_1(a1192)))),
% 0.65/0.69 inference(quant_inst,[status(thm)],[])).
% 0.65/0.69 tff(822,plain,
% 0.65/0.69 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1192) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c3_1(a1192) | (~c1_1(a1192))),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[821, 820])).
% 0.65/0.69 tff(823,plain,
% 0.65/0.69 (c3_1(a1192)),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[822, 187, 22, 816, 540, 805, 528, 802, 782])).
% 0.65/0.69 tff(824,plain,
% 0.65/0.69 (~c2_1(a1192)),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[580, 804])).
% 0.65/0.69 tff(825,assumption,(c3_1(a1192)), introduced(assumption)).
% 0.65/0.69 tff(826,assumption,(hskp8), introduced(assumption)).
% 0.65/0.69 tff(827,plain,
% 0.65/0.69 (((~hskp8) | (~c3_1(a1180))) <=> ((~hskp8) | (~c3_1(a1180)))),
% 0.65/0.69 inference(rewrite,[status(thm)],[])).
% 0.65/0.69 tff(828,plain,
% 0.65/0.69 (((~c3_1(a1180)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a1180)))),
% 0.65/0.69 inference(rewrite,[status(thm)],[])).
% 0.65/0.69 tff(829,axiom,((~c3_1(a1180)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.65/0.69 tff(830,plain,
% 0.65/0.69 ((~hskp8) | (~c3_1(a1180))),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[829, 828])).
% 0.65/0.69 tff(831,plain,
% 0.65/0.69 ((~hskp8) | (~c3_1(a1180))),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[830, 827])).
% 0.65/0.69 tff(832,plain,
% 0.65/0.69 (~c3_1(a1180)),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[831, 826])).
% 0.65/0.69 tff(833,plain,
% 0.65/0.69 (((~hskp8) | (~c0_1(a1180))) <=> ((~hskp8) | (~c0_1(a1180)))),
% 0.65/0.69 inference(rewrite,[status(thm)],[])).
% 0.65/0.69 tff(834,plain,
% 0.65/0.69 (((~c0_1(a1180)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a1180)))),
% 0.65/0.69 inference(rewrite,[status(thm)],[])).
% 0.65/0.69 tff(835,axiom,((~c0_1(a1180)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 0.65/0.69 tff(836,plain,
% 0.65/0.69 ((~hskp8) | (~c0_1(a1180))),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[835, 834])).
% 0.65/0.69 tff(837,plain,
% 0.65/0.69 ((~hskp8) | (~c0_1(a1180))),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[836, 833])).
% 0.65/0.69 tff(838,plain,
% 0.65/0.69 (~c0_1(a1180)),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[837, 826])).
% 0.65/0.69 tff(839,assumption,(~c2_1(a1192)), introduced(assumption)).
% 0.65/0.69 tff(840,plain,
% 0.65/0.69 (((~hskp8) | c1_1(a1180)) <=> ((~hskp8) | c1_1(a1180))),
% 0.65/0.69 inference(rewrite,[status(thm)],[])).
% 0.65/0.69 tff(841,axiom,((~hskp8) | c1_1(a1180)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 0.65/0.69 tff(842,plain,
% 0.65/0.69 ((~hskp8) | c1_1(a1180)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[841, 840])).
% 0.65/0.69 tff(843,plain,
% 0.65/0.69 ((~hskp8) | c1_1(a1180)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[842, 840])).
% 0.65/0.69 tff(844,plain,
% 0.65/0.69 ((~hskp8) | c1_1(a1180)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[843, 840])).
% 0.65/0.69 tff(845,plain,
% 0.65/0.69 ((~hskp8) | c1_1(a1180)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[844, 840])).
% 0.65/0.69 tff(846,plain,
% 0.65/0.69 ((~hskp8) | c1_1(a1180)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[845, 840])).
% 0.65/0.69 tff(847,plain,
% 0.65/0.69 ((~hskp8) | c1_1(a1180)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[846, 840])).
% 0.65/0.69 tff(848,plain,
% 0.65/0.69 ((~hskp8) | c1_1(a1180)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[847, 840])).
% 0.65/0.69 tff(849,plain,
% 0.65/0.69 ((~hskp8) | c1_1(a1180)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[848, 840])).
% 0.65/0.69 tff(850,plain,
% 0.65/0.69 (c1_1(a1180)),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[849, 826])).
% 0.65/0.69 tff(851,assumption,(c1_1(a1192)), introduced(assumption)).
% 0.65/0.69 tff(852,plain,
% 0.65/0.69 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a1192) | c0_1(a1180) | c3_1(a1180) | (~ndr1_0) | (~c1_1(a1180)) | (~c3_1(a1192)) | (~c1_1(a1192)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1192) | c0_1(a1180) | c3_1(a1180) | (~ndr1_0) | (~c1_1(a1180)) | (~c3_1(a1192)) | (~c1_1(a1192)))),
% 0.65/0.69 inference(rewrite,[status(thm)],[])).
% 0.65/0.69 tff(853,plain,
% 0.65/0.69 ((hskp3 | (~ndr1_0) | c2_1(a1192) | (~c1_1(a1192)) | (~c3_1(a1192)) | c0_1(a1180) | c3_1(a1180) | (~c1_1(a1180))) <=> (hskp3 | c2_1(a1192) | c0_1(a1180) | c3_1(a1180) | (~ndr1_0) | (~c1_1(a1180)) | (~c3_1(a1192)) | (~c1_1(a1192)))),
% 0.65/0.69 inference(rewrite,[status(thm)],[])).
% 0.65/0.69 tff(854,plain,
% 0.65/0.69 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1192) | (~c1_1(a1192)) | (~c3_1(a1192)) | c0_1(a1180) | c3_1(a1180) | (~c1_1(a1180)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a1192) | c0_1(a1180) | c3_1(a1180) | (~ndr1_0) | (~c1_1(a1180)) | (~c3_1(a1192)) | (~c1_1(a1192))))),
% 0.65/0.69 inference(monotonicity,[status(thm)],[853])).
% 0.65/0.69 tff(855,plain,
% 0.65/0.69 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1192) | (~c1_1(a1192)) | (~c3_1(a1192)) | c0_1(a1180) | c3_1(a1180) | (~c1_1(a1180)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1192) | c0_1(a1180) | c3_1(a1180) | (~ndr1_0) | (~c1_1(a1180)) | (~c3_1(a1192)) | (~c1_1(a1192)))),
% 0.65/0.69 inference(transitivity,[status(thm)],[854, 852])).
% 0.65/0.69 tff(856,plain,
% 0.65/0.69 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1192) | (~c1_1(a1192)) | (~c3_1(a1192)) | c0_1(a1180) | c3_1(a1180) | (~c1_1(a1180)))),
% 0.65/0.69 inference(quant_inst,[status(thm)],[])).
% 0.65/0.69 tff(857,plain,
% 0.65/0.69 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1192) | c0_1(a1180) | c3_1(a1180) | (~ndr1_0) | (~c1_1(a1180)) | (~c3_1(a1192)) | (~c1_1(a1192))),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[856, 855])).
% 0.65/0.69 tff(858,plain,
% 0.65/0.69 ($false),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[857, 187, 22, 851, 850, 839, 838, 832, 802, 825])).
% 0.65/0.69 tff(859,plain,((~hskp8) | hskp3 | (~c1_1(a1192)) | c2_1(a1192) | (~c3_1(a1192))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.69 tff(860,plain,
% 0.65/0.69 (~hskp8),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[859, 816, 22, 824, 823])).
% 0.65/0.69 tff(861,plain,
% 0.65/0.69 (hskp28),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[185, 860])).
% 0.65/0.69 tff(862,plain,
% 0.65/0.69 (((~hskp28) | c3_1(a1236)) <=> ((~hskp28) | c3_1(a1236))),
% 0.65/0.69 inference(rewrite,[status(thm)],[])).
% 0.65/0.69 tff(863,axiom,((~hskp28) | c3_1(a1236)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.65/0.69 tff(864,plain,
% 0.65/0.69 ((~hskp28) | c3_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[863, 862])).
% 0.65/0.69 tff(865,plain,
% 0.65/0.69 ((~hskp28) | c3_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[864, 862])).
% 0.65/0.69 tff(866,plain,
% 0.65/0.69 ((~hskp28) | c3_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[865, 862])).
% 0.65/0.69 tff(867,plain,
% 0.65/0.69 ((~hskp28) | c3_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[866, 862])).
% 0.65/0.69 tff(868,plain,
% 0.65/0.69 ((~hskp28) | c3_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[867, 862])).
% 0.65/0.69 tff(869,plain,
% 0.65/0.69 ((~hskp28) | c3_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[868, 862])).
% 0.65/0.69 tff(870,plain,
% 0.65/0.69 ((~hskp28) | c3_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[869, 862])).
% 0.65/0.69 tff(871,plain,
% 0.65/0.69 ((~hskp28) | c3_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[870, 862])).
% 0.65/0.69 tff(872,plain,
% 0.65/0.69 (c3_1(a1236)),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[871, 861])).
% 0.65/0.69 tff(873,plain,
% 0.65/0.69 (((~hskp28) | c2_1(a1236)) <=> ((~hskp28) | c2_1(a1236))),
% 0.65/0.69 inference(rewrite,[status(thm)],[])).
% 0.65/0.69 tff(874,axiom,((~hskp28) | c2_1(a1236)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.65/0.69 tff(875,plain,
% 0.65/0.69 ((~hskp28) | c2_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[874, 873])).
% 0.65/0.69 tff(876,plain,
% 0.65/0.69 ((~hskp28) | c2_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[875, 873])).
% 0.65/0.69 tff(877,plain,
% 0.65/0.69 ((~hskp28) | c2_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[876, 873])).
% 0.65/0.69 tff(878,plain,
% 0.65/0.69 ((~hskp28) | c2_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[877, 873])).
% 0.65/0.69 tff(879,plain,
% 0.65/0.69 ((~hskp28) | c2_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[878, 873])).
% 0.65/0.69 tff(880,plain,
% 0.65/0.69 ((~hskp28) | c2_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[879, 873])).
% 0.65/0.69 tff(881,plain,
% 0.65/0.69 ((~hskp28) | c2_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[880, 873])).
% 0.65/0.69 tff(882,plain,
% 0.65/0.69 ((~hskp28) | c2_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[881, 873])).
% 0.65/0.69 tff(883,plain,
% 0.65/0.69 (c2_1(a1236)),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[882, 861])).
% 0.65/0.69 tff(884,plain,
% 0.65/0.69 (((~hskp28) | c0_1(a1236)) <=> ((~hskp28) | c0_1(a1236))),
% 0.65/0.69 inference(rewrite,[status(thm)],[])).
% 0.65/0.69 tff(885,axiom,((~hskp28) | c0_1(a1236)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.65/0.69 tff(886,plain,
% 0.65/0.69 ((~hskp28) | c0_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[885, 884])).
% 0.65/0.69 tff(887,plain,
% 0.65/0.69 ((~hskp28) | c0_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[886, 884])).
% 0.65/0.69 tff(888,plain,
% 0.65/0.69 ((~hskp28) | c0_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[887, 884])).
% 0.65/0.69 tff(889,plain,
% 0.65/0.69 ((~hskp28) | c0_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[888, 884])).
% 0.65/0.69 tff(890,plain,
% 0.65/0.69 ((~hskp28) | c0_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[889, 884])).
% 0.65/0.69 tff(891,plain,
% 0.65/0.69 ((~hskp28) | c0_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[890, 884])).
% 0.65/0.69 tff(892,plain,
% 0.65/0.69 ((~hskp28) | c0_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[891, 884])).
% 0.65/0.69 tff(893,plain,
% 0.65/0.69 ((~hskp28) | c0_1(a1236)),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[892, 884])).
% 0.65/0.69 tff(894,plain,
% 0.65/0.69 (c0_1(a1236)),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[893, 861])).
% 0.65/0.69 tff(895,plain,
% 0.65/0.69 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c2_1(a1236)) | (~c3_1(a1236)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c2_1(a1236)) | (~c3_1(a1236)))),
% 0.65/0.69 inference(rewrite,[status(thm)],[])).
% 0.65/0.69 tff(896,plain,
% 0.65/0.69 ((hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c3_1(a1236)) | (~c2_1(a1236))) <=> (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c2_1(a1236)) | (~c3_1(a1236)))),
% 0.65/0.69 inference(rewrite,[status(thm)],[])).
% 0.65/0.69 tff(897,plain,
% 0.65/0.69 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c3_1(a1236)) | (~c2_1(a1236)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c2_1(a1236)) | (~c3_1(a1236))))),
% 0.65/0.69 inference(monotonicity,[status(thm)],[896])).
% 0.65/0.69 tff(898,plain,
% 0.65/0.69 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c3_1(a1236)) | (~c2_1(a1236)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c2_1(a1236)) | (~c3_1(a1236)))),
% 0.65/0.69 inference(transitivity,[status(thm)],[897, 895])).
% 0.65/0.69 tff(899,plain,
% 0.65/0.69 ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c3_1(a1236)) | (~c2_1(a1236)))),
% 0.65/0.69 inference(quant_inst,[status(thm)],[])).
% 0.65/0.69 tff(900,plain,
% 0.65/0.69 ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1236)) | (~c2_1(a1236)) | (~c3_1(a1236))),
% 0.65/0.69 inference(modus_ponens,[status(thm)],[899, 898])).
% 0.65/0.69 tff(901,plain,
% 0.65/0.69 ($false),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[900, 187, 773, 803, 894, 883, 872, 792])).
% 0.65/0.69 tff(902,plain,(hskp2 | hskp3 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.65/0.69 tff(903,plain,
% 0.65/0.69 (hskp2),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[902, 23, 22])).
% 0.65/0.69 tff(904,assumption,(hskp16), introduced(assumption)).
% 0.65/0.69 tff(905,plain,
% 0.65/0.69 (c2_1(a1199)),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[479, 904])).
% 0.65/0.69 tff(906,plain,
% 0.65/0.69 (~c3_1(a1199)),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[455, 904])).
% 0.65/0.69 tff(907,plain,
% 0.65/0.69 (~c0_1(a1199)),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[461, 904])).
% 0.65/0.69 tff(908,plain,
% 0.65/0.69 (c1_1(a1199)),
% 0.65/0.69 inference(unit_resolution,[status(thm)],[729, 907, 690, 906, 905])).
% 0.65/0.69 tff(909,assumption,(c3_1(a1168)), introduced(assumption)).
% 0.65/0.69 tff(910,plain,
% 0.65/0.69 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1199) | c3_1(a1199) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1199)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1199) | c3_1(a1199) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1199)))),
% 0.65/0.70 inference(rewrite,[status(thm)],[])).
% 0.65/0.70 tff(911,plain,
% 0.65/0.70 ((hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1199) | c3_1(a1199) | (~c1_1(a1199))) <=> (hskp3 | c0_1(a1199) | c3_1(a1199) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1199)))),
% 0.65/0.70 inference(rewrite,[status(thm)],[])).
% 0.65/0.70 tff(912,plain,
% 0.65/0.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1199) | c3_1(a1199) | (~c1_1(a1199)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a1199) | c3_1(a1199) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1199))))),
% 0.65/0.70 inference(monotonicity,[status(thm)],[911])).
% 0.65/0.70 tff(913,plain,
% 0.65/0.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1199) | c3_1(a1199) | (~c1_1(a1199)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1199) | c3_1(a1199) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1199)))),
% 0.65/0.70 inference(transitivity,[status(thm)],[912, 910])).
% 0.65/0.70 tff(914,plain,
% 0.65/0.70 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1199) | c3_1(a1199) | (~c1_1(a1199)))),
% 0.65/0.70 inference(quant_inst,[status(thm)],[])).
