TSTP Solution File: SYN447-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN447-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 23:55:28 EDT 2022
% Result : Unsatisfiable 2.08s 1.54s
% Output : Proof 2.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN447-1 : TPTP v8.1.0. Released v2.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 03:41:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 2.08/1.54 % SZS status Unsatisfiable
% 2.08/1.54 % SZS output start Proof
% 2.08/1.54 tff(c2_1_type, type, (
% 2.08/1.54 c2_1: $i > $o)).
% 2.08/1.54 tff(c0_1_type, type, (
% 2.08/1.54 c0_1: $i > $o)).
% 2.08/1.54 tff(c3_1_type, type, (
% 2.08/1.54 c3_1: $i > $o)).
% 2.08/1.54 tff(c1_1_type, type, (
% 2.08/1.54 c1_1: $i > $o)).
% 2.08/1.54 tff(ndr1_0_type, type, (
% 2.08/1.54 ndr1_0: $o)).
% 2.08/1.54 tff(a1073_type, type, (
% 2.08/1.54 a1073: $i)).
% 2.08/1.54 tff(hskp53_type, type, (
% 2.08/1.54 hskp53: $o)).
% 2.08/1.54 tff(a1031_type, type, (
% 2.08/1.54 a1031: $i)).
% 2.08/1.54 tff(hskp33_type, type, (
% 2.08/1.54 hskp33: $o)).
% 2.08/1.54 tff(a1043_type, type, (
% 2.08/1.54 a1043: $i)).
% 2.08/1.54 tff(a1059_type, type, (
% 2.08/1.54 a1059: $i)).
% 2.08/1.54 tff(hskp15_type, type, (
% 2.08/1.54 hskp15: $o)).
% 2.08/1.54 tff(a1083_type, type, (
% 2.08/1.54 a1083: $i)).
% 2.08/1.54 tff(hskp22_type, type, (
% 2.08/1.54 hskp22: $o)).
% 2.08/1.54 tff(hskp56_type, type, (
% 2.08/1.54 hskp56: $o)).
% 2.08/1.54 tff(a1088_type, type, (
% 2.08/1.54 a1088: $i)).
% 2.08/1.54 tff(hskp23_type, type, (
% 2.08/1.54 hskp23: $o)).
% 2.08/1.54 tff(a1062_type, type, (
% 2.08/1.54 a1062: $i)).
% 2.08/1.54 tff(hskp48_type, type, (
% 2.08/1.54 hskp48: $o)).
% 2.08/1.54 tff(a1039_type, type, (
% 2.08/1.54 a1039: $i)).
% 2.08/1.54 tff(hskp10_type, type, (
% 2.08/1.54 hskp10: $o)).
% 2.08/1.54 tff(a1049_type, type, (
% 2.08/1.54 a1049: $i)).
% 2.08/1.54 tff(hskp43_type, type, (
% 2.08/1.54 hskp43: $o)).
% 2.08/1.54 tff(a1095_type, type, (
% 2.08/1.54 a1095: $i)).
% 2.08/1.54 tff(hskp59_type, type, (
% 2.08/1.54 hskp59: $o)).
% 2.08/1.54 tff(a1080_type, type, (
% 2.08/1.54 a1080: $i)).
% 2.08/1.54 tff(hskp20_type, type, (
% 2.08/1.54 hskp20: $o)).
% 2.08/1.54 tff(hskp19_type, type, (
% 2.08/1.54 hskp19: $o)).
% 2.08/1.54 tff(a1079_type, type, (
% 2.08/1.54 a1079: $i)).
% 2.08/1.54 tff(hskp63_type, type, (
% 2.08/1.54 hskp63: $o)).
% 2.08/1.54 tff(hskp62_type, type, (
% 2.08/1.54 hskp62: $o)).
% 2.08/1.54 tff(a1085_type, type, (
% 2.08/1.54 a1085: $i)).
% 2.08/1.54 tff(hskp57_type, type, (
% 2.08/1.54 hskp57: $o)).
% 2.08/1.54 tff(a1046_type, type, (
% 2.08/1.54 a1046: $i)).
% 2.08/1.54 tff(a1033_type, type, (
% 2.08/1.54 a1033: $i)).
% 2.08/1.54 tff(hskp35_type, type, (
% 2.08/1.54 hskp35: $o)).
% 2.08/1.54 tff(a1091_type, type, (
% 2.08/1.54 a1091: $i)).
% 2.08/1.54 tff(a1023_type, type, (
% 2.08/1.54 a1023: $i)).
% 2.08/1.54 tff(hskp1_type, type, (
% 2.08/1.54 hskp1: $o)).
% 2.08/1.54 tff(a1084_type, type, (
% 2.08/1.54 a1084: $i)).
% 2.08/1.54 tff(hskp25_type, type, (
% 2.08/1.54 hskp25: $o)).
% 2.08/1.54 tff(a1032_type, type, (
% 2.08/1.54 a1032: $i)).
% 2.08/1.54 tff(hskp34_type, type, (
% 2.08/1.54 hskp34: $o)).
% 2.08/1.54 tff(a1056_type, type, (
% 2.08/1.54 a1056: $i)).
% 2.08/1.54 tff(hskp47_type, type, (
% 2.08/1.54 hskp47: $o)).
% 2.08/1.54 tff(a1034_type, type, (
% 2.08/1.54 a1034: $i)).
% 2.08/1.54 tff(hskp36_type, type, (
% 2.08/1.54 hskp36: $o)).
% 2.08/1.54 tff(hskp42_type, type, (
% 2.08/1.54 hskp42: $o)).
% 2.08/1.54 tff(a1035_type, type, (
% 2.08/1.54 a1035: $i)).
% 2.08/1.54 tff(hskp12_type, type, (
% 2.08/1.54 hskp12: $o)).
% 2.08/1.54 tff(hskp7_type, type, (
% 2.08/1.54 hskp7: $o)).
% 2.08/1.54 tff(a1055_type, type, (
% 2.08/1.54 a1055: $i)).
% 2.08/1.54 tff(hskp14_type, type, (
% 2.08/1.54 hskp14: $o)).
% 2.08/1.54 tff(hskp38_type, type, (
% 2.08/1.54 hskp38: $o)).
% 2.08/1.54 tff(a1040_type, type, (
% 2.08/1.54 a1040: $i)).
% 2.08/1.54 tff(hskp46_type, type, (
% 2.08/1.54 hskp46: $o)).
% 2.08/1.54 tff(a1053_type, type, (
% 2.08/1.54 a1053: $i)).
% 2.08/1.54 tff(a1105_type, type, (
% 2.08/1.54 a1105: $i)).
% 2.08/1.54 tff(a1103_type, type, (
% 2.08/1.54 a1103: $i)).
% 2.08/1.54 tff(1,plain,
% 2.08/1.54 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))))),
% 2.08/1.54 inference(bind,[status(th)],[])).
% 2.08/1.54 tff(2,plain,
% 2.08/1.54 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.54 inference(quant_intro,[status(thm)],[1])).
% 2.08/1.54 tff(3,plain,
% 2.08/1.54 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.54 inference(rewrite,[status(thm)],[])).
% 2.08/1.54 tff(4,plain,
% 2.08/1.54 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) | (~c2_1(V))) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) | (~c2_1(V))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) | (~c2_1(V))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) | (~c2_1(V))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) | (~c2_1(V))) | (~ndr1_0)) | (~c2_1(U))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~c2_1(U))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~c2_1(U))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) | (~c2_1(V))) | (~ndr1_0)) | (~c2_1(U))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(5,plain,
% 2.08/1.55 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) | (~c2_1(V))) | (~ndr1_0)) | (~c2_1(U))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[4])).
% 2.08/1.55 tff(6,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c0_1(V))) | (~c1_1(U))) | (~c3_1(V))) | (~c2_1(V))) | (~ndr1_0)) | (~c2_1(U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause311')).
% 2.08/1.55 tff(7,plain,
% 2.08/1.55 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[6, 5])).
% 2.08/1.55 tff(8,plain,
% 2.08/1.55 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[7, 3])).
% 2.08/1.55 tff(9,plain,(
% 2.08/1.55 ![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.55 inference(skolemize,[status(sab)],[8])).
% 2.08/1.55 tff(10,plain,
% 2.08/1.55 (![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[9, 2])).
% 2.08/1.55 tff(11,plain,
% 2.08/1.55 (^[V: $i, U: $i] : refl((hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(12,plain,
% 2.08/1.55 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[11])).
% 2.08/1.55 tff(13,plain,
% 2.08/1.55 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(14,plain,
% 2.08/1.55 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c2_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))))), (((((~c3_1(U)) | (~c2_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)))), (((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | hskp53) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | hskp53))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | hskp53) <=> (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | hskp53) <=> (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(15,plain,
% 2.08/1.55 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | hskp53) <=> ![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[14])).