% 0.65/0.70 tff(915,plain,
% 0.65/0.70 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a1199) | c3_1(a1199) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1199))),
% 0.65/0.70 inference(modus_ponens,[status(thm)],[914, 913])).
% 0.65/0.70 tff(916,plain,
% 0.65/0.70 ($false),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[915, 187, 22, 540, 907, 906, 528, 802, 909, 908])).
% 0.65/0.70 tff(917,plain,((~hskp16) | hskp3 | (~c3_1(a1168)) | (~hskp2)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.70 tff(918,plain,
% 0.65/0.70 (~hskp16),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[917, 782, 22, 903])).
% 0.65/0.70 tff(919,plain,
% 0.65/0.70 (hskp1),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[449, 918, 23])).
% 0.65/0.70 tff(920,plain,
% 0.65/0.70 (~c3_1(a1169)),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[112, 919])).
% 0.65/0.70 tff(921,plain,
% 0.65/0.70 (~c2_1(a1169)),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[118, 919])).
% 0.65/0.70 tff(922,plain,
% 0.65/0.70 (((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)))) <=> ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp17 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)))),
% 0.65/0.70 inference(rewrite,[status(thm)],[])).
% 0.65/0.70 tff(923,plain,
% 0.65/0.70 ((hskp22 | hskp17 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169))) <=> (hskp22 | hskp17 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)))),
% 0.65/0.70 inference(rewrite,[status(thm)],[])).
% 0.65/0.70 tff(924,plain,
% 0.65/0.70 (((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)))) <=> ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169))))),
% 0.65/0.70 inference(monotonicity,[status(thm)],[923])).
% 0.65/0.70 tff(925,plain,
% 0.65/0.70 (((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)))) <=> ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp17 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)))),
% 0.65/0.70 inference(transitivity,[status(thm)],[924, 922])).
% 0.65/0.70 tff(926,plain,
% 0.65/0.70 ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp17 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)))),
% 0.65/0.70 inference(quant_inst,[status(thm)],[])).
% 0.65/0.70 tff(927,plain,
% 0.65/0.70 ((~![U: $i] : (hskp22 | hskp17 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp17 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169))),
% 0.65/0.70 inference(modus_ponens,[status(thm)],[926, 925])).
% 0.65/0.70 tff(928,plain,
% 0.65/0.70 (~c0_1(a1169)),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[927, 187, 773, 23, 921, 920, 508])).
% 0.65/0.70 tff(929,plain,
% 0.65/0.70 (c1_1(a1169)),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[129, 919])).
% 0.65/0.70 tff(930,plain,
% 0.65/0.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c3_1(a1169) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1169)) | c0_1(a1169))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c3_1(a1169) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1169)) | c0_1(a1169))),
% 0.65/0.70 inference(rewrite,[status(thm)],[])).
% 0.65/0.70 tff(931,plain,
% 0.65/0.70 ((hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1169) | c3_1(a1169) | (~c1_1(a1169))) <=> (hskp3 | c3_1(a1169) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1169)) | c0_1(a1169))),
% 0.65/0.70 inference(rewrite,[status(thm)],[])).
% 0.65/0.70 tff(932,plain,
% 0.65/0.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1169) | c3_1(a1169) | (~c1_1(a1169)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c3_1(a1169) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1169)) | c0_1(a1169)))),
% 0.65/0.70 inference(monotonicity,[status(thm)],[931])).
% 0.65/0.70 tff(933,plain,
% 0.65/0.70 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1169) | c3_1(a1169) | (~c1_1(a1169)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c3_1(a1169) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1169)) | c0_1(a1169))),
% 0.65/0.70 inference(transitivity,[status(thm)],[932, 930])).
% 0.65/0.70 tff(934,plain,
% 0.65/0.70 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1169) | c3_1(a1169) | (~c1_1(a1169)))),
% 0.65/0.70 inference(quant_inst,[status(thm)],[])).
% 0.65/0.70 tff(935,plain,
% 0.65/0.70 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c3_1(a1169) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | (~c1_1(a1169)) | c0_1(a1169)),
% 0.65/0.70 inference(modus_ponens,[status(thm)],[934, 933])).
% 0.65/0.70 tff(936,plain,
% 0.65/0.70 ($false),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[935, 187, 22, 929, 540, 920, 528, 802, 928, 782])).
% 0.65/0.70 tff(937,plain,(hskp17 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.65/0.70 tff(938,plain,
% 0.65/0.70 (hskp17),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[937, 22])).
% 0.65/0.70 tff(939,plain,
% 0.65/0.70 (~c2_1(a1200)),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[359, 938])).
% 0.65/0.70 tff(940,plain,
% 0.65/0.70 (~c1_1(a1200)),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[365, 938])).
% 0.65/0.70 tff(941,plain,
% 0.65/0.70 (c0_1(a1200)),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[376, 938])).
% 0.65/0.70 tff(942,plain,
% 0.65/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1200)) | (~c0_1(a1200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1200)) | (~c0_1(a1200)))),
% 0.65/0.70 inference(rewrite,[status(thm)],[])).
% 0.65/0.70 tff(943,plain,
% 0.65/0.70 (((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1200) | (~c3_1(a1200)) | (~c0_1(a1200)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200))) <=> (c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1200)) | (~c0_1(a1200)))),
% 0.65/0.70 inference(rewrite,[status(thm)],[])).
% 0.65/0.70 tff(944,plain,
% 0.65/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1200) | (~c3_1(a1200)) | (~c0_1(a1200)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1200)) | (~c0_1(a1200))))),
% 0.65/0.70 inference(monotonicity,[status(thm)],[943])).
% 0.65/0.70 tff(945,plain,
% 0.65/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1200) | (~c3_1(a1200)) | (~c0_1(a1200)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1200)) | (~c0_1(a1200)))),
% 0.65/0.70 inference(transitivity,[status(thm)],[944, 942])).
% 0.65/0.70 tff(946,plain,
% 0.65/0.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c1_1(a1200) | (~c3_1(a1200)) | (~c0_1(a1200)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))),
% 0.65/0.70 inference(quant_inst,[status(thm)],[])).
% 0.65/0.70 tff(947,plain,
% 0.65/0.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c3_1(a1200)) | (~c0_1(a1200))),
% 0.65/0.70 inference(modus_ponens,[status(thm)],[946, 945])).
% 0.65/0.70 tff(948,plain,
% 0.65/0.70 (~c3_1(a1200)),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[947, 187, 941, 551, 540, 940, 939, 528, 63])).
% 0.65/0.70 tff(949,plain,
% 0.65/0.70 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.65/0.70 inference(bind,[status(th)],[])).
% 0.65/0.70 tff(950,plain,
% 0.65/0.70 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.70 inference(quant_intro,[status(thm)],[949])).
% 0.65/0.70 tff(951,plain,
% 0.65/0.70 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.70 inference(rewrite,[status(thm)],[])).
% 0.65/0.70 tff(952,plain,
% 0.65/0.70 (^[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) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.65/0.70 inference(bind,[status(th)],[])).
% 0.65/0.70 tff(953,plain,
% 0.65/0.70 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.70 inference(quant_intro,[status(thm)],[952])).
% 0.65/0.70 tff(954,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 0.65/0.70 tff(955,plain,
% 0.65/0.70 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.70 inference(modus_ponens,[status(thm)],[954, 953])).
% 0.65/0.70 tff(956,plain,
% 0.65/0.70 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.70 inference(modus_ponens,[status(thm)],[955, 951])).
% 0.65/0.70 tff(957,plain,(
% 0.65/0.70 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.70 inference(skolemize,[status(sab)],[956])).
% 0.65/0.70 tff(958,plain,
% 0.65/0.70 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.70 inference(modus_ponens,[status(thm)],[957, 950])).
% 0.65/0.70 tff(959,plain,
% 0.65/0.70 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp6 | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | c3_1(a1200))),
% 0.65/0.70 inference(rewrite,[status(thm)],[])).
% 0.65/0.70 tff(960,plain,
% 0.65/0.70 ((hskp6 | (~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200)) <=> (hskp6 | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | c3_1(a1200))),
% 0.65/0.70 inference(rewrite,[status(thm)],[])).
% 0.65/0.70 tff(961,plain,
% 0.65/0.70 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | c3_1(a1200)))),
% 0.65/0.70 inference(monotonicity,[status(thm)],[960])).
% 0.65/0.70 tff(962,plain,
% 0.65/0.70 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp6 | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | c3_1(a1200))),
% 0.65/0.70 inference(transitivity,[status(thm)],[961, 959])).
% 0.65/0.70 tff(963,plain,
% 0.65/0.70 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1168) | (~c0_1(a1168)) | (~c1_1(a1168)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))),
% 0.65/0.70 inference(quant_inst,[status(thm)],[])).
% 0.65/0.70 tff(964,plain,
% 0.65/0.70 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp6 | c1_1(a1200) | c2_1(a1200) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | c3_1(a1200)),
% 0.65/0.70 inference(modus_ponens,[status(thm)],[963, 962])).
% 0.65/0.70 tff(965,plain,
% 0.65/0.70 (hskp6),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[964, 187, 551, 540, 940, 939, 528, 958, 948])).
% 0.65/0.70 tff(966,plain,
% 0.65/0.70 (((~hskp6) | (~c3_1(a1178))) <=> ((~hskp6) | (~c3_1(a1178)))),
% 0.65/0.70 inference(rewrite,[status(thm)],[])).
% 0.65/0.70 tff(967,plain,
% 0.65/0.70 (((~c3_1(a1178)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a1178)))),
% 0.65/0.70 inference(rewrite,[status(thm)],[])).
% 0.65/0.70 tff(968,axiom,((~c3_1(a1178)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 0.65/0.70 tff(969,plain,
% 0.65/0.70 ((~hskp6) | (~c3_1(a1178))),
% 0.65/0.70 inference(modus_ponens,[status(thm)],[968, 967])).
% 0.65/0.70 tff(970,plain,
% 0.65/0.70 ((~hskp6) | (~c3_1(a1178))),
% 0.65/0.70 inference(modus_ponens,[status(thm)],[969, 966])).
% 0.65/0.70 tff(971,plain,
% 0.65/0.70 (~c3_1(a1178)),
% 0.65/0.70 inference(unit_resolution,[status(thm)],[970, 965])).
% 0.65/0.70 tff(972,plain,
% 0.65/0.70 (^[U: $i] : refl((hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 0.65/0.70 inference(bind,[status(th)],[])).
% 0.65/0.70 tff(973,plain,
% 0.65/0.70 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.65/0.70 inference(quant_intro,[status(thm)],[972])).
% 0.65/0.70 tff(974,plain,
% 0.65/0.70 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.65/0.70 inference(rewrite,[status(thm)],[])).
% 0.65/0.70 tff(975,plain,
% 0.65/0.70 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp20))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp12) <=> ((hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp12))), rewrite(((hskp20 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp12) <=> (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp12) <=> (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.65/0.71 inference(bind,[status(th)],[])).
% 0.65/0.71 tff(976,plain,
% 0.65/0.71 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp12) <=> ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.65/0.71 inference(quant_intro,[status(thm)],[975])).
% 0.65/0.71 tff(977,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp20) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 0.65/0.71 tff(978,plain,
% 0.65/0.71 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[977, 976])).
% 0.65/0.71 tff(979,plain,
% 0.65/0.71 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[978, 974])).
% 0.65/0.71 tff(980,plain,(
% 0.65/0.71 ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.65/0.71 inference(skolemize,[status(sab)],[979])).
% 0.65/0.71 tff(981,plain,
% 0.65/0.71 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[980, 973])).
% 0.65/0.71 tff(982,plain,
% 0.65/0.71 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(983,plain,
% 0.65/0.71 ((hskp22 | hskp14 | (~ndr1_0) | c3_1(a1168) | c2_1(a1168) | (~c0_1(a1168))) <=> (hskp22 | hskp14 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(984,plain,
% 0.65/0.71 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1168) | c2_1(a1168) | (~c0_1(a1168)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168))))),
% 0.65/0.71 inference(monotonicity,[status(thm)],[983])).
% 0.65/0.71 tff(985,plain,
% 0.65/0.71 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1168) | c2_1(a1168) | (~c0_1(a1168)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168)))),
% 0.65/0.71 inference(transitivity,[status(thm)],[984, 982])).
% 0.65/0.71 tff(986,plain,
% 0.65/0.71 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1168) | c2_1(a1168) | (~c0_1(a1168)))),
% 0.65/0.71 inference(quant_inst,[status(thm)],[])).
% 0.65/0.71 tff(987,plain,
% 0.65/0.71 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c2_1(a1168) | (~ndr1_0) | c3_1(a1168) | (~c0_1(a1168))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[986, 985])).
% 0.65/0.71 tff(988,plain,
% 0.65/0.71 (hskp22 | hskp14 | c3_1(a1168)),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[987, 187, 551, 528, 294])).
% 0.65/0.71 tff(989,plain,
% 0.65/0.71 (c3_1(a1168)),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[988, 277, 85])).
% 0.65/0.71 tff(990,assumption,(hskp6), introduced(assumption)).
% 0.65/0.71 tff(991,plain,
% 0.65/0.71 (~c3_1(a1178)),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[970, 990])).
% 0.65/0.71 tff(992,plain,
% 0.65/0.71 (((~hskp6) | c2_1(a1178)) <=> ((~hskp6) | c2_1(a1178))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(993,axiom,((~hskp6) | c2_1(a1178)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.65/0.71 tff(994,plain,
% 0.65/0.71 ((~hskp6) | c2_1(a1178)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[993, 992])).
% 0.65/0.71 tff(995,plain,
% 0.65/0.71 ((~hskp6) | c2_1(a1178)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[994, 992])).
% 0.65/0.71 tff(996,plain,
% 0.65/0.71 ((~hskp6) | c2_1(a1178)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[995, 992])).
% 0.65/0.71 tff(997,plain,
% 0.65/0.71 ((~hskp6) | c2_1(a1178)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[996, 992])).
% 0.65/0.71 tff(998,plain,
% 0.65/0.71 ((~hskp6) | c2_1(a1178)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[997, 992])).
% 0.65/0.71 tff(999,plain,
% 0.65/0.71 ((~hskp6) | c2_1(a1178)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[998, 992])).
% 0.65/0.71 tff(1000,plain,
% 0.65/0.71 ((~hskp6) | c2_1(a1178)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[999, 992])).
% 0.65/0.71 tff(1001,plain,
% 0.65/0.71 ((~hskp6) | c2_1(a1178)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1000, 992])).
% 0.65/0.71 tff(1002,plain,
% 0.65/0.71 (c2_1(a1178)),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[1001, 990])).
% 0.65/0.71 tff(1003,plain,
% 0.65/0.71 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | c3_1(a1178) | (~ndr1_0) | (~c0_1(a1178)) | (~c2_1(a1178)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp22 | hskp14 | c3_1(a1178) | (~ndr1_0) | (~c0_1(a1178)) | (~c2_1(a1178)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1004,plain,
% 0.65/0.71 ((hskp22 | hskp14 | (~ndr1_0) | c3_1(a1178) | (~c0_1(a1178)) | (~c2_1(a1178))) <=> (hskp22 | hskp14 | c3_1(a1178) | (~ndr1_0) | (~c0_1(a1178)) | (~c2_1(a1178)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1005,plain,
% 0.65/0.71 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1178) | (~c0_1(a1178)) | (~c2_1(a1178)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | c3_1(a1178) | (~ndr1_0) | (~c0_1(a1178)) | (~c2_1(a1178))))),
% 0.65/0.71 inference(monotonicity,[status(thm)],[1004])).
% 0.65/0.71 tff(1006,plain,
% 0.65/0.71 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1178) | (~c0_1(a1178)) | (~c2_1(a1178)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp22 | hskp14 | c3_1(a1178) | (~ndr1_0) | (~c0_1(a1178)) | (~c2_1(a1178)))),
% 0.65/0.71 inference(transitivity,[status(thm)],[1005, 1003])).
% 0.65/0.71 tff(1007,plain,
% 0.65/0.71 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1178) | (~c0_1(a1178)) | (~c2_1(a1178)))),
% 0.65/0.71 inference(quant_inst,[status(thm)],[])).
% 0.65/0.71 tff(1008,plain,
% 0.65/0.71 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp22 | hskp14 | c3_1(a1178) | (~ndr1_0) | (~c0_1(a1178)) | (~c2_1(a1178))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 0.65/0.71 tff(1009,plain,
% 0.65/0.71 (~c0_1(a1178)),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[1008, 187, 277, 85, 1002, 991, 258])).
% 0.65/0.71 tff(1010,plain,
% 0.65/0.71 (((~hskp6) | c1_1(a1178)) <=> ((~hskp6) | c1_1(a1178))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1011,axiom,((~hskp6) | c1_1(a1178)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 0.65/0.71 tff(1012,plain,
% 0.65/0.71 ((~hskp6) | c1_1(a1178)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1011, 1010])).
% 0.65/0.71 tff(1013,plain,
% 0.65/0.71 ((~hskp6) | c1_1(a1178)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1012, 1010])).
% 0.65/0.71 tff(1014,plain,
% 0.65/0.71 ((~hskp6) | c1_1(a1178)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1013, 1010])).
% 0.65/0.71 tff(1015,plain,
% 0.65/0.71 ((~hskp6) | c1_1(a1178)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1014, 1010])).
% 0.65/0.71 tff(1016,plain,
% 0.65/0.71 ((~hskp6) | c1_1(a1178)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1015, 1010])).
% 0.65/0.71 tff(1017,plain,
% 0.65/0.71 ((~hskp6) | c1_1(a1178)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1016, 1010])).
% 0.65/0.71 tff(1018,plain,
% 0.65/0.71 ((~hskp6) | c1_1(a1178)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1017, 1010])).
% 0.65/0.71 tff(1019,plain,
% 0.65/0.71 ((~hskp6) | c1_1(a1178)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1018, 1010])).
% 0.65/0.71 tff(1020,plain,
% 0.65/0.71 (c1_1(a1178)),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[1019, 990])).
% 0.65/0.71 tff(1021,plain,
% 0.65/0.71 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c3_1(a1178) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | (~c1_1(a1178)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c3_1(a1178) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | (~c1_1(a1178)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1022,plain,
% 0.65/0.71 ((hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | c3_1(a1178) | (~c1_1(a1178))) <=> (hskp3 | c3_1(a1178) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | (~c1_1(a1178)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1023,plain,
% 0.65/0.71 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | c3_1(a1178) | (~c1_1(a1178)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c3_1(a1178) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | (~c1_1(a1178))))),
% 0.65/0.71 inference(monotonicity,[status(thm)],[1022])).
% 0.65/0.71 tff(1024,plain,
% 0.65/0.71 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | c3_1(a1178) | (~c1_1(a1178)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c3_1(a1178) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | (~c1_1(a1178)))),
% 0.65/0.71 inference(transitivity,[status(thm)],[1023, 1021])).
% 0.65/0.71 tff(1025,plain,
% 0.65/0.71 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1168) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | c3_1(a1178) | (~c1_1(a1178)))),
% 0.65/0.71 inference(quant_inst,[status(thm)],[])).
% 0.65/0.71 tff(1026,plain,
% 0.65/0.71 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c3_1(a1178) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c3_1(a1168)) | c0_1(a1178) | (~c1_1(a1178))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1025, 1024])).
% 0.65/0.71 tff(1027,plain,
% 0.65/0.71 ($false),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[1026, 187, 22, 1020, 540, 991, 528, 802, 1009, 989])).
% 0.65/0.71 tff(1028,plain,((~hskp6) | hskp3 | hskp22 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.65/0.71 tff(1029,plain,
% 0.65/0.71 (~hskp6),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[1028, 277, 22, 85])).
% 0.65/0.71 tff(1030,plain,
% 0.65/0.71 ((hskp21 | hskp14 | hskp6) <=> (hskp21 | hskp14 | hskp6)),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1031,plain,
% 0.65/0.71 (((hskp21 | hskp6) | hskp14) <=> (hskp21 | hskp14 | hskp6)),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1032,plain,
% 0.65/0.71 ((hskp6 | hskp21) <=> (hskp21 | hskp6)),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1033,plain,
% 0.65/0.71 (((hskp6 | hskp21) | hskp14) <=> ((hskp21 | hskp6) | hskp14)),
% 0.65/0.71 inference(monotonicity,[status(thm)],[1032])).
% 0.65/0.71 tff(1034,plain,
% 0.65/0.71 (((hskp6 | hskp21) | hskp14) <=> (hskp21 | hskp14 | hskp6)),
% 0.65/0.71 inference(transitivity,[status(thm)],[1033, 1031])).
% 0.65/0.71 tff(1035,axiom,((hskp6 | hskp21) | hskp14), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 0.65/0.71 tff(1036,plain,
% 0.65/0.71 (hskp21 | hskp14 | hskp6),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 0.65/0.71 tff(1037,plain,
% 0.65/0.71 (hskp21 | hskp14 | hskp6),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1036, 1030])).
% 0.65/0.71 tff(1038,plain,
% 0.65/0.71 (hskp21 | hskp14 | hskp6),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1037, 1030])).
% 0.65/0.71 tff(1039,plain,
% 0.65/0.71 (hskp21 | hskp14 | hskp6),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1038, 1030])).
% 0.65/0.71 tff(1040,plain,
% 0.65/0.71 (hskp21 | hskp14 | hskp6),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1039, 1030])).
% 0.65/0.71 tff(1041,plain,
% 0.65/0.71 (hskp21 | hskp14 | hskp6),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1040, 1030])).
% 0.65/0.71 tff(1042,plain,
% 0.65/0.71 (hskp21 | hskp14 | hskp6),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1041, 1030])).
% 0.65/0.71 tff(1043,plain,
% 0.65/0.71 (hskp21 | hskp14 | hskp6),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1042, 1030])).
% 0.65/0.71 tff(1044,plain,
% 0.65/0.71 (hskp21),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[1043, 1029, 85])).
% 0.65/0.71 tff(1045,plain,
% 0.65/0.71 (((~hskp21) | (~c1_1(a1207))) <=> ((~hskp21) | (~c1_1(a1207)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1046,plain,
% 0.65/0.71 (((~c1_1(a1207)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a1207)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1047,axiom,((~c1_1(a1207)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.65/0.71 tff(1048,plain,
% 0.65/0.71 ((~hskp21) | (~c1_1(a1207))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1047, 1046])).
% 0.65/0.71 tff(1049,plain,
% 0.65/0.71 ((~hskp21) | (~c1_1(a1207))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1048, 1045])).
% 0.65/0.71 tff(1050,plain,
% 0.65/0.71 (~c1_1(a1207)),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[1049, 1044])).
% 0.65/0.71 tff(1051,plain,
% 0.65/0.71 (((~hskp21) | c3_1(a1207)) <=> ((~hskp21) | c3_1(a1207))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1052,axiom,((~hskp21) | c3_1(a1207)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.65/0.71 tff(1053,plain,
% 0.65/0.71 ((~hskp21) | c3_1(a1207)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1052, 1051])).
% 0.65/0.71 tff(1054,plain,
% 0.65/0.71 ((~hskp21) | c3_1(a1207)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1053, 1051])).
% 0.65/0.71 tff(1055,plain,
% 0.65/0.71 ((~hskp21) | c3_1(a1207)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1054, 1051])).
% 0.65/0.71 tff(1056,plain,
% 0.65/0.71 ((~hskp21) | c3_1(a1207)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1055, 1051])).
% 0.65/0.71 tff(1057,plain,
% 0.65/0.71 ((~hskp21) | c3_1(a1207)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1056, 1051])).
% 0.65/0.71 tff(1058,plain,
% 0.65/0.71 ((~hskp21) | c3_1(a1207)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1057, 1051])).
% 0.65/0.71 tff(1059,plain,
% 0.65/0.71 ((~hskp21) | c3_1(a1207)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1058, 1051])).
% 0.65/0.71 tff(1060,plain,
% 0.65/0.71 ((~hskp21) | c3_1(a1207)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1059, 1051])).
% 0.65/0.71 tff(1061,plain,
% 0.65/0.71 (c3_1(a1207)),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[1060, 1044])).
% 0.65/0.71 tff(1062,plain,
% 0.65/0.71 (((~hskp21) | c2_1(a1207)) <=> ((~hskp21) | c2_1(a1207))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1063,axiom,((~hskp21) | c2_1(a1207)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.65/0.71 tff(1064,plain,
% 0.65/0.71 ((~hskp21) | c2_1(a1207)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1063, 1062])).
% 0.65/0.71 tff(1065,plain,
% 0.65/0.71 ((~hskp21) | c2_1(a1207)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1064, 1062])).
% 0.65/0.71 tff(1066,plain,
% 0.65/0.71 ((~hskp21) | c2_1(a1207)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1065, 1062])).
% 0.65/0.71 tff(1067,plain,
% 0.65/0.71 ((~hskp21) | c2_1(a1207)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1066, 1062])).
% 0.65/0.71 tff(1068,plain,
% 0.65/0.71 ((~hskp21) | c2_1(a1207)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1067, 1062])).
% 0.65/0.71 tff(1069,plain,
% 0.65/0.71 ((~hskp21) | c2_1(a1207)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1068, 1062])).
% 0.65/0.71 tff(1070,plain,
% 0.65/0.71 ((~hskp21) | c2_1(a1207)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1069, 1062])).
% 0.65/0.71 tff(1071,plain,
% 0.65/0.71 ((~hskp21) | c2_1(a1207)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1070, 1062])).
% 0.65/0.71 tff(1072,plain,
% 0.65/0.71 (c2_1(a1207)),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[1071, 1044])).
% 0.65/0.71 tff(1073,plain,
% 0.65/0.71 (^[U: $i] : refl((hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))),
% 0.65/0.71 inference(bind,[status(th)],[])).
% 0.65/0.71 tff(1074,plain,
% 0.65/0.71 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.65/0.71 inference(quant_intro,[status(thm)],[1073])).
% 0.65/0.71 tff(1075,plain,
% 0.65/0.71 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1076,plain,
% 0.65/0.71 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_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))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp6) <=> ((hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp6))), rewrite(((hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp6) <=> (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp6) <=> (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))))),
% 0.65/0.71 inference(bind,[status(th)],[])).
% 0.65/0.71 tff(1077,plain,
% 0.65/0.71 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp6) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.65/0.71 inference(quant_intro,[status(thm)],[1076])).
% 0.65/0.71 tff(1078,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.65/0.71 tff(1079,plain,
% 0.65/0.71 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 0.65/0.71 tff(1080,plain,
% 0.65/0.71 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1079, 1075])).
% 0.65/0.71 tff(1081,plain,(
% 0.65/0.71 ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.65/0.71 inference(skolemize,[status(sab)],[1080])).
% 0.65/0.71 tff(1082,plain,
% 0.65/0.71 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1081, 1074])).
% 0.65/0.71 tff(1083,assumption,(hskp12), introduced(assumption)).
% 0.65/0.71 tff(1084,plain,
% 0.65/0.71 (((~hskp12) | (~c3_1(a1187))) <=> ((~hskp12) | (~c3_1(a1187)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1085,plain,
% 0.65/0.71 (((~c3_1(a1187)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a1187)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1086,axiom,((~c3_1(a1187)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.65/0.71 tff(1087,plain,
% 0.65/0.71 ((~hskp12) | (~c3_1(a1187))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 0.65/0.71 tff(1088,plain,
% 0.65/0.71 ((~hskp12) | (~c3_1(a1187))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1087, 1084])).
% 0.65/0.71 tff(1089,plain,
% 0.65/0.71 (~c3_1(a1187)),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[1088, 1083])).
% 0.65/0.71 tff(1090,plain,
% 0.65/0.71 (((~hskp12) | (~c2_1(a1187))) <=> ((~hskp12) | (~c2_1(a1187)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1091,plain,
% 0.65/0.71 (((~c2_1(a1187)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a1187)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1092,axiom,((~c2_1(a1187)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.65/0.71 tff(1093,plain,
% 0.65/0.71 ((~hskp12) | (~c2_1(a1187))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 0.65/0.71 tff(1094,plain,
% 0.65/0.71 ((~hskp12) | (~c2_1(a1187))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1093, 1090])).
% 0.65/0.71 tff(1095,plain,
% 0.65/0.71 (~c2_1(a1187)),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[1094, 1083])).
% 0.65/0.71 tff(1096,plain,
% 0.65/0.71 (((~hskp12) | (~c0_1(a1187))) <=> ((~hskp12) | (~c0_1(a1187)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1097,plain,
% 0.65/0.71 (((~c0_1(a1187)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a1187)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1098,axiom,((~c0_1(a1187)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.65/0.71 tff(1099,plain,
% 0.65/0.71 ((~hskp12) | (~c0_1(a1187))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 0.65/0.71 tff(1100,plain,
% 0.65/0.71 ((~hskp12) | (~c0_1(a1187))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1099, 1096])).
% 0.65/0.71 tff(1101,plain,
% 0.65/0.71 (~c0_1(a1187)),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[1100, 1083])).
% 0.65/0.71 tff(1102,assumption,(~hskp6), introduced(assumption)).
% 0.65/0.71 tff(1103,plain,
% 0.65/0.71 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | c0_1(a1187) | c2_1(a1187) | c3_1(a1187) | (~ndr1_0))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | hskp3 | c0_1(a1187) | c2_1(a1187) | c3_1(a1187) | (~ndr1_0))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1104,plain,
% 0.65/0.71 ((hskp6 | hskp3 | (~ndr1_0) | c3_1(a1187) | c0_1(a1187) | c2_1(a1187)) <=> (hskp6 | hskp3 | c0_1(a1187) | c2_1(a1187) | c3_1(a1187) | (~ndr1_0))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1105,plain,
% 0.65/0.71 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | (~ndr1_0) | c3_1(a1187) | c0_1(a1187) | c2_1(a1187))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | c0_1(a1187) | c2_1(a1187) | c3_1(a1187) | (~ndr1_0)))),
% 0.65/0.71 inference(monotonicity,[status(thm)],[1104])).
% 0.65/0.71 tff(1106,plain,
% 0.65/0.71 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | (~ndr1_0) | c3_1(a1187) | c0_1(a1187) | c2_1(a1187))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | hskp3 | c0_1(a1187) | c2_1(a1187) | c3_1(a1187) | (~ndr1_0))),
% 0.65/0.71 inference(transitivity,[status(thm)],[1105, 1103])).
% 0.65/0.71 tff(1107,plain,
% 0.65/0.71 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | (~ndr1_0) | c3_1(a1187) | c0_1(a1187) | c2_1(a1187))),
% 0.65/0.71 inference(quant_inst,[status(thm)],[])).
% 0.65/0.71 tff(1108,plain,
% 0.65/0.71 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | hskp3 | c0_1(a1187) | c2_1(a1187) | c3_1(a1187) | (~ndr1_0)),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1107, 1106])).
% 0.65/0.71 tff(1109,plain,
% 0.65/0.71 ($false),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[1108, 187, 1102, 22, 1101, 1095, 1089, 1082])).
% 0.65/0.71 tff(1110,plain,((~hskp12) | hskp6 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.65/0.71 tff(1111,plain,
% 0.65/0.71 (~hskp12),
% 0.65/0.71 inference(unit_resolution,[status(thm)],[1110, 1029, 22])).