% 2.08/1.55 tff(16,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | hskp53)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause309')).
% 2.08/1.55 tff(17,plain,
% 2.08/1.55 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[16, 15])).
% 2.08/1.55 tff(18,plain,
% 2.08/1.55 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[17, 13])).
% 2.08/1.55 tff(19,plain,(
% 2.08/1.55 ![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.55 inference(skolemize,[status(sab)],[18])).
% 2.08/1.55 tff(20,plain,
% 2.08/1.55 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[19, 12])).
% 2.08/1.55 tff(21,assumption,(~hskp33), introduced(assumption)).
% 2.08/1.55 tff(22,plain,
% 2.08/1.55 (^[U: $i] : refl((hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(23,plain,
% 2.08/1.55 (![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[22])).
% 2.08/1.55 tff(24,plain,
% 2.08/1.55 (![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(25,plain,
% 2.08/1.55 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) | hskp56) <=> ((hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp56))), rewrite(((hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp56) <=> (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) | hskp56) <=> (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(26,plain,
% 2.08/1.55 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) | hskp56) <=> ![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[25])).
% 2.08/1.55 tff(27,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) | hskp56)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause281')).
% 2.08/1.55 tff(28,plain,
% 2.08/1.55 (![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[27, 26])).
% 2.08/1.55 tff(29,plain,
% 2.08/1.55 (![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[28, 24])).
% 2.08/1.55 tff(30,plain,(
% 2.08/1.55 ![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 2.08/1.55 inference(skolemize,[status(sab)],[29])).
% 2.08/1.55 tff(31,plain,
% 2.08/1.55 (![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[30, 23])).
% 2.08/1.55 tff(32,plain,
% 2.08/1.55 (^[U: $i] : refl((hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(33,plain,
% 2.08/1.55 (![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[32])).
% 2.08/1.55 tff(34,plain,
% 2.08/1.55 (![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(35,plain,
% 2.08/1.55 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp33) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp33))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp33) <=> (hskp33 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp33) <=> (hskp33 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp33) | hskp23) <=> ((hskp33 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp23))), rewrite(((hskp33 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp23) <=> (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp33) | hskp23) <=> (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(36,plain,
% 2.08/1.55 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp33) | hskp23) <=> ![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[35])).
% 2.08/1.55 tff(37,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp33) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause284')).
% 2.08/1.55 tff(38,plain,
% 2.08/1.55 (![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[37, 36])).
% 2.08/1.55 tff(39,plain,
% 2.08/1.55 (![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[38, 34])).
% 2.08/1.55 tff(40,plain,(
% 2.08/1.55 ![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.08/1.55 inference(skolemize,[status(sab)],[39])).
% 2.08/1.55 tff(41,plain,
% 2.08/1.55 (![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[40, 33])).
% 2.08/1.55 tff(42,assumption,(~hskp15), introduced(assumption)).
% 2.08/1.55 tff(43,plain,
% 2.08/1.55 (^[U: $i] : refl((hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(44,plain,
% 2.08/1.55 (![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[43])).
% 2.08/1.55 tff(45,plain,
% 2.08/1.55 (![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(46,plain,
% 2.08/1.55 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp15) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp15))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp15) | hskp33) <=> ((hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp33))), rewrite(((hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp33) <=> (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp15) | hskp33) <=> (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(47,plain,
% 2.08/1.55 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp15) | hskp33) <=> ![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[46])).
% 2.08/1.55 tff(48,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp15) | hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause266')).
% 2.08/1.55 tff(49,plain,
% 2.08/1.55 (![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[48, 47])).
% 2.08/1.55 tff(50,plain,
% 2.08/1.55 (![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[49, 45])).
% 2.08/1.55 tff(51,plain,(
% 2.08/1.55 ![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.08/1.55 inference(skolemize,[status(sab)],[50])).
% 2.08/1.55 tff(52,plain,
% 2.08/1.55 (![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[51, 44])).
% 2.08/1.55 tff(53,assumption,(~hskp10), introduced(assumption)).
% 2.08/1.55 tff(54,plain,
% 2.08/1.55 (^[U: $i] : refl((hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(55,plain,
% 2.08/1.55 (![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[54])).
% 2.08/1.55 tff(56,plain,
% 2.08/1.55 (![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(57,plain,
% 2.08/1.55 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp10))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) | hskp43) <=> ((hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp43))), rewrite(((hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp43) <=> (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) | hskp43) <=> (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(58,plain,
% 2.08/1.55 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) | hskp43) <=> ![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[57])).