% 0.65/0.71 tff(1112,plain,
% 0.65/0.71 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | hskp12 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | (~c2_1(a1207)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | (~c2_1(a1207)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1113,plain,
% 0.65/0.71 ((hskp20 | hskp12 | (~ndr1_0) | c1_1(a1207) | (~c3_1(a1207)) | (~c2_1(a1207))) <=> (hskp20 | hskp12 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | (~c2_1(a1207)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(1114,plain,
% 0.65/0.71 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c1_1(a1207) | (~c3_1(a1207)) | (~c2_1(a1207)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | hskp12 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | (~c2_1(a1207))))),
% 0.65/0.71 inference(monotonicity,[status(thm)],[1113])).
% 0.65/0.71 tff(1115,plain,
% 0.65/0.71 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c1_1(a1207) | (~c3_1(a1207)) | (~c2_1(a1207)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | (~c2_1(a1207)))),
% 0.65/0.71 inference(transitivity,[status(thm)],[1114, 1112])).
% 0.65/0.71 tff(1116,plain,
% 0.65/0.71 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c1_1(a1207) | (~c3_1(a1207)) | (~c2_1(a1207)))),
% 0.65/0.71 inference(quant_inst,[status(thm)],[])).
% 0.65/0.71 tff(1117,plain,
% 0.65/0.71 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp20 | hskp12 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | (~c2_1(a1207))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[1116, 1115])).
% 0.65/0.71 tff(1118,plain,
% 0.65/0.72 (hskp20),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[1117, 187, 1111, 1072, 1061, 1050, 981])).
% 0.65/0.72 tff(1119,plain,
% 0.65/0.72 (((~hskp20) | (~c2_1(a1205))) <=> ((~hskp20) | (~c2_1(a1205)))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1120,plain,
% 0.65/0.72 (((~c2_1(a1205)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a1205)))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1121,axiom,((~c2_1(a1205)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.65/0.72 tff(1122,plain,
% 0.65/0.72 ((~hskp20) | (~c2_1(a1205))),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 0.65/0.72 tff(1123,plain,
% 0.65/0.72 ((~hskp20) | (~c2_1(a1205))),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1122, 1119])).
% 0.65/0.72 tff(1124,plain,
% 0.65/0.72 (~c2_1(a1205)),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[1123, 1118])).
% 0.65/0.72 tff(1125,plain,
% 0.65/0.72 (((~hskp20) | c3_1(a1205)) <=> ((~hskp20) | c3_1(a1205))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1126,axiom,((~hskp20) | c3_1(a1205)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.65/0.72 tff(1127,plain,
% 0.65/0.72 ((~hskp20) | c3_1(a1205)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 0.65/0.72 tff(1128,plain,
% 0.65/0.72 ((~hskp20) | c3_1(a1205)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1127, 1125])).
% 0.65/0.72 tff(1129,plain,
% 0.65/0.72 ((~hskp20) | c3_1(a1205)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1128, 1125])).
% 0.65/0.72 tff(1130,plain,
% 0.65/0.72 ((~hskp20) | c3_1(a1205)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1129, 1125])).
% 0.65/0.72 tff(1131,plain,
% 0.65/0.72 ((~hskp20) | c3_1(a1205)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1130, 1125])).
% 0.65/0.72 tff(1132,plain,
% 0.65/0.72 ((~hskp20) | c3_1(a1205)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1131, 1125])).
% 0.65/0.72 tff(1133,plain,
% 0.65/0.72 ((~hskp20) | c3_1(a1205)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1132, 1125])).
% 0.65/0.72 tff(1134,plain,
% 0.65/0.72 ((~hskp20) | c3_1(a1205)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1133, 1125])).
% 0.65/0.72 tff(1135,plain,
% 0.65/0.72 (c3_1(a1205)),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[1134, 1118])).
% 0.65/0.72 tff(1136,plain,
% 0.65/0.72 (((~hskp20) | c1_1(a1205)) <=> ((~hskp20) | c1_1(a1205))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1137,axiom,((~hskp20) | c1_1(a1205)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.65/0.72 tff(1138,plain,
% 0.65/0.72 ((~hskp20) | c1_1(a1205)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 0.65/0.72 tff(1139,plain,
% 0.65/0.72 ((~hskp20) | c1_1(a1205)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1138, 1136])).
% 0.65/0.72 tff(1140,plain,
% 0.65/0.72 ((~hskp20) | c1_1(a1205)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1139, 1136])).
% 0.65/0.72 tff(1141,plain,
% 0.65/0.72 ((~hskp20) | c1_1(a1205)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1140, 1136])).
% 0.65/0.72 tff(1142,plain,
% 0.65/0.72 ((~hskp20) | c1_1(a1205)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1141, 1136])).
% 0.65/0.72 tff(1143,plain,
% 0.65/0.72 ((~hskp20) | c1_1(a1205)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1142, 1136])).
% 0.65/0.72 tff(1144,plain,
% 0.65/0.72 ((~hskp20) | c1_1(a1205)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1143, 1136])).
% 0.65/0.72 tff(1145,plain,
% 0.65/0.72 ((~hskp20) | c1_1(a1205)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1144, 1136])).
% 0.65/0.72 tff(1146,plain,
% 0.65/0.72 (c1_1(a1205)),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[1145, 1118])).
% 0.65/0.72 tff(1147,plain,
% 0.65/0.72 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | c2_1(a1200) | (~ndr1_0) | c3_1(a1200) | (~c0_1(a1200)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c2_1(a1200) | (~ndr1_0) | c3_1(a1200) | (~c0_1(a1200)))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1148,plain,
% 0.65/0.72 ((hskp22 | hskp14 | (~ndr1_0) | c3_1(a1200) | c2_1(a1200) | (~c0_1(a1200))) <=> (hskp22 | hskp14 | c2_1(a1200) | (~ndr1_0) | c3_1(a1200) | (~c0_1(a1200)))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1149,plain,
% 0.65/0.72 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1200) | c2_1(a1200) | (~c0_1(a1200)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | c2_1(a1200) | (~ndr1_0) | c3_1(a1200) | (~c0_1(a1200))))),
% 0.65/0.72 inference(monotonicity,[status(thm)],[1148])).
% 0.65/0.72 tff(1150,plain,
% 0.65/0.72 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1200) | c2_1(a1200) | (~c0_1(a1200)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c2_1(a1200) | (~ndr1_0) | c3_1(a1200) | (~c0_1(a1200)))),
% 0.65/0.72 inference(transitivity,[status(thm)],[1149, 1147])).
% 0.65/0.72 tff(1151,plain,
% 0.65/0.72 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1200) | c2_1(a1200) | (~c0_1(a1200)))),
% 0.65/0.72 inference(quant_inst,[status(thm)],[])).
% 0.65/0.72 tff(1152,plain,
% 0.65/0.72 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c2_1(a1200) | (~ndr1_0) | c3_1(a1200) | (~c0_1(a1200))),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 0.65/0.72 tff(1153,plain,
% 0.65/0.72 (c3_1(a1200)),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[1152, 187, 277, 85, 377, 360, 294])).
% 0.65/0.72 tff(1154,plain,
% 0.65/0.72 ($false),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[947, 187, 377, 551, 540, 366, 360, 528, 63, 1153])).
% 0.65/0.72 tff(1155,plain,((~hskp17) | hskp22 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.65/0.72 tff(1156,plain,
% 0.65/0.72 (~hskp17),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[1155, 277, 85])).
% 0.65/0.72 tff(1157,plain,
% 0.65/0.72 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1158,plain,
% 0.65/0.72 ((hskp22 | hskp14 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169))) <=> (hskp22 | hskp14 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1159,plain,
% 0.65/0.72 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169))))),
% 0.65/0.72 inference(monotonicity,[status(thm)],[1158])).
% 0.65/0.72 tff(1160,plain,
% 0.65/0.72 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169)))),
% 0.65/0.72 inference(transitivity,[status(thm)],[1159, 1157])).
% 0.65/0.72 tff(1161,plain,
% 0.65/0.72 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a1169) | c2_1(a1169) | (~c0_1(a1169)))),
% 0.65/0.72 inference(quant_inst,[status(thm)],[])).
% 0.65/0.72 tff(1162,plain,
% 0.65/0.72 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp14 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | (~c0_1(a1169))),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1161, 1160])).
% 0.65/0.72 tff(1163,plain,
% 0.65/0.72 (~c0_1(a1169)),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[1162, 187, 277, 85, 429, 428, 294])).
% 0.65/0.72 tff(1164,plain,
% 0.65/0.72 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | hskp3 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1165,plain,
% 0.65/0.72 ((hskp6 | hskp3 | (~ndr1_0) | c3_1(a1169) | c0_1(a1169) | c2_1(a1169)) <=> (hskp6 | hskp3 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1166,plain,
% 0.65/0.72 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | (~ndr1_0) | c3_1(a1169) | c0_1(a1169) | c2_1(a1169))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169)))),
% 0.65/0.72 inference(monotonicity,[status(thm)],[1165])).
% 0.65/0.72 tff(1167,plain,
% 0.65/0.72 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | (~ndr1_0) | c3_1(a1169) | c0_1(a1169) | c2_1(a1169))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | hskp3 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169))),
% 0.65/0.72 inference(transitivity,[status(thm)],[1166, 1164])).
% 0.65/0.72 tff(1168,plain,
% 0.65/0.72 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp6 | hskp3 | (~ndr1_0) | c3_1(a1169) | c0_1(a1169) | c2_1(a1169))),
% 0.65/0.72 inference(quant_inst,[status(thm)],[])).
% 0.65/0.72 tff(1169,plain,
% 0.65/0.72 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp6 | hskp3 | c2_1(a1169) | c3_1(a1169) | (~ndr1_0) | c0_1(a1169)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1168, 1167])).
% 0.65/0.72 tff(1170,plain,
% 0.65/0.72 ($false),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[1169, 187, 1029, 22, 429, 428, 1082, 1163])).
% 0.65/0.72 tff(1171,plain,((~hskp1) | hskp3 | hskp22 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.65/0.72 tff(1172,plain,
% 0.65/0.72 (~hskp1),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[1171, 277, 22, 85])).
% 0.65/0.72 tff(1173,plain,
% 0.65/0.72 (hskp16),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[449, 1172, 1156])).
% 0.65/0.72 tff(1174,plain,
% 0.65/0.72 (~c3_1(a1199)),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[455, 1173])).
% 0.65/0.72 tff(1175,plain,
% 0.65/0.72 (~c0_1(a1199)),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[461, 1173])).
% 0.65/0.72 tff(1176,plain,
% 0.65/0.72 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a1205) | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | (~c1_1(a1199)) | (~c1_1(a1205)) | (~c3_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1205) | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | (~c1_1(a1199)) | (~c1_1(a1205)) | (~c3_1(a1205)))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1177,plain,
% 0.65/0.72 ((hskp3 | (~ndr1_0) | c2_1(a1205) | (~c1_1(a1205)) | (~c3_1(a1205)) | c0_1(a1199) | c3_1(a1199) | (~c1_1(a1199))) <=> (hskp3 | c2_1(a1205) | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | (~c1_1(a1199)) | (~c1_1(a1205)) | (~c3_1(a1205)))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1178,plain,
% 0.65/0.72 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1205) | (~c1_1(a1205)) | (~c3_1(a1205)) | c0_1(a1199) | c3_1(a1199) | (~c1_1(a1199)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a1205) | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | (~c1_1(a1199)) | (~c1_1(a1205)) | (~c3_1(a1205))))),
% 0.65/0.72 inference(monotonicity,[status(thm)],[1177])).
% 0.65/0.72 tff(1179,plain,
% 0.65/0.72 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1205) | (~c1_1(a1205)) | (~c3_1(a1205)) | c0_1(a1199) | c3_1(a1199) | (~c1_1(a1199)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1205) | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | (~c1_1(a1199)) | (~c1_1(a1205)) | (~c3_1(a1205)))),
% 0.65/0.72 inference(transitivity,[status(thm)],[1178, 1176])).
% 0.65/0.72 tff(1180,plain,
% 0.65/0.72 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1205) | (~c1_1(a1205)) | (~c3_1(a1205)) | c0_1(a1199) | c3_1(a1199) | (~c1_1(a1199)))),
% 0.65/0.72 inference(quant_inst,[status(thm)],[])).
% 0.65/0.72 tff(1181,plain,
% 0.65/0.72 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1205) | c0_1(a1199) | c3_1(a1199) | (~ndr1_0) | (~c1_1(a1199)) | (~c1_1(a1205)) | (~c3_1(a1205))),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 0.65/0.72 tff(1182,plain,
% 0.65/0.72 (~c1_1(a1199)),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[1181, 187, 22, 1146, 1135, 1124, 1175, 1174, 802])).
% 0.65/0.72 tff(1183,plain,
% 0.65/0.72 (c2_1(a1199)),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[479, 1173])).
% 0.65/0.72 tff(1184,plain,
% 0.65/0.72 (~hskp2),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[729, 1183, 1175, 1174, 1182])).
% 0.65/0.72 tff(1185,plain,
% 0.65/0.72 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1207)) | (~c0_1(a1207)) | (~c2_1(a1207)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1207)) | (~c0_1(a1207)) | (~c2_1(a1207)))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1186,plain,
% 0.65/0.72 ((hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1207)) | (~c3_1(a1207)) | (~c2_1(a1207))) <=> (hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1207)) | (~c0_1(a1207)) | (~c2_1(a1207)))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1187,plain,
% 0.65/0.72 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1207)) | (~c3_1(a1207)) | (~c2_1(a1207)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1207)) | (~c0_1(a1207)) | (~c2_1(a1207))))),
% 0.65/0.72 inference(monotonicity,[status(thm)],[1186])).
% 0.65/0.72 tff(1188,plain,
% 0.65/0.72 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1207)) | (~c3_1(a1207)) | (~c2_1(a1207)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1207)) | (~c0_1(a1207)) | (~c2_1(a1207)))),
% 0.65/0.72 inference(transitivity,[status(thm)],[1187, 1185])).
% 0.65/0.72 tff(1189,plain,
% 0.65/0.72 ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1207)) | (~c3_1(a1207)) | (~c2_1(a1207)))),
% 0.65/0.72 inference(quant_inst,[status(thm)],[])).
% 0.65/0.72 tff(1190,plain,
% 0.65/0.72 ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1207)) | (~c0_1(a1207)) | (~c2_1(a1207))),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 0.65/0.72 tff(1191,plain,
% 0.65/0.72 (hskp2 | (~c0_1(a1207))),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[1190, 187, 277, 1072, 1061, 792])).
% 0.65/0.72 tff(1192,plain,
% 0.65/0.72 (~c0_1(a1207)),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[1191, 1184])).
% 0.65/0.72 tff(1193,plain,
% 0.65/0.72 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.65/0.72 inference(bind,[status(th)],[])).
% 0.65/0.72 tff(1194,plain,
% 0.65/0.72 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.65/0.72 inference(quant_intro,[status(thm)],[1193])).
% 0.65/0.72 tff(1195,plain,
% 0.65/0.72 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1196,plain,
% 0.65/0.72 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.65/0.72 inference(bind,[status(th)],[])).
% 0.65/0.72 tff(1197,plain,
% 0.65/0.72 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.65/0.72 inference(quant_intro,[status(thm)],[1196])).
% 0.65/0.72 tff(1198,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 0.65/0.72 tff(1199,plain,
% 0.65/0.72 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 0.65/0.72 tff(1200,plain,
% 0.65/0.72 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1199, 1195])).
% 0.65/0.72 tff(1201,plain,(
% 0.65/0.72 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.65/0.72 inference(skolemize,[status(sab)],[1200])).
% 0.65/0.72 tff(1202,plain,
% 0.65/0.72 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1201, 1194])).