% 2.08/1.55 tff(59,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) | hskp43)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause277')).
% 2.08/1.55 tff(60,plain,
% 2.08/1.55 (![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[59, 58])).
% 2.08/1.55 tff(61,plain,
% 2.08/1.55 (![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[60, 56])).
% 2.08/1.55 tff(62,plain,(
% 2.08/1.55 ![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.08/1.55 inference(skolemize,[status(sab)],[61])).
% 2.08/1.55 tff(63,plain,
% 2.08/1.55 (![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[62, 55])).
% 2.08/1.55 tff(64,plain,
% 2.08/1.55 (^[U: $i] : refl((hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U)) <=> (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U)))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(65,plain,
% 2.08/1.55 (![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U)) <=> ![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[64])).
% 2.08/1.55 tff(66,plain,
% 2.08/1.55 (![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U)) <=> ![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(67,plain,
% 2.08/1.55 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U))), ((((~ndr1_0) | c3_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c3_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c3_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U))), ((((~ndr1_0) | c3_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U)))), (((((~ndr1_0) | c3_1(U)) | c2_1(U)) | c0_1(U)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U)) | c0_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))), (((((~ndr1_0) | c3_1(U)) | c2_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U)))), ((((((~ndr1_0) | c3_1(U)) | c2_1(U)) | c0_1(U)) | hskp10) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U)) | hskp10))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))), ((((((~ndr1_0) | c3_1(U)) | c2_1(U)) | c0_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(68,plain,
% 2.08/1.55 (![U: $i] : (((((~ndr1_0) | c3_1(U)) | c2_1(U)) | c0_1(U)) | hskp10) <=> ![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[67])).
% 2.08/1.55 tff(69,axiom,(![U: $i] : (((((~ndr1_0) | c3_1(U)) | c2_1(U)) | c0_1(U)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause262')).
% 2.08/1.55 tff(70,plain,
% 2.08/1.55 (![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[69, 68])).
% 2.08/1.55 tff(71,plain,
% 2.08/1.55 (![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[70, 66])).
% 2.08/1.55 tff(72,plain,(
% 2.08/1.55 ![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))),
% 2.08/1.55 inference(skolemize,[status(sab)],[71])).
% 2.08/1.55 tff(73,plain,
% 2.08/1.55 (![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[72, 65])).
% 2.08/1.55 tff(74,assumption,(hskp19), introduced(assumption)).
% 2.08/1.55 tff(75,plain,
% 2.08/1.55 (((~hskp19) | (~c2_1(a1079))) <=> ((~hskp19) | (~c2_1(a1079)))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(76,plain,
% 2.08/1.55 (((~c2_1(a1079)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a1079)))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(77,axiom,((~c2_1(a1079)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause227')).
% 2.08/1.55 tff(78,plain,
% 2.08/1.55 ((~hskp19) | (~c2_1(a1079))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[77, 76])).
% 2.08/1.55 tff(79,plain,
% 2.08/1.55 ((~hskp19) | (~c2_1(a1079))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[78, 75])).
% 2.08/1.55 tff(80,plain,
% 2.08/1.55 (~c2_1(a1079)),
% 2.08/1.55 inference(unit_resolution,[status(thm)],[79, 74])).
% 2.08/1.55 tff(81,plain,
% 2.08/1.55 (((~hskp19) | (~c0_1(a1079))) <=> ((~hskp19) | (~c0_1(a1079)))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(82,plain,
% 2.08/1.55 (((~c0_1(a1079)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a1079)))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(83,axiom,((~c0_1(a1079)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause226')).
% 2.08/1.55 tff(84,plain,
% 2.08/1.55 ((~hskp19) | (~c0_1(a1079))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[83, 82])).
% 2.08/1.55 tff(85,plain,
% 2.08/1.55 ((~hskp19) | (~c0_1(a1079))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[84, 81])).
% 2.08/1.55 tff(86,plain,
% 2.08/1.55 (~c0_1(a1079)),
% 2.08/1.55 inference(unit_resolution,[status(thm)],[85, 74])).
% 2.08/1.55 tff(87,assumption,(~ndr1_0), introduced(assumption)).
% 2.08/1.55 tff(88,plain,
% 2.08/1.55 ((ndr1_0 | (~hskp56)) <=> (ndr1_0 | (~hskp56))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(89,plain,
% 2.08/1.55 (((~hskp56) | ndr1_0) <=> (ndr1_0 | (~hskp56))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(90,axiom,((~hskp56) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause8')).
% 2.08/1.55 tff(91,plain,
% 2.08/1.55 (ndr1_0 | (~hskp56)),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[90, 89])).
% 2.08/1.55 tff(92,plain,
% 2.08/1.55 (ndr1_0 | (~hskp56)),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[91, 88])).
% 2.08/1.55 tff(93,plain,
% 2.08/1.55 (~hskp56),
% 2.08/1.55 inference(unit_resolution,[status(thm)],[92, 87])).
% 2.08/1.55 tff(94,plain,
% 2.08/1.55 (((~hskp63) | ndr1_0) <=> ((~hskp63) | ndr1_0)),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(95,axiom,((~hskp63) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 2.08/1.55 tff(96,plain,
% 2.08/1.55 ((~hskp63) | ndr1_0),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[95, 94])).
% 2.08/1.55 tff(97,plain,
% 2.08/1.55 ((~hskp63) | ndr1_0),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[96, 94])).
% 2.08/1.55 tff(98,plain,
% 2.08/1.55 ((~hskp63) | ndr1_0),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[97, 94])).
% 2.08/1.55 tff(99,plain,
% 2.08/1.55 ((~hskp63) | ndr1_0),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[98, 94])).
% 2.08/1.55 tff(100,plain,
% 2.08/1.55 ((~hskp63) | ndr1_0),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[99, 94])).
% 2.08/1.55 tff(101,plain,
% 2.08/1.55 ((~hskp63) | ndr1_0),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[100, 94])).
% 2.08/1.55 tff(102,plain,
% 2.08/1.55 ((~hskp63) | ndr1_0),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[101, 94])).
% 2.08/1.55 tff(103,plain,
% 2.08/1.55 ((~hskp63) | ndr1_0),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[102, 94])).
% 2.08/1.55 tff(104,plain,
% 2.08/1.55 (~hskp63),
% 2.08/1.55 inference(unit_resolution,[status(thm)],[103, 87])).
% 2.08/1.55 tff(105,plain,
% 2.08/1.55 ((ndr1_0 | (~hskp62)) <=> (ndr1_0 | (~hskp62))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(106,plain,
% 2.08/1.55 (((~hskp62) | ndr1_0) <=> (ndr1_0 | (~hskp62))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(107,axiom,((~hskp62) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 2.08/1.55 tff(108,plain,
% 2.08/1.55 (ndr1_0 | (~hskp62)),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[107, 106])).
% 2.08/1.55 tff(109,plain,
% 2.08/1.55 (ndr1_0 | (~hskp62)),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[108, 105])).
% 2.08/1.55 tff(110,plain,
% 2.08/1.55 (~hskp62),
% 2.08/1.55 inference(unit_resolution,[status(thm)],[109, 87])).
% 2.08/1.55 tff(111,plain,
% 2.08/1.55 ((hskp63 | hskp62 | hskp56) <=> (hskp63 | hskp62 | hskp56)),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(112,plain,
% 2.08/1.55 (((hskp62 | hskp56) | hskp63) <=> (hskp63 | hskp62 | hskp56)),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(113,plain,
% 2.08/1.55 ((hskp62 | hskp56) <=> (hskp62 | hskp56)),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(114,plain,
% 2.08/1.55 (((hskp62 | hskp56) | hskp63) <=> ((hskp62 | hskp56) | hskp63)),
% 2.08/1.55 inference(monotonicity,[status(thm)],[113])).
% 2.08/1.55 tff(115,plain,
% 2.08/1.55 (((hskp62 | hskp56) | hskp63) <=> (hskp63 | hskp62 | hskp56)),
% 2.08/1.55 inference(transitivity,[status(thm)],[114, 112])).
% 2.08/1.55 tff(116,axiom,((hskp62 | hskp56) | hskp63), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 2.08/1.55 tff(117,plain,
% 2.08/1.55 (hskp63 | hskp62 | hskp56),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[116, 115])).
% 2.08/1.55 tff(118,plain,
% 2.08/1.55 (hskp63 | hskp62 | hskp56),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[117, 111])).
% 2.08/1.55 tff(119,plain,
% 2.08/1.55 (hskp63 | hskp62 | hskp56),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[118, 111])).
% 2.08/1.55 tff(120,plain,
% 2.08/1.55 (hskp63 | hskp62 | hskp56),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[119, 111])).