% 0.65/0.72 tff(1203,plain,
% 0.65/0.72 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1207) | (~c2_1(a1207)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1207) | (~c2_1(a1207)))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1204,plain,
% 0.65/0.72 ((hskp4 | (~ndr1_0) | c1_1(a1207) | c0_1(a1207) | (~c3_1(a1207)) | c1_1(a1207) | c0_1(a1207) | (~c2_1(a1207))) <=> (hskp4 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1207) | (~c2_1(a1207)))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1205,plain,
% 0.65/0.72 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a1207) | c0_1(a1207) | (~c3_1(a1207)) | c1_1(a1207) | c0_1(a1207) | (~c2_1(a1207)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1207) | (~c2_1(a1207))))),
% 0.65/0.72 inference(monotonicity,[status(thm)],[1204])).
% 0.65/0.72 tff(1206,plain,
% 0.65/0.72 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a1207) | c0_1(a1207) | (~c3_1(a1207)) | c1_1(a1207) | c0_1(a1207) | (~c2_1(a1207)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1207) | (~c2_1(a1207)))),
% 0.65/0.72 inference(transitivity,[status(thm)],[1205, 1203])).
% 0.65/0.72 tff(1207,plain,
% 0.65/0.72 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a1207) | c0_1(a1207) | (~c3_1(a1207)) | c1_1(a1207) | c0_1(a1207) | (~c2_1(a1207)))),
% 0.65/0.72 inference(quant_inst,[status(thm)],[])).
% 0.65/0.72 tff(1208,plain,
% 0.65/0.72 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a1207) | (~ndr1_0) | (~c3_1(a1207)) | c0_1(a1207) | (~c2_1(a1207))),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 0.65/0.72 tff(1209,plain,
% 0.65/0.72 (hskp4 | c0_1(a1207)),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[1208, 187, 1072, 1061, 1050, 1202])).
% 0.65/0.72 tff(1210,plain,
% 0.65/0.72 (hskp4),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[1209, 1192])).
% 0.65/0.72 tff(1211,plain,
% 0.65/0.72 (((~hskp4) | (~c0_1(a1175))) <=> ((~hskp4) | (~c0_1(a1175)))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1212,plain,
% 0.65/0.72 (((~c0_1(a1175)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a1175)))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1213,axiom,((~c0_1(a1175)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.65/0.72 tff(1214,plain,
% 0.65/0.72 ((~hskp4) | (~c0_1(a1175))),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1213, 1212])).
% 0.65/0.72 tff(1215,plain,
% 0.65/0.72 ((~hskp4) | (~c0_1(a1175))),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1214, 1211])).
% 0.65/0.72 tff(1216,plain,
% 0.65/0.72 (~c0_1(a1175)),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[1215, 1210])).
% 0.65/0.72 tff(1217,assumption,(~c2_1(a1205)), introduced(assumption)).
% 0.65/0.72 tff(1218,assumption,(c3_1(a1205)), introduced(assumption)).
% 0.65/0.72 tff(1219,assumption,(c1_1(a1205)), introduced(assumption)).
% 0.65/0.72 tff(1220,assumption,(~c0_1(a1175)), introduced(assumption)).
% 0.65/0.72 tff(1221,assumption,(hskp4), introduced(assumption)).
% 0.65/0.72 tff(1222,plain,
% 0.65/0.72 (((~hskp4) | c2_1(a1175)) <=> ((~hskp4) | c2_1(a1175))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1223,axiom,((~hskp4) | c2_1(a1175)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.65/0.72 tff(1224,plain,
% 0.65/0.72 ((~hskp4) | c2_1(a1175)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 0.65/0.72 tff(1225,plain,
% 0.65/0.72 ((~hskp4) | c2_1(a1175)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1224, 1222])).
% 0.65/0.72 tff(1226,plain,
% 0.65/0.72 ((~hskp4) | c2_1(a1175)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1225, 1222])).
% 0.65/0.72 tff(1227,plain,
% 0.65/0.72 ((~hskp4) | c2_1(a1175)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1226, 1222])).
% 0.65/0.72 tff(1228,plain,
% 0.65/0.72 ((~hskp4) | c2_1(a1175)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1227, 1222])).
% 0.65/0.72 tff(1229,plain,
% 0.65/0.72 ((~hskp4) | c2_1(a1175)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1228, 1222])).
% 0.65/0.72 tff(1230,plain,
% 0.65/0.72 ((~hskp4) | c2_1(a1175)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1229, 1222])).
% 0.65/0.72 tff(1231,plain,
% 0.65/0.72 ((~hskp4) | c2_1(a1175)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1230, 1222])).
% 0.65/0.72 tff(1232,plain,
% 0.65/0.72 (c2_1(a1175)),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[1231, 1221])).
% 0.65/0.72 tff(1233,plain,
% 0.65/0.72 (((~hskp4) | c1_1(a1175)) <=> ((~hskp4) | c1_1(a1175))),
% 0.65/0.72 inference(rewrite,[status(thm)],[])).
% 0.65/0.72 tff(1234,axiom,((~hskp4) | c1_1(a1175)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.65/0.72 tff(1235,plain,
% 0.65/0.72 ((~hskp4) | c1_1(a1175)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1234, 1233])).
% 0.65/0.72 tff(1236,plain,
% 0.65/0.72 ((~hskp4) | c1_1(a1175)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1235, 1233])).
% 0.65/0.72 tff(1237,plain,
% 0.65/0.72 ((~hskp4) | c1_1(a1175)),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[1236, 1233])).
% 0.65/0.73 tff(1238,plain,
% 0.65/0.73 ((~hskp4) | c1_1(a1175)),
% 0.65/0.73 inference(modus_ponens,[status(thm)],[1237, 1233])).
% 0.65/0.73 tff(1239,plain,
% 0.65/0.73 ((~hskp4) | c1_1(a1175)),
% 0.65/0.73 inference(modus_ponens,[status(thm)],[1238, 1233])).
% 0.65/0.73 tff(1240,plain,
% 0.65/0.73 ((~hskp4) | c1_1(a1175)),
% 0.65/0.73 inference(modus_ponens,[status(thm)],[1239, 1233])).
% 0.65/0.73 tff(1241,plain,
% 0.65/0.73 ((~hskp4) | c1_1(a1175)),
% 0.65/0.73 inference(modus_ponens,[status(thm)],[1240, 1233])).
% 0.65/0.73 tff(1242,plain,
% 0.65/0.73 ((~hskp4) | c1_1(a1175)),
% 0.65/0.73 inference(modus_ponens,[status(thm)],[1241, 1233])).
% 0.65/0.73 tff(1243,plain,
% 0.65/0.73 (c1_1(a1175)),
% 0.65/0.73 inference(unit_resolution,[status(thm)],[1242, 1221])).
% 0.65/0.73 tff(1244,plain,
% 0.65/0.73 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a1205) | c0_1(a1175) | (~ndr1_0) | c3_1(a1175) | (~c1_1(a1175)) | (~c1_1(a1205)) | (~c3_1(a1205)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1205) | c0_1(a1175) | (~ndr1_0) | c3_1(a1175) | (~c1_1(a1175)) | (~c1_1(a1205)) | (~c3_1(a1205)))),
% 0.65/0.73 inference(rewrite,[status(thm)],[])).
% 0.65/0.73 tff(1245,plain,
% 0.65/0.73 ((hskp3 | (~ndr1_0) | c2_1(a1205) | (~c1_1(a1205)) | (~c3_1(a1205)) | c0_1(a1175) | c3_1(a1175) | (~c1_1(a1175))) <=> (hskp3 | c2_1(a1205) | c0_1(a1175) | (~ndr1_0) | c3_1(a1175) | (~c1_1(a1175)) | (~c1_1(a1205)) | (~c3_1(a1205)))),
% 0.65/0.73 inference(rewrite,[status(thm)],[])).
% 0.65/0.73 tff(1246,plain,
% 0.65/0.73 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1205) | (~c1_1(a1205)) | (~c3_1(a1205)) | c0_1(a1175) | c3_1(a1175) | (~c1_1(a1175)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a1205) | c0_1(a1175) | (~ndr1_0) | c3_1(a1175) | (~c1_1(a1175)) | (~c1_1(a1205)) | (~c3_1(a1205))))),
% 0.65/0.73 inference(monotonicity,[status(thm)],[1245])).
% 0.65/0.73 tff(1247,plain,
% 0.65/0.73 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1205) | (~c1_1(a1205)) | (~c3_1(a1205)) | c0_1(a1175) | c3_1(a1175) | (~c1_1(a1175)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1205) | c0_1(a1175) | (~ndr1_0) | c3_1(a1175) | (~c1_1(a1175)) | (~c1_1(a1205)) | (~c3_1(a1205)))),
% 0.65/0.73 inference(transitivity,[status(thm)],[1246, 1244])).
% 0.65/0.73 tff(1248,plain,
% 0.65/0.73 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a1205) | (~c1_1(a1205)) | (~c3_1(a1205)) | c0_1(a1175) | c3_1(a1175) | (~c1_1(a1175)))),
% 0.65/0.73 inference(quant_inst,[status(thm)],[])).
% 0.65/0.73 tff(1249,plain,
% 0.65/0.73 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a1205) | c0_1(a1175) | (~ndr1_0) | c3_1(a1175) | (~c1_1(a1175)) | (~c1_1(a1205)) | (~c3_1(a1205))),
% 0.65/0.73 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 0.65/0.73 tff(1250,plain,
% 0.65/0.73 (c3_1(a1175) | (~c1_1(a1175))),
% 0.65/0.73 inference(unit_resolution,[status(thm)],[1249, 187, 22, 1219, 1218, 1217, 1220, 802])).
% 0.65/0.73 tff(1251,plain,
% 0.65/0.73 (c3_1(a1175)),
% 0.65/0.73 inference(unit_resolution,[status(thm)],[1250, 1243])).
% 0.65/0.73 tff(1252,plain,
% 0.65/0.73 (~c1_1(a1199)),
% 0.65/0.73 inference(unit_resolution,[status(thm)],[1181, 187, 22, 1219, 1218, 1217, 907, 906, 802])).
% 0.65/0.73 tff(1253,assumption,(c3_1(a1175)), introduced(assumption)).
% 0.65/0.73 tff(1254,assumption,(c2_1(a1175)), introduced(assumption)).
% 0.65/0.73 tff(1255,plain,
% 0.65/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1199) | c3_1(a1199) | c0_1(a1175) | (~ndr1_0) | (~c3_1(a1175)) | (~c2_1(a1175)) | c1_1(a1199) | (~c2_1(a1199)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1199) | c3_1(a1199) | c0_1(a1175) | (~ndr1_0) | (~c3_1(a1175)) | (~c2_1(a1175)) | c1_1(a1199) | (~c2_1(a1199)))),
% 0.65/0.73 inference(rewrite,[status(thm)],[])).
% 0.65/0.73 tff(1256,plain,
% 0.65/0.73 (((~ndr1_0) | c0_1(a1175) | (~c3_1(a1175)) | (~c2_1(a1175)) | c0_1(a1199) | c3_1(a1199) | (~c2_1(a1199)) | c1_1(a1199) | c0_1(a1199) | c3_1(a1199)) <=> (c0_1(a1199) | c3_1(a1199) | c0_1(a1175) | (~ndr1_0) | (~c3_1(a1175)) | (~c2_1(a1175)) | c1_1(a1199) | (~c2_1(a1199)))),
% 0.65/0.73 inference(rewrite,[status(thm)],[])).
% 0.65/0.73 tff(1257,plain,
% 0.65/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1175) | (~c3_1(a1175)) | (~c2_1(a1175)) | c0_1(a1199) | c3_1(a1199) | (~c2_1(a1199)) | c1_1(a1199) | c0_1(a1199) | c3_1(a1199))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1199) | c3_1(a1199) | c0_1(a1175) | (~ndr1_0) | (~c3_1(a1175)) | (~c2_1(a1175)) | c1_1(a1199) | (~c2_1(a1199))))),
% 0.65/0.73 inference(monotonicity,[status(thm)],[1256])).
% 0.65/0.73 tff(1258,plain,
% 0.65/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1175) | (~c3_1(a1175)) | (~c2_1(a1175)) | c0_1(a1199) | c3_1(a1199) | (~c2_1(a1199)) | c1_1(a1199) | c0_1(a1199) | c3_1(a1199))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1199) | c3_1(a1199) | c0_1(a1175) | (~ndr1_0) | (~c3_1(a1175)) | (~c2_1(a1175)) | c1_1(a1199) | (~c2_1(a1199)))),
% 0.65/0.73 inference(transitivity,[status(thm)],[1257, 1255])).
% 0.65/0.73 tff(1259,plain,
% 0.65/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1175) | (~c3_1(a1175)) | (~c2_1(a1175)) | c0_1(a1199) | c3_1(a1199) | (~c2_1(a1199)) | c1_1(a1199) | c0_1(a1199) | c3_1(a1199))),
% 0.65/0.73 inference(quant_inst,[status(thm)],[])).
% 0.65/0.73 tff(1260,plain,
% 0.65/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1199) | c3_1(a1199) | c0_1(a1175) | (~ndr1_0) | (~c3_1(a1175)) | (~c2_1(a1175)) | c1_1(a1199) | (~c2_1(a1199))),
% 0.65/0.73 inference(modus_ponens,[status(thm)],[1259, 1258])).
% 0.65/0.73 tff(1261,plain,
% 0.65/0.73 ($false),
% 0.65/0.73 inference(unit_resolution,[status(thm)],[1260, 187, 905, 1254, 907, 906, 1220, 689, 1253, 1252])).
% 0.65/0.73 tff(1262,plain,((~hskp16) | (~c2_1(a1175)) | c0_1(a1175) | (~c3_1(a1175)) | hskp3 | (~c1_1(a1205)) | (~c3_1(a1205)) | c2_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.73 tff(1263,plain,
% 0.65/0.73 ($false),
% 0.65/0.73 inference(unit_resolution,[status(thm)],[1262, 1251, 1232, 904, 1220, 22, 1219, 1218, 1217])).
% 0.65/0.73 tff(1264,plain,((~hskp4) | (~hskp16) | c0_1(a1175) | hskp3 | (~c1_1(a1205)) | (~c3_1(a1205)) | c2_1(a1205)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.73 tff(1265,plain,
% 0.65/0.73 ($false),
% 0.65/0.73 inference(unit_resolution,[status(thm)],[1264, 1216, 1210, 1173, 22, 1146, 1135, 1124])).
% 0.65/0.73 tff(1266,plain,(hskp22 | hskp3 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.65/0.73 tff(1267,plain,
% 0.65/0.73 (hskp3 | hskp14),
% 0.65/0.73 inference(unit_resolution,[status(thm)],[1266, 773])).
% 0.65/0.73 tff(1268,plain,
% 0.65/0.73 (hskp14),
% 0.65/0.73 inference(unit_resolution,[status(thm)],[1267, 22])).
% 0.65/0.73 tff(1269,plain,
% 0.65/0.73 (~c1_1(a1194)),
% 0.65/0.73 inference(unit_resolution,[status(thm)],[400, 1268])).
% 0.65/0.73 tff(1270,plain,
% 0.65/0.73 (~c0_1(a1194)),
% 0.65/0.73 inference(unit_resolution,[status(thm)],[406, 1268])).
% 0.65/0.73 tff(1271,plain,
% 0.65/0.73 (c2_1(a1178)),
% 0.65/0.73 inference(unit_resolution,[status(thm)],[1001, 965])).
% 0.65/0.73 tff(1272,plain,
% 0.65/0.73 (c1_1(a1178)),
% 0.65/0.73 inference(unit_resolution,[status(thm)],[1019, 965])).