% 2.08/1.55 tff(121,plain,
% 2.08/1.55 (hskp63 | hskp62 | hskp56),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[120, 111])).
% 2.08/1.55 tff(122,plain,
% 2.08/1.55 (hskp63 | hskp62 | hskp56),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[121, 111])).
% 2.08/1.55 tff(123,plain,
% 2.08/1.55 (hskp63 | hskp62 | hskp56),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[122, 111])).
% 2.08/1.55 tff(124,plain,
% 2.08/1.55 (hskp63 | hskp62 | hskp56),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[123, 111])).
% 2.08/1.55 tff(125,plain,
% 2.08/1.55 ($false),
% 2.08/1.55 inference(unit_resolution,[status(thm)],[124, 110, 104, 93])).
% 2.08/1.55 tff(126,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 2.08/1.55 tff(127,plain,
% 2.08/1.55 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | c3_1(a1079))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | c3_1(a1079))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(128,plain,
% 2.08/1.55 ((hskp10 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | c3_1(a1079)) <=> (hskp10 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | c3_1(a1079))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(129,plain,
% 2.08/1.55 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | c3_1(a1079))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | c3_1(a1079)))),
% 2.08/1.55 inference(monotonicity,[status(thm)],[128])).
% 2.08/1.55 tff(130,plain,
% 2.08/1.55 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | c3_1(a1079))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | c3_1(a1079))),
% 2.08/1.55 inference(transitivity,[status(thm)],[129, 127])).
% 2.08/1.55 tff(131,plain,
% 2.08/1.55 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | c3_1(a1079))),
% 2.08/1.55 inference(quant_inst,[status(thm)],[])).
% 2.08/1.55 tff(132,plain,
% 2.08/1.55 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | c3_1(a1079)),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[131, 130])).
% 2.08/1.55 tff(133,plain,
% 2.08/1.55 (c3_1(a1079)),
% 2.08/1.55 inference(unit_resolution,[status(thm)],[132, 126, 53, 86, 80, 73])).
% 2.08/1.55 tff(134,plain,
% 2.08/1.55 (^[V: $i, U: $i] : refl((hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(135,plain,
% 2.08/1.55 (![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[134])).
% 2.08/1.55 tff(136,plain,
% 2.08/1.55 (![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(137,plain,
% 2.08/1.55 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c2_1(V)) | hskp59) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp59))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp59) <=> (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c2_1(V)) | hskp59) <=> (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(138,plain,
% 2.08/1.55 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c2_1(V)) | hskp59) <=> ![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[137])).
% 2.08/1.55 tff(139,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c2_1(V)) | hskp59)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause297')).
% 2.08/1.55 tff(140,plain,
% 2.08/1.55 (![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[139, 138])).
% 2.08/1.55 tff(141,plain,
% 2.08/1.55 (![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[140, 136])).
% 2.08/1.55 tff(142,plain,(
% 2.08/1.55 ![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.08/1.55 inference(skolemize,[status(sab)],[141])).
% 2.08/1.55 tff(143,plain,
% 2.08/1.55 (![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[142, 135])).
% 2.08/1.55 tff(144,plain,
% 2.08/1.55 (((~hskp19) | c1_1(a1079)) <=> ((~hskp19) | c1_1(a1079))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(145,axiom,((~hskp19) | c1_1(a1079)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 2.08/1.55 tff(146,plain,
% 2.08/1.55 ((~hskp19) | c1_1(a1079)),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[145, 144])).
% 2.08/1.55 tff(147,plain,
% 2.08/1.55 ((~hskp19) | c1_1(a1079)),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[146, 144])).
% 2.08/1.55 tff(148,plain,
% 2.08/1.55 ((~hskp19) | c1_1(a1079)),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[147, 144])).
% 2.08/1.55 tff(149,plain,
% 2.08/1.55 ((~hskp19) | c1_1(a1079)),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[148, 144])).
% 2.08/1.55 tff(150,plain,
% 2.08/1.55 ((~hskp19) | c1_1(a1079)),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[149, 144])).
% 2.08/1.55 tff(151,plain,
% 2.08/1.55 ((~hskp19) | c1_1(a1079)),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[150, 144])).
% 2.08/1.55 tff(152,plain,
% 2.08/1.55 ((~hskp19) | c1_1(a1079)),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[151, 144])).
% 2.08/1.55 tff(153,plain,
% 2.08/1.55 ((~hskp19) | c1_1(a1079)),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[152, 144])).