% 0.65/0.73 tff(1273,plain,
% 0.65/0.73 (c2_1(a1194)),
% 0.65/0.73 inference(unit_resolution,[status(thm)],[417, 1268])).
% 0.65/0.73 tff(1274,plain,
% 0.65/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1194) | c1_1(a1194) | c3_1(a1178) | (~ndr1_0) | (~c2_1(a1178)) | (~c1_1(a1178)) | (~c3_1(a1194)) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1194) | c1_1(a1194) | c3_1(a1178) | (~ndr1_0) | (~c2_1(a1178)) | (~c1_1(a1178)) | (~c3_1(a1194)) | (~c2_1(a1194)))),
% 0.65/0.73 inference(rewrite,[status(thm)],[])).
% 0.65/0.73 tff(1275,plain,
% 0.65/0.73 (((~ndr1_0) | c3_1(a1178) | (~c1_1(a1178)) | (~c2_1(a1178)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194))) <=> (c0_1(a1194) | c1_1(a1194) | c3_1(a1178) | (~ndr1_0) | (~c2_1(a1178)) | (~c1_1(a1178)) | (~c3_1(a1194)) | (~c2_1(a1194)))),
% 0.65/0.73 inference(rewrite,[status(thm)],[])).
% 0.65/0.73 tff(1276,plain,
% 0.65/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a1178) | (~c1_1(a1178)) | (~c2_1(a1178)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1194) | c1_1(a1194) | c3_1(a1178) | (~ndr1_0) | (~c2_1(a1178)) | (~c1_1(a1178)) | (~c3_1(a1194)) | (~c2_1(a1194))))),
% 0.65/0.73 inference(monotonicity,[status(thm)],[1275])).
% 0.65/0.73 tff(1277,plain,
% 0.65/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a1178) | (~c1_1(a1178)) | (~c2_1(a1178)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1194) | c1_1(a1194) | c3_1(a1178) | (~ndr1_0) | (~c2_1(a1178)) | (~c1_1(a1178)) | (~c3_1(a1194)) | (~c2_1(a1194)))),
% 0.65/0.73 inference(transitivity,[status(thm)],[1276, 1274])).
% 0.65/0.73 tff(1278,plain,
% 0.65/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a1178) | (~c1_1(a1178)) | (~c2_1(a1178)) | c1_1(a1194) | c0_1(a1194) | (~c3_1(a1194)) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)))),
% 0.65/0.73 inference(quant_inst,[status(thm)],[])).
% 0.65/0.73 tff(1279,plain,
% 0.65/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1194) | c1_1(a1194) | c3_1(a1178) | (~ndr1_0) | (~c2_1(a1178)) | (~c1_1(a1178)) | (~c3_1(a1194)) | (~c2_1(a1194))),
% 0.65/0.73 inference(modus_ponens,[status(thm)],[1278, 1277])).
% 0.65/0.73 tff(1280,plain,
% 0.65/0.73 (~c3_1(a1194)),
% 0.65/0.73 inference(unit_resolution,[status(thm)],[1279, 187, 1273, 1272, 1271, 1270, 1269, 971, 21])).
% 0.65/0.73 tff(1281,plain,
% 0.65/0.73 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 0.65/0.73 inference(bind,[status(th)],[])).
% 0.65/0.73 tff(1282,plain,
% 0.65/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.65/0.73 inference(quant_intro,[status(thm)],[1281])).
% 0.65/0.73 tff(1283,plain,
% 0.65/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.65/0.73 inference(rewrite,[status(thm)],[])).
% 0.65/0.73 tff(1284,plain,
% 0.65/0.73 (^[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))) <=> ((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 0.65/0.73 inference(bind,[status(th)],[])).
% 0.65/0.73 tff(1285,plain,
% 0.65/0.73 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.65/0.73 inference(quant_intro,[status(thm)],[1284])).
% 0.65/0.73 tff(1286,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 0.65/0.73 tff(1287,plain,
% 0.65/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.65/0.73 inference(modus_ponens,[status(thm)],[1286, 1285])).
% 0.65/0.73 tff(1288,plain,
% 0.65/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.65/0.73 inference(modus_ponens,[status(thm)],[1287, 1283])).
% 0.65/0.73 tff(1289,plain,(
% 0.65/0.73 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.65/0.73 inference(skolemize,[status(sab)],[1288])).
% 0.65/0.73 tff(1290,plain,
% 0.65/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.65/0.73 inference(modus_ponens,[status(thm)],[1289, 1282])).
% 0.65/0.73 tff(1291,plain,
% 0.65/0.73 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.65/0.73 inference(bind,[status(th)],[])).
% 0.65/0.73 tff(1292,plain,
% 0.65/0.73 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.73 inference(quant_intro,[status(thm)],[1291])).
% 0.65/0.73 tff(1293,plain,
% 0.65/0.73 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.73 inference(rewrite,[status(thm)],[])).
% 0.65/0.73 tff(1294,plain,
% 0.65/0.73 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V))), (((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V)))), ((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), ((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.65/0.73 inference(bind,[status(th)],[])).
% 0.65/0.73 tff(1295,plain,
% 0.65/0.73 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.73 inference(quant_intro,[status(thm)],[1294])).
% 0.65/0.73 tff(1296,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 0.65/0.73 tff(1297,plain,
% 0.65/0.73 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.73 inference(modus_ponens,[status(thm)],[1296, 1295])).
% 0.65/0.73 tff(1298,plain,
% 0.65/0.73 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.73 inference(modus_ponens,[status(thm)],[1297, 1293])).
% 0.65/0.73 tff(1299,plain,(
% 0.65/0.73 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.73 inference(skolemize,[status(sab)],[1298])).
% 0.65/0.73 tff(1300,plain,
% 0.65/0.73 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.73 inference(modus_ponens,[status(thm)],[1299, 1292])).
% 0.65/0.73 tff(1301,plain,
% 0.65/0.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp5 | c1_1(a1200) | c2_1(a1200) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c2_1(a1194)) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp5 | c1_1(a1200) | c2_1(a1200) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c2_1(a1194)) | c3_1(a1200))),
% 0.65/0.73 inference(rewrite,[status(thm)],[])).
% 0.65/0.73 tff(1302,plain,
% 0.65/0.73 ((hskp5 | (~ndr1_0) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200)) <=> (hskp5 | c1_1(a1200) | c2_1(a1200) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c2_1(a1194)) | c3_1(a1200))),
% 0.65/0.73 inference(rewrite,[status(thm)],[])).
% 0.65/0.73 tff(1303,plain,
% 0.65/0.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp5 | c1_1(a1200) | c2_1(a1200) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c2_1(a1194)) | c3_1(a1200)))),
% 0.65/0.73 inference(monotonicity,[status(thm)],[1302])).
% 0.65/0.73 tff(1304,plain,
% 0.65/0.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp5 | c1_1(a1200) | c2_1(a1200) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c2_1(a1194)) | c3_1(a1200))),
% 0.65/0.73 inference(transitivity,[status(thm)],[1303, 1301])).
% 0.65/0.73 tff(1305,plain,
% 0.65/0.73 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a1194) | c0_1(a1194) | (~c2_1(a1194)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))),
% 0.65/0.73 inference(quant_inst,[status(thm)],[])).
% 0.65/0.73 tff(1306,plain,
% 0.65/0.73 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp5 | c1_1(a1200) | c2_1(a1200) | c0_1(a1194) | c1_1(a1194) | (~ndr1_0) | (~c2_1(a1194)) | c3_1(a1200)),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 0.65/0.74 tff(1307,plain,
% 0.65/0.74 (hskp5),
% 0.65/0.74 inference(unit_resolution,[status(thm)],[1306, 187, 1273, 940, 939, 1270, 1269, 1300, 948])).
% 0.65/0.74 tff(1308,plain,
% 0.65/0.74 (((~hskp5) | c2_1(a1176)) <=> ((~hskp5) | c2_1(a1176))),
% 0.65/0.74 inference(rewrite,[status(thm)],[])).
% 0.65/0.74 tff(1309,axiom,((~hskp5) | c2_1(a1176)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 0.65/0.74 tff(1310,plain,
% 0.65/0.74 ((~hskp5) | c2_1(a1176)),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1309, 1308])).
% 0.65/0.74 tff(1311,plain,
% 0.65/0.74 ((~hskp5) | c2_1(a1176)),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1310, 1308])).
% 0.65/0.74 tff(1312,plain,
% 0.65/0.74 ((~hskp5) | c2_1(a1176)),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1311, 1308])).
% 0.65/0.74 tff(1313,plain,
% 0.65/0.74 ((~hskp5) | c2_1(a1176)),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1312, 1308])).
% 0.65/0.74 tff(1314,plain,
% 0.65/0.74 ((~hskp5) | c2_1(a1176)),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1313, 1308])).
% 0.65/0.74 tff(1315,plain,
% 0.65/0.74 ((~hskp5) | c2_1(a1176)),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1314, 1308])).
% 0.65/0.74 tff(1316,plain,
% 0.65/0.74 ((~hskp5) | c2_1(a1176)),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1315, 1308])).
% 0.65/0.74 tff(1317,plain,
% 0.65/0.74 ((~hskp5) | c2_1(a1176)),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1316, 1308])).
% 0.65/0.74 tff(1318,plain,
% 0.65/0.74 (c2_1(a1176)),
% 0.65/0.74 inference(unit_resolution,[status(thm)],[1317, 1307])).
% 0.65/0.74 tff(1319,plain,
% 0.65/0.74 (((~hskp5) | c0_1(a1176)) <=> ((~hskp5) | c0_1(a1176))),
% 0.65/0.74 inference(rewrite,[status(thm)],[])).
% 0.65/0.74 tff(1320,axiom,((~hskp5) | c0_1(a1176)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.65/0.74 tff(1321,plain,
% 0.65/0.74 ((~hskp5) | c0_1(a1176)),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1320, 1319])).
% 0.65/0.74 tff(1322,plain,
% 0.65/0.74 ((~hskp5) | c0_1(a1176)),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1321, 1319])).
% 0.65/0.74 tff(1323,plain,
% 0.65/0.74 ((~hskp5) | c0_1(a1176)),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1322, 1319])).
% 0.65/0.74 tff(1324,plain,
% 0.65/0.74 ((~hskp5) | c0_1(a1176)),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1323, 1319])).
% 0.65/0.74 tff(1325,plain,
% 0.65/0.74 ((~hskp5) | c0_1(a1176)),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1324, 1319])).
% 0.65/0.74 tff(1326,plain,
% 0.65/0.74 ((~hskp5) | c0_1(a1176)),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1325, 1319])).
% 0.65/0.74 tff(1327,plain,
% 0.65/0.74 ((~hskp5) | c0_1(a1176)),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1326, 1319])).
% 0.65/0.74 tff(1328,plain,
% 0.65/0.74 ((~hskp5) | c0_1(a1176)),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1327, 1319])).
% 0.65/0.74 tff(1329,plain,
% 0.65/0.74 (c0_1(a1176)),
% 0.65/0.74 inference(unit_resolution,[status(thm)],[1328, 1307])).
% 0.65/0.74 tff(1330,plain,
% 0.65/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a1200) | c0_1(a1194) | (~ndr1_0) | (~c1_1(a1176)) | (~c2_1(a1176)) | (~c0_1(a1176)) | c3_1(a1194) | (~c2_1(a1194)) | c3_1(a1200) | (~c0_1(a1200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a1200) | c0_1(a1194) | (~ndr1_0) | (~c1_1(a1176)) | (~c2_1(a1176)) | (~c0_1(a1176)) | c3_1(a1194) | (~c2_1(a1194)) | c3_1(a1200) | (~c0_1(a1200)))),
% 0.65/0.74 inference(rewrite,[status(thm)],[])).
% 0.65/0.74 tff(1331,plain,
% 0.65/0.74 (((~ndr1_0) | (~c0_1(a1176)) | (~c1_1(a1176)) | (~c2_1(a1176)) | c2_1(a1200) | c3_1(a1200) | (~c0_1(a1200)) | c0_1(a1194) | c3_1(a1194) | (~c2_1(a1194))) <=> (c2_1(a1200) | c0_1(a1194) | (~ndr1_0) | (~c1_1(a1176)) | (~c2_1(a1176)) | (~c0_1(a1176)) | c3_1(a1194) | (~c2_1(a1194)) | c3_1(a1200) | (~c0_1(a1200)))),
% 0.65/0.74 inference(rewrite,[status(thm)],[])).
% 0.65/0.74 tff(1332,plain,
% 0.65/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a1176)) | (~c1_1(a1176)) | (~c2_1(a1176)) | c2_1(a1200) | c3_1(a1200) | (~c0_1(a1200)) | c0_1(a1194) | c3_1(a1194) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a1200) | c0_1(a1194) | (~ndr1_0) | (~c1_1(a1176)) | (~c2_1(a1176)) | (~c0_1(a1176)) | c3_1(a1194) | (~c2_1(a1194)) | c3_1(a1200) | (~c0_1(a1200))))),
% 0.65/0.74 inference(monotonicity,[status(thm)],[1331])).
% 0.65/0.74 tff(1333,plain,
% 0.65/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a1176)) | (~c1_1(a1176)) | (~c2_1(a1176)) | c2_1(a1200) | c3_1(a1200) | (~c0_1(a1200)) | c0_1(a1194) | c3_1(a1194) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a1200) | c0_1(a1194) | (~ndr1_0) | (~c1_1(a1176)) | (~c2_1(a1176)) | (~c0_1(a1176)) | c3_1(a1194) | (~c2_1(a1194)) | c3_1(a1200) | (~c0_1(a1200)))),
% 0.65/0.74 inference(transitivity,[status(thm)],[1332, 1330])).
% 0.65/0.74 tff(1334,plain,
% 0.65/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c0_1(a1176)) | (~c1_1(a1176)) | (~c2_1(a1176)) | c2_1(a1200) | c3_1(a1200) | (~c0_1(a1200)) | c0_1(a1194) | c3_1(a1194) | (~c2_1(a1194)))),
% 0.65/0.74 inference(quant_inst,[status(thm)],[])).
% 0.65/0.74 tff(1335,plain,
% 0.65/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a1200) | c0_1(a1194) | (~ndr1_0) | (~c1_1(a1176)) | (~c2_1(a1176)) | (~c0_1(a1176)) | c3_1(a1194) | (~c2_1(a1194)) | c3_1(a1200) | (~c0_1(a1200))),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1334, 1333])).
% 0.65/0.74 tff(1336,plain,
% 0.65/0.74 (~c1_1(a1176)),
% 0.65/0.74 inference(unit_resolution,[status(thm)],[1335, 187, 941, 1273, 1329, 1318, 939, 1270, 1290, 1280, 948])).
% 0.65/0.74 tff(1337,plain,
% 0.65/0.74 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.65/0.74 inference(bind,[status(th)],[])).
% 0.65/0.74 tff(1338,plain,
% 0.65/0.74 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.74 inference(quant_intro,[status(thm)],[1337])).
% 0.65/0.74 tff(1339,plain,
% 0.65/0.74 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.74 inference(rewrite,[status(thm)],[])).
% 0.65/0.74 tff(1340,plain,
% 0.65/0.74 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp26) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp26))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.65/0.74 inference(bind,[status(th)],[])).
% 0.65/0.74 tff(1341,plain,
% 0.65/0.74 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.74 inference(quant_intro,[status(thm)],[1340])).
% 0.65/0.74 tff(1342,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 0.65/0.74 tff(1343,plain,
% 0.65/0.74 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 0.65/0.74 tff(1344,plain,
% 0.65/0.74 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1343, 1339])).
% 0.65/0.74 tff(1345,plain,(
% 0.65/0.74 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.74 inference(skolemize,[status(sab)],[1344])).
% 0.65/0.74 tff(1346,plain,
% 0.65/0.74 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1345, 1338])).