% 2.08/1.55 tff(154,plain,
% 2.08/1.55 (c1_1(a1079)),
% 2.08/1.55 inference(unit_resolution,[status(thm)],[153, 74])).
% 2.08/1.55 tff(155,plain,
% 2.08/1.55 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(156,plain,
% 2.08/1.55 ((hskp59 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | (~c3_1(a1079)) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079))) <=> (hskp59 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(157,plain,
% 2.08/1.55 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | (~c3_1(a1079)) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079))))),
% 2.08/1.56 inference(monotonicity,[status(thm)],[156])).
% 2.08/1.56 tff(158,plain,
% 2.08/1.56 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | (~c3_1(a1079)) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)))),
% 2.08/1.56 inference(transitivity,[status(thm)],[157, 155])).
% 2.08/1.56 tff(159,plain,
% 2.08/1.56 ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | (~c3_1(a1079)) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)))),
% 2.08/1.56 inference(quant_inst,[status(thm)],[])).
% 2.08/1.56 tff(160,plain,
% 2.08/1.56 ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[159, 158])).
% 2.08/1.56 tff(161,plain,
% 2.08/1.56 (hskp59 | (~c3_1(a1079))),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[160, 126, 154, 86, 80, 143])).
% 2.08/1.56 tff(162,plain,
% 2.08/1.56 (hskp59),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[161, 133])).
% 2.08/1.56 tff(163,plain,
% 2.08/1.56 (((~hskp59) | (~c3_1(a1095))) <=> ((~hskp59) | (~c3_1(a1095)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(164,plain,
% 2.08/1.56 (((~c3_1(a1095)) | (~hskp59)) <=> ((~hskp59) | (~c3_1(a1095)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(165,axiom,((~c3_1(a1095)) | (~hskp59)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 2.08/1.56 tff(166,plain,
% 2.08/1.56 ((~hskp59) | (~c3_1(a1095))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[165, 164])).
% 2.08/1.56 tff(167,plain,
% 2.08/1.56 ((~hskp59) | (~c3_1(a1095))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[166, 163])).
% 2.08/1.56 tff(168,plain,
% 2.08/1.56 (~c3_1(a1095)),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[167, 162])).
% 2.08/1.56 tff(169,plain,
% 2.08/1.56 (((~hskp59) | (~c0_1(a1095))) <=> ((~hskp59) | (~c0_1(a1095)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(170,plain,
% 2.08/1.56 (((~c0_1(a1095)) | (~hskp59)) <=> ((~hskp59) | (~c0_1(a1095)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(171,axiom,((~c0_1(a1095)) | (~hskp59)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 2.08/1.56 tff(172,plain,
% 2.08/1.56 ((~hskp59) | (~c0_1(a1095))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[171, 170])).
% 2.08/1.56 tff(173,plain,
% 2.08/1.56 ((~hskp59) | (~c0_1(a1095))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[172, 169])).
% 2.08/1.56 tff(174,plain,
% 2.08/1.56 (~c0_1(a1095)),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[173, 162])).
% 2.08/1.56 tff(175,plain,
% 2.08/1.56 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c0_1(a1095) | c3_1(a1095) | (~ndr1_0) | c2_1(a1095))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1095) | c3_1(a1095) | (~ndr1_0) | c2_1(a1095))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(176,plain,
% 2.08/1.56 ((hskp10 | (~ndr1_0) | c0_1(a1095) | c2_1(a1095) | c3_1(a1095)) <=> (hskp10 | c0_1(a1095) | c3_1(a1095) | (~ndr1_0) | c2_1(a1095))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(177,plain,
% 2.08/1.56 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1095) | c2_1(a1095) | c3_1(a1095))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c0_1(a1095) | c3_1(a1095) | (~ndr1_0) | c2_1(a1095)))),
% 2.08/1.56 inference(monotonicity,[status(thm)],[176])).
% 2.08/1.56 tff(178,plain,
% 2.08/1.56 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1095) | c2_1(a1095) | c3_1(a1095))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1095) | c3_1(a1095) | (~ndr1_0) | c2_1(a1095))),
% 2.08/1.56 inference(transitivity,[status(thm)],[177, 175])).
% 2.08/1.56 tff(179,plain,
% 2.08/1.56 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1095) | c2_1(a1095) | c3_1(a1095))),
% 2.08/1.56 inference(quant_inst,[status(thm)],[])).