% 0.65/0.74 tff(1347,plain,
% 0.65/0.74 (((~hskp5) | (~c3_1(a1176))) <=> ((~hskp5) | (~c3_1(a1176)))),
% 0.65/0.74 inference(rewrite,[status(thm)],[])).
% 0.65/0.74 tff(1348,plain,
% 0.65/0.74 (((~c3_1(a1176)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a1176)))),
% 0.65/0.74 inference(rewrite,[status(thm)],[])).
% 0.65/0.74 tff(1349,axiom,((~c3_1(a1176)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.65/0.74 tff(1350,plain,
% 0.65/0.74 ((~hskp5) | (~c3_1(a1176))),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1349, 1348])).
% 0.65/0.74 tff(1351,plain,
% 0.65/0.74 ((~hskp5) | (~c3_1(a1176))),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[1350, 1347])).
% 0.65/0.74 tff(1352,plain,
% 0.65/0.74 (~c3_1(a1176)),
% 0.65/0.74 inference(unit_resolution,[status(thm)],[1351, 1307])).
% 0.65/0.74 tff(1353,plain,
% 0.65/0.74 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp26 | c1_1(a1200) | c2_1(a1200) | c3_1(a1176) | (~ndr1_0) | c1_1(a1176) | (~c2_1(a1176)) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp26 | c1_1(a1200) | c2_1(a1200) | c3_1(a1176) | (~ndr1_0) | c1_1(a1176) | (~c2_1(a1176)) | c3_1(a1200))),
% 0.65/0.74 inference(rewrite,[status(thm)],[])).
% 0.65/0.74 tff(1354,plain,
% 0.65/0.74 ((hskp26 | (~ndr1_0) | c3_1(a1176) | c1_1(a1176) | (~c2_1(a1176)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200)) <=> (hskp26 | c1_1(a1200) | c2_1(a1200) | c3_1(a1176) | (~ndr1_0) | c1_1(a1176) | (~c2_1(a1176)) | c3_1(a1200))),
% 0.65/0.74 inference(rewrite,[status(thm)],[])).
% 0.65/0.74 tff(1355,plain,
% 0.65/0.74 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp26 | (~ndr1_0) | c3_1(a1176) | c1_1(a1176) | (~c2_1(a1176)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp26 | c1_1(a1200) | c2_1(a1200) | c3_1(a1176) | (~ndr1_0) | c1_1(a1176) | (~c2_1(a1176)) | c3_1(a1200)))),
% 0.71/0.74 inference(monotonicity,[status(thm)],[1354])).
% 0.71/0.74 tff(1356,plain,
% 0.71/0.74 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp26 | (~ndr1_0) | c3_1(a1176) | c1_1(a1176) | (~c2_1(a1176)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp26 | c1_1(a1200) | c2_1(a1200) | c3_1(a1176) | (~ndr1_0) | c1_1(a1176) | (~c2_1(a1176)) | c3_1(a1200))),
% 0.71/0.74 inference(transitivity,[status(thm)],[1355, 1353])).
% 0.71/0.74 tff(1357,plain,
% 0.71/0.74 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp26 | (~ndr1_0) | c3_1(a1176) | c1_1(a1176) | (~c2_1(a1176)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(1358,plain,
% 0.71/0.74 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp26 | c1_1(a1200) | c2_1(a1200) | c3_1(a1176) | (~ndr1_0) | c1_1(a1176) | (~c2_1(a1176)) | c3_1(a1200)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1357, 1356])).
% 0.71/0.74 tff(1359,plain,
% 0.71/0.74 (hskp26 | c1_1(a1176)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[1358, 187, 1318, 940, 939, 1352, 1346, 948])).
% 0.71/0.74 tff(1360,plain,
% 0.71/0.74 (hskp26),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[1359, 1336])).
% 0.71/0.74 tff(1361,plain,
% 0.71/0.74 (((~hskp26) | c3_1(a1190)) <=> ((~hskp26) | c3_1(a1190))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(1362,axiom,((~hskp26) | c3_1(a1190)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.71/0.74 tff(1363,plain,
% 0.71/0.74 ((~hskp26) | c3_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1362, 1361])).
% 0.71/0.74 tff(1364,plain,
% 0.71/0.74 ((~hskp26) | c3_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1363, 1361])).
% 0.71/0.74 tff(1365,plain,
% 0.71/0.74 ((~hskp26) | c3_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1364, 1361])).
% 0.71/0.74 tff(1366,plain,
% 0.71/0.74 ((~hskp26) | c3_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1365, 1361])).
% 0.71/0.74 tff(1367,plain,
% 0.71/0.74 ((~hskp26) | c3_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1366, 1361])).
% 0.71/0.74 tff(1368,plain,
% 0.71/0.74 ((~hskp26) | c3_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1367, 1361])).
% 0.71/0.74 tff(1369,plain,
% 0.71/0.74 ((~hskp26) | c3_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1368, 1361])).
% 0.71/0.74 tff(1370,plain,
% 0.71/0.74 ((~hskp26) | c3_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1369, 1361])).
% 0.71/0.74 tff(1371,plain,
% 0.71/0.74 (c3_1(a1190)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[1370, 1360])).
% 0.71/0.74 tff(1372,plain,
% 0.71/0.74 (((~hskp26) | c1_1(a1190)) <=> ((~hskp26) | c1_1(a1190))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(1373,axiom,((~hskp26) | c1_1(a1190)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.71/0.74 tff(1374,plain,
% 0.71/0.74 ((~hskp26) | c1_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1373, 1372])).
% 0.71/0.74 tff(1375,plain,
% 0.71/0.74 ((~hskp26) | c1_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1374, 1372])).
% 0.71/0.74 tff(1376,plain,
% 0.71/0.74 ((~hskp26) | c1_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1375, 1372])).
% 0.71/0.74 tff(1377,plain,
% 0.71/0.74 ((~hskp26) | c1_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1376, 1372])).
% 0.71/0.74 tff(1378,plain,
% 0.71/0.74 ((~hskp26) | c1_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1377, 1372])).
% 0.71/0.74 tff(1379,plain,
% 0.71/0.74 ((~hskp26) | c1_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1378, 1372])).
% 0.71/0.74 tff(1380,plain,
% 0.71/0.74 ((~hskp26) | c1_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1379, 1372])).
% 0.71/0.74 tff(1381,plain,
% 0.71/0.74 ((~hskp26) | c1_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1380, 1372])).
% 0.71/0.74 tff(1382,plain,
% 0.71/0.74 (c1_1(a1190)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[1381, 1360])).
% 0.71/0.74 tff(1383,plain,
% 0.71/0.74 (((~hskp26) | c0_1(a1190)) <=> ((~hskp26) | c0_1(a1190))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(1384,axiom,((~hskp26) | c0_1(a1190)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.71/0.74 tff(1385,plain,
% 0.71/0.74 ((~hskp26) | c0_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1384, 1383])).
% 0.71/0.74 tff(1386,plain,
% 0.71/0.74 ((~hskp26) | c0_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1385, 1383])).
% 0.71/0.74 tff(1387,plain,
% 0.71/0.74 ((~hskp26) | c0_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1386, 1383])).
% 0.71/0.74 tff(1388,plain,
% 0.71/0.74 ((~hskp26) | c0_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1387, 1383])).
% 0.71/0.74 tff(1389,plain,
% 0.71/0.74 ((~hskp26) | c0_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1388, 1383])).
% 0.71/0.74 tff(1390,plain,
% 0.71/0.74 ((~hskp26) | c0_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1389, 1383])).
% 0.71/0.74 tff(1391,plain,
% 0.71/0.74 ((~hskp26) | c0_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1390, 1383])).
% 0.71/0.74 tff(1392,plain,
% 0.71/0.74 ((~hskp26) | c0_1(a1190)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1391, 1383])).
% 0.71/0.74 tff(1393,plain,
% 0.71/0.74 (c0_1(a1190)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[1392, 1360])).
% 0.71/0.74 tff(1394,plain,
% 0.71/0.74 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c3_1(a1190)) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c0_1(a1200)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c3_1(a1190)) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c0_1(a1200)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(1395,plain,
% 0.71/0.74 (((~ndr1_0) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c3_1(a1190)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200))) <=> (c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c3_1(a1190)) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c0_1(a1200)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(1396,plain,
% 0.71/0.74 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c3_1(a1190)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c3_1(a1190)) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c0_1(a1200))))),
% 0.71/0.74 inference(monotonicity,[status(thm)],[1395])).
% 0.71/0.74 tff(1397,plain,
% 0.71/0.74 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c3_1(a1190)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c3_1(a1190)) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c0_1(a1200)))),
% 0.71/0.74 inference(transitivity,[status(thm)],[1396, 1394])).
% 0.71/0.74 tff(1398,plain,
% 0.71/0.74 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | ((~ndr1_0) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c3_1(a1190)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(1399,plain,
% 0.71/0.74 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c3_1(a1190)) | (~c0_1(a1190)) | (~c1_1(a1190)) | (~c0_1(a1200))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1398, 1397])).
% 0.71/0.74 tff(1400,plain,
% 0.71/0.74 ($false),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[1399, 187, 1393, 1382, 1371, 941, 940, 939, 10])).
% 0.71/0.74 tff(1401,plain,(hskp3), inference(lemma,lemma(discharge,[]))).
% 0.71/0.74 tff(1402,plain,
% 0.71/0.74 (~c3_1(a1174)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[264, 1401])).
% 0.71/0.74 tff(1403,plain,
% 0.71/0.74 ((~hskp3) | hskp14),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[302, 773])).
% 0.71/0.74 tff(1404,plain,
% 0.71/0.74 (hskp14),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[1403, 1401])).
% 0.71/0.74 tff(1405,plain,
% 0.71/0.74 (~c1_1(a1194)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[400, 1404])).
% 0.71/0.74 tff(1406,plain,
% 0.71/0.74 (~c0_1(a1194)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[406, 1404])).
% 0.71/0.74 tff(1407,plain,
% 0.71/0.74 (c1_1(a1174)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[332, 1401])).
% 0.71/0.74 tff(1408,plain,
% 0.71/0.74 (c2_1(a1194)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[417, 1404])).
% 0.71/0.74 tff(1409,plain,
% 0.71/0.74 ((~c2_1(a1174)) | (~c3_1(a1194))),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[497, 187, 1408, 1407, 1406, 1405, 1402, 21])).
% 0.71/0.74 tff(1410,plain,
% 0.71/0.74 (~c3_1(a1194)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[1409, 11])).
% 0.71/0.74 tff(1411,assumption,(~c0_1(a1182)), introduced(assumption)).
% 0.71/0.74 tff(1412,plain,
% 0.71/0.74 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))))),
% 0.71/0.74 inference(bind,[status(th)],[])).
% 0.71/0.74 tff(1413,plain,
% 0.71/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_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) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.71/0.74 inference(quant_intro,[status(thm)],[1412])).
% 0.71/0.74 tff(1414,plain,
% 0.71/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_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) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(1415,plain,
% 0.71/0.74 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))))),
% 0.71/0.74 inference(bind,[status(th)],[])).
% 0.71/0.74 tff(1416,plain,
% 0.71/0.74 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.71/0.74 inference(quant_intro,[status(thm)],[1415])).
% 0.71/0.74 tff(1417,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 0.71/0.74 tff(1418,plain,
% 0.71/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1417, 1416])).
% 0.71/0.74 tff(1419,plain,
% 0.71/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1418, 1414])).
% 0.71/0.74 tff(1420,plain,(
% 0.71/0.74 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.71/0.74 inference(skolemize,[status(sab)],[1419])).
% 0.71/0.74 tff(1421,plain,
% 0.71/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[1420, 1413])).
% 0.71/0.74 tff(1422,plain,
% 0.71/0.74 (c0_1(a1174)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[275, 1401])).
% 0.71/0.74 tff(1423,plain,
% 0.71/0.74 (^[V: $i, U: $i] : refl((hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.71/0.74 inference(bind,[status(th)],[])).
% 0.71/0.74 tff(1424,plain,
% 0.71/0.74 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.74 inference(quant_intro,[status(thm)],[1423])).
% 0.71/0.74 tff(1425,plain,
% 0.71/0.74 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(1426,plain,
% 0.71/0.75 (^[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) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp25) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp25))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.71/0.75 inference(bind,[status(th)],[])).
% 0.71/0.75 tff(1427,plain,
% 0.71/0.75 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp25) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.75 inference(quant_intro,[status(thm)],[1426])).
% 0.71/0.75 tff(1428,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 0.71/0.75 tff(1429,plain,
% 0.71/0.75 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 0.71/0.75 tff(1430,plain,
% 0.71/0.75 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1429, 1425])).
% 0.71/0.75 tff(1431,plain,(
% 0.71/0.75 ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.75 inference(skolemize,[status(sab)],[1430])).
% 0.71/0.75 tff(1432,plain,
% 0.71/0.75 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1431, 1424])).
% 0.71/0.75 tff(1433,plain,
% 0.71/0.75 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp25 | c3_1(a1174) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c1_1(a1174)) | (~c0_1(a1174)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp25 | c3_1(a1174) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c1_1(a1174)) | (~c0_1(a1174)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(1434,plain,
% 0.71/0.75 ((hskp25 | (~ndr1_0) | c3_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c2_1(a1168) | (~c1_1(a1168)) | (~c0_1(a1168))) <=> (hskp25 | c3_1(a1174) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c1_1(a1174)) | (~c0_1(a1174)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(1435,plain,
% 0.71/0.75 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp25 | (~ndr1_0) | c3_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c2_1(a1168) | (~c1_1(a1168)) | (~c0_1(a1168)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp25 | c3_1(a1174) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c1_1(a1174)) | (~c0_1(a1174))))),
% 0.71/0.75 inference(monotonicity,[status(thm)],[1434])).
% 0.71/0.75 tff(1436,plain,
% 0.71/0.75 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp25 | (~ndr1_0) | c3_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c2_1(a1168) | (~c1_1(a1168)) | (~c0_1(a1168)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp25 | c3_1(a1174) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c1_1(a1174)) | (~c0_1(a1174)))),
% 0.71/0.75 inference(transitivity,[status(thm)],[1435, 1433])).
% 0.71/0.75 tff(1437,plain,
% 0.71/0.75 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp25 | (~ndr1_0) | c3_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c2_1(a1168) | (~c1_1(a1168)) | (~c0_1(a1168)))),
% 0.71/0.75 inference(quant_inst,[status(thm)],[])).
% 0.71/0.75 tff(1438,plain,
% 0.71/0.75 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp25 | c3_1(a1174) | c2_1(a1168) | (~ndr1_0) | (~c1_1(a1168)) | (~c0_1(a1168)) | (~c1_1(a1174)) | (~c0_1(a1174))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 0.71/0.75 tff(1439,plain,
% 0.71/0.75 (hskp25),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[1438, 187, 1422, 1407, 551, 540, 1402, 528, 1432])).
% 0.71/0.75 tff(1440,plain,
% 0.71/0.75 (((~hskp25) | c3_1(a1182)) <=> ((~hskp25) | c3_1(a1182))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(1441,axiom,((~hskp25) | c3_1(a1182)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.71/0.75 tff(1442,plain,
% 0.71/0.75 ((~hskp25) | c3_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1441, 1440])).
% 0.71/0.75 tff(1443,plain,
% 0.71/0.75 ((~hskp25) | c3_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1442, 1440])).
% 0.71/0.75 tff(1444,plain,
% 0.71/0.75 ((~hskp25) | c3_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1443, 1440])).
% 0.71/0.75 tff(1445,plain,
% 0.71/0.75 ((~hskp25) | c3_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1444, 1440])).
% 0.71/0.75 tff(1446,plain,
% 0.71/0.75 ((~hskp25) | c3_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1445, 1440])).
% 0.71/0.75 tff(1447,plain,
% 0.71/0.75 ((~hskp25) | c3_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1446, 1440])).
% 0.71/0.75 tff(1448,plain,
% 0.71/0.75 ((~hskp25) | c3_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1447, 1440])).
% 0.71/0.75 tff(1449,plain,
% 0.71/0.75 ((~hskp25) | c3_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1448, 1440])).
% 0.71/0.75 tff(1450,plain,
% 0.71/0.75 (c3_1(a1182)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[1449, 1439])).
% 0.71/0.75 tff(1451,plain,
% 0.71/0.75 (((~hskp25) | c1_1(a1182)) <=> ((~hskp25) | c1_1(a1182))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(1452,axiom,((~hskp25) | c1_1(a1182)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.71/0.75 tff(1453,plain,
% 0.71/0.75 ((~hskp25) | c1_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1452, 1451])).
% 0.71/0.75 tff(1454,plain,
% 0.71/0.75 ((~hskp25) | c1_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1453, 1451])).
% 0.71/0.75 tff(1455,plain,
% 0.71/0.75 ((~hskp25) | c1_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1454, 1451])).
% 0.71/0.75 tff(1456,plain,
% 0.71/0.75 ((~hskp25) | c1_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1455, 1451])).
% 0.71/0.75 tff(1457,plain,
% 0.71/0.75 ((~hskp25) | c1_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1456, 1451])).
% 0.71/0.75 tff(1458,plain,
% 0.71/0.75 ((~hskp25) | c1_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1457, 1451])).
% 0.71/0.75 tff(1459,plain,
% 0.71/0.75 ((~hskp25) | c1_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1458, 1451])).
% 0.71/0.75 tff(1460,plain,
% 0.71/0.75 ((~hskp25) | c1_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1459, 1451])).
% 0.71/0.75 tff(1461,plain,
% 0.71/0.75 (c1_1(a1182)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[1460, 1439])).
% 0.71/0.75 tff(1462,plain,
% 0.71/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(1463,plain,
% 0.71/0.75 (((~ndr1_0) | c3_1(a1174) | (~c1_1(a1174)) | (~c2_1(a1174)) | c3_1(a1174) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182))) <=> (c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(1464,plain,
% 0.71/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1174) | (~c1_1(a1174)) | (~c2_1(a1174)) | c3_1(a1174) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182))))),
% 0.71/0.75 inference(monotonicity,[status(thm)],[1463])).
% 0.71/0.75 tff(1465,plain,
% 0.71/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1174) | (~c1_1(a1174)) | (~c2_1(a1174)) | c3_1(a1174) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182)))),
% 0.71/0.75 inference(transitivity,[status(thm)],[1464, 1462])).
% 0.71/0.75 tff(1466,plain,
% 0.71/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1174) | (~c1_1(a1174)) | (~c2_1(a1174)) | c3_1(a1174) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182)))),
% 0.71/0.75 inference(quant_inst,[status(thm)],[])).
% 0.71/0.75 tff(1467,plain,
% 0.71/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a1174) | (~ndr1_0) | (~c1_1(a1174)) | (~c2_1(a1174)) | (~c0_1(a1174)) | c0_1(a1182) | (~c3_1(a1182)) | (~c1_1(a1182))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1466, 1465])).
% 0.71/0.75 tff(1468,plain,
% 0.71/0.75 ($false),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[1467, 187, 1461, 1450, 1422, 1407, 1402, 1421, 11, 1411])).
% 0.71/0.75 tff(1469,plain,(c0_1(a1182) | (~c2_1(a1174))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.75 tff(1470,plain,
% 0.71/0.75 (c0_1(a1182)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[1469, 11])).
% 0.71/0.75 tff(1471,plain,
% 0.71/0.75 (((~hskp25) | c2_1(a1182)) <=> ((~hskp25) | c2_1(a1182))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(1472,axiom,((~hskp25) | c2_1(a1182)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.71/0.75 tff(1473,plain,
% 0.71/0.75 ((~hskp25) | c2_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1472, 1471])).
% 0.71/0.75 tff(1474,plain,
% 0.71/0.75 ((~hskp25) | c2_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1473, 1471])).
% 0.71/0.75 tff(1475,plain,
% 0.71/0.75 ((~hskp25) | c2_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1474, 1471])).
% 0.71/0.75 tff(1476,plain,
% 0.71/0.75 ((~hskp25) | c2_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1475, 1471])).
% 0.71/0.75 tff(1477,plain,
% 0.71/0.75 ((~hskp25) | c2_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1476, 1471])).
% 0.71/0.75 tff(1478,plain,
% 0.71/0.75 ((~hskp25) | c2_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1477, 1471])).
% 0.71/0.75 tff(1479,plain,
% 0.71/0.75 ((~hskp25) | c2_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1478, 1471])).
% 0.71/0.75 tff(1480,plain,
% 0.71/0.75 ((~hskp25) | c2_1(a1182)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1479, 1471])).
% 0.71/0.75 tff(1481,plain,
% 0.71/0.75 (c2_1(a1182)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[1480, 1439])).
% 0.71/0.75 tff(1482,plain,
% 0.71/0.75 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1182)) | (~c0_1(a1182)) | (~c2_1(a1182)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1182)) | (~c0_1(a1182)) | (~c2_1(a1182)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(1483,plain,
% 0.71/0.75 ((hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1182)) | (~c3_1(a1182)) | (~c2_1(a1182))) <=> (hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1182)) | (~c0_1(a1182)) | (~c2_1(a1182)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(1484,plain,
% 0.71/0.75 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1182)) | (~c3_1(a1182)) | (~c2_1(a1182)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1182)) | (~c0_1(a1182)) | (~c2_1(a1182))))),
% 0.71/0.75 inference(monotonicity,[status(thm)],[1483])).
% 0.71/0.75 tff(1485,plain,
% 0.71/0.75 (((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1182)) | (~c3_1(a1182)) | (~c2_1(a1182)))) <=> ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1182)) | (~c0_1(a1182)) | (~c2_1(a1182)))),
% 0.71/0.75 inference(transitivity,[status(thm)],[1484, 1482])).
% 0.71/0.75 tff(1486,plain,
% 0.71/0.75 ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(a1182)) | (~c3_1(a1182)) | (~c2_1(a1182)))),
% 0.71/0.75 inference(quant_inst,[status(thm)],[])).
% 0.71/0.75 tff(1487,plain,
% 0.71/0.75 ((~![U: $i] : (hskp22 | hskp2 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp2 | (~ndr1_0) | (~c3_1(a1182)) | (~c0_1(a1182)) | (~c2_1(a1182))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 0.71/0.75 tff(1488,plain,
% 0.71/0.75 (hskp2 | (~c0_1(a1182))),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[1487, 187, 773, 1481, 1450, 792])).
% 0.71/0.75 tff(1489,plain,
% 0.71/0.75 (hskp2),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[1488, 1470])).
% 0.71/0.75 tff(1490,plain,
% 0.71/0.75 (~c0_1(a1172)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[695, 1489])).
% 0.71/0.75 tff(1491,plain,
% 0.71/0.75 (c3_1(a1172)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[708, 1489])).
% 0.71/0.75 tff(1492,plain,
% 0.71/0.75 (c2_1(a1172)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[719, 1489])).
% 0.71/0.75 tff(1493,plain,
% 0.71/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1194) | c1_1(a1194) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c3_1(a1194) | (~c2_1(a1194)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1194) | c1_1(a1194) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c3_1(a1194) | (~c2_1(a1194)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(1494,plain,
% 0.71/0.75 (((~ndr1_0) | c0_1(a1172) | (~c3_1(a1172)) | (~c2_1(a1172)) | c0_1(a1194) | c3_1(a1194) | (~c2_1(a1194)) | c1_1(a1194) | c0_1(a1194) | c3_1(a1194)) <=> (c0_1(a1194) | c1_1(a1194) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c3_1(a1194) | (~c2_1(a1194)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(1495,plain,
% 0.71/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1172) | (~c3_1(a1172)) | (~c2_1(a1172)) | c0_1(a1194) | c3_1(a1194) | (~c2_1(a1194)) | c1_1(a1194) | c0_1(a1194) | c3_1(a1194))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a1194) | c1_1(a1194) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c3_1(a1194) | (~c2_1(a1194))))),
% 0.71/0.75 inference(monotonicity,[status(thm)],[1494])).
% 0.71/0.75 tff(1496,plain,
% 0.71/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1172) | (~c3_1(a1172)) | (~c2_1(a1172)) | c0_1(a1194) | c3_1(a1194) | (~c2_1(a1194)) | c1_1(a1194) | c0_1(a1194) | c3_1(a1194))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1194) | c1_1(a1194) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c3_1(a1194) | (~c2_1(a1194)))),
% 0.71/0.75 inference(transitivity,[status(thm)],[1495, 1493])).
% 0.71/0.75 tff(1497,plain,
% 0.71/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a1172) | (~c3_1(a1172)) | (~c2_1(a1172)) | c0_1(a1194) | c3_1(a1194) | (~c2_1(a1194)) | c1_1(a1194) | c0_1(a1194) | c3_1(a1194))),
% 0.71/0.75 inference(quant_inst,[status(thm)],[])).
% 0.71/0.75 tff(1498,plain,
% 0.71/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a1194) | c1_1(a1194) | c0_1(a1172) | (~ndr1_0) | (~c3_1(a1172)) | (~c2_1(a1172)) | c3_1(a1194) | (~c2_1(a1194))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[1497, 1496])).
% 0.71/0.75 tff(1499,plain,
% 0.71/0.75 ($false),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[1498, 187, 1408, 1492, 1491, 1406, 1405, 1490, 689, 1410])).
% 0.71/0.75 tff(1500,plain,(~c2_1(a1174)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.75 tff(1501,plain,
% 0.71/0.75 (hskp17 | c2_1(a1174)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[515, 187, 773, 1422, 1402, 508])).
% 0.71/0.75 tff(1502,plain,
% 0.71/0.75 (hskp17),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[1501, 1500])).
% 0.71/0.75 tff(1503,plain,
% 0.71/0.75 (~c2_1(a1200)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[359, 1502])).
% 0.71/0.75 tff(1504,plain,
% 0.71/0.75 (~c1_1(a1200)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[365, 1502])).
% 0.71/0.75 tff(1505,plain,
% 0.71/0.75 (c0_1(a1200)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[376, 1502])).
% 0.71/0.75 tff(1506,plain,
% 0.71/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | (~c3_1(a1200)) | (~c0_1(a1200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | (~c3_1(a1200)) | (~c0_1(a1200)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(1507,plain,
% 0.71/0.75 (((~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c1_1(a1200) | (~c3_1(a1200)) | (~c0_1(a1200)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200))) <=> (c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | (~c3_1(a1200)) | (~c0_1(a1200)))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(1508,plain,
% 0.71/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c1_1(a1200) | (~c3_1(a1200)) | (~c0_1(a1200)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | (~c3_1(a1200)) | (~c0_1(a1200))))),
% 0.71/0.76 inference(monotonicity,[status(thm)],[1507])).
% 0.71/0.76 tff(1509,plain,
% 0.71/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c1_1(a1200) | (~c3_1(a1200)) | (~c0_1(a1200)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | (~c3_1(a1200)) | (~c0_1(a1200)))),
% 0.71/0.76 inference(transitivity,[status(thm)],[1508, 1506])).
% 0.71/0.76 tff(1510,plain,
% 0.71/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c1_1(a1200) | (~c3_1(a1200)) | (~c0_1(a1200)) | c2_1(a1200) | c1_1(a1200) | (~c0_1(a1200)))),
% 0.71/0.76 inference(quant_inst,[status(thm)],[])).
% 0.71/0.76 tff(1511,plain,
% 0.71/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | (~c3_1(a1200)) | (~c0_1(a1200))),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[1510, 1509])).
% 0.71/0.76 tff(1512,plain,
% 0.71/0.76 (~c3_1(a1200)),
% 0.71/0.76 inference(unit_resolution,[status(thm)],[1511, 187, 1505, 1422, 1407, 1504, 1503, 63, 1500])).
% 0.71/0.76 tff(1513,plain,
% 0.71/0.76 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp6 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | c3_1(a1200))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(1514,plain,
% 0.71/0.76 ((hskp6 | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200)) <=> (hskp6 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | c3_1(a1200))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(1515,plain,
% 0.71/0.76 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | c3_1(a1200)))),
% 0.71/0.76 inference(monotonicity,[status(thm)],[1514])).
% 0.71/0.76 tff(1516,plain,
% 0.71/0.76 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp6 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | c3_1(a1200))),
% 0.71/0.76 inference(transitivity,[status(thm)],[1515, 1513])).
% 0.73/0.76 tff(1517,plain,
% 0.73/0.76 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a1174) | (~c0_1(a1174)) | (~c1_1(a1174)) | c2_1(a1200) | c1_1(a1200) | c3_1(a1200))),
% 0.73/0.76 inference(quant_inst,[status(thm)],[])).
% 0.73/0.76 tff(1518,plain,
% 0.73/0.76 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp6 | c1_1(a1200) | c2_1(a1200) | (~ndr1_0) | (~c1_1(a1174)) | c2_1(a1174) | (~c0_1(a1174)) | c3_1(a1200)),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[1517, 1516])).
% 0.73/0.76 tff(1519,plain,
% 0.73/0.76 (hskp6),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[1518, 187, 1422, 1407, 1504, 1503, 958, 1500, 1512])).
% 0.73/0.76 tff(1520,plain,
% 0.73/0.76 (~c3_1(a1178)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[970, 1519])).
% 0.73/0.76 tff(1521,plain,
% 0.73/0.76 (c2_1(a1178)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[1001, 1519])).
% 0.73/0.76 tff(1522,plain,
% 0.73/0.76 (c1_1(a1178)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[1019, 1519])).
% 0.73/0.76 tff(1523,plain,
% 0.73/0.76 (~c3_1(a1194)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[1279, 187, 1408, 1522, 1521, 1406, 1405, 1520, 21])).
% 0.73/0.76 tff(1524,plain,
% 0.73/0.76 (hskp5),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[1306, 187, 1408, 1504, 1503, 1406, 1405, 1300, 1512])).
% 0.73/0.76 tff(1525,plain,
% 0.73/0.76 (c2_1(a1176)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[1317, 1524])).
% 0.73/0.76 tff(1526,plain,
% 0.73/0.76 (c0_1(a1176)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[1328, 1524])).
% 0.73/0.76 tff(1527,plain,
% 0.73/0.76 (~c1_1(a1176)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[1335, 187, 1505, 1408, 1526, 1525, 1503, 1406, 1290, 1523, 1512])).
% 0.73/0.76 tff(1528,plain,
% 0.73/0.76 (~c3_1(a1176)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[1351, 1524])).
% 0.73/0.76 tff(1529,plain,
% 0.73/0.76 (hskp26 | c1_1(a1176)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[1358, 187, 1525, 1504, 1503, 1528, 1346, 1512])).
% 0.73/0.76 tff(1530,plain,
% 0.73/0.76 (hskp26),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[1529, 1527])).
% 0.73/0.76 tff(1531,plain,
% 0.73/0.76 (c3_1(a1190)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[1370, 1530])).
% 0.73/0.76 tff(1532,plain,
% 0.73/0.76 (c1_1(a1190)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[1381, 1530])).
% 0.73/0.76 tff(1533,plain,
% 0.73/0.76 (c0_1(a1190)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[1392, 1530])).
% 0.73/0.76 tff(1534,plain,
% 0.73/0.76 ($false),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[1399, 187, 1533, 1532, 1531, 1505, 1504, 1503, 10])).
% 0.73/0.76 % SZS output end Proof
%------------------------------------------------------------------------------