% 2.08/1.56 tff(180,plain,
% 2.08/1.56 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1095) | c3_1(a1095) | (~ndr1_0) | c2_1(a1095)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[179, 178])).
% 2.08/1.56 tff(181,plain,
% 2.08/1.56 (c2_1(a1095)),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[180, 126, 53, 174, 168, 73])).
% 2.08/1.56 tff(182,plain,
% 2.08/1.56 (((~hskp59) | c1_1(a1095)) <=> ((~hskp59) | c1_1(a1095))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(183,axiom,((~hskp59) | c1_1(a1095)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 2.08/1.56 tff(184,plain,
% 2.08/1.56 ((~hskp59) | c1_1(a1095)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[183, 182])).
% 2.08/1.56 tff(185,plain,
% 2.08/1.56 ((~hskp59) | c1_1(a1095)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[184, 182])).
% 2.08/1.56 tff(186,plain,
% 2.08/1.56 ((~hskp59) | c1_1(a1095)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[185, 182])).
% 2.08/1.56 tff(187,plain,
% 2.08/1.56 ((~hskp59) | c1_1(a1095)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[186, 182])).
% 2.08/1.56 tff(188,plain,
% 2.08/1.56 ((~hskp59) | c1_1(a1095)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[187, 182])).
% 2.08/1.56 tff(189,plain,
% 2.08/1.56 ((~hskp59) | c1_1(a1095)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[188, 182])).
% 2.08/1.56 tff(190,plain,
% 2.08/1.56 ((~hskp59) | c1_1(a1095)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[189, 182])).
% 2.08/1.56 tff(191,plain,
% 2.08/1.56 ((~hskp59) | c1_1(a1095)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[190, 182])).
% 2.08/1.56 tff(192,plain,
% 2.08/1.56 (c1_1(a1095)),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[191, 162])).
% 2.08/1.56 tff(193,plain,
% 2.08/1.56 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | c0_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | c0_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(194,plain,
% 2.08/1.56 ((hskp43 | hskp10 | (~ndr1_0) | c0_1(a1095) | (~c1_1(a1095)) | (~c2_1(a1095))) <=> (hskp43 | hskp10 | c0_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(195,plain,
% 2.08/1.56 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1095) | (~c1_1(a1095)) | (~c2_1(a1095)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | c0_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095))))),
% 2.08/1.56 inference(monotonicity,[status(thm)],[194])).
% 2.08/1.56 tff(196,plain,
% 2.08/1.56 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1095) | (~c1_1(a1095)) | (~c2_1(a1095)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | c0_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095)))),
% 2.08/1.56 inference(transitivity,[status(thm)],[195, 193])).
% 2.08/1.56 tff(197,plain,
% 2.08/1.56 ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1095) | (~c1_1(a1095)) | (~c2_1(a1095)))),
% 2.08/1.56 inference(quant_inst,[status(thm)],[])).
% 2.08/1.56 tff(198,plain,
% 2.08/1.56 ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | c0_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[197, 196])).
% 2.08/1.56 tff(199,plain,
% 2.08/1.56 (hskp43),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[198, 126, 53, 192, 174, 63, 181])).
% 2.08/1.56 tff(200,plain,
% 2.08/1.56 (((~hskp43) | c1_1(a1049)) <=> ((~hskp43) | c1_1(a1049))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(201,axiom,((~hskp43) | c1_1(a1049)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 2.08/1.56 tff(202,plain,
% 2.08/1.56 ((~hskp43) | c1_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[201, 200])).
% 2.08/1.56 tff(203,plain,
% 2.08/1.56 ((~hskp43) | c1_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[202, 200])).
% 2.08/1.56 tff(204,plain,
% 2.08/1.56 ((~hskp43) | c1_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[203, 200])).
% 2.08/1.56 tff(205,plain,
% 2.08/1.56 ((~hskp43) | c1_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[204, 200])).
% 2.08/1.56 tff(206,plain,
% 2.08/1.56 ((~hskp43) | c1_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[205, 200])).
% 2.08/1.56 tff(207,plain,
% 2.08/1.56 ((~hskp43) | c1_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[206, 200])).
% 2.08/1.56 tff(208,plain,
% 2.08/1.56 ((~hskp43) | c1_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[207, 200])).
% 2.08/1.56 tff(209,plain,
% 2.08/1.56 ((~hskp43) | c1_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[208, 200])).
% 2.08/1.56 tff(210,plain,
% 2.08/1.56 (c1_1(a1049)),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[209, 199])).
% 2.08/1.56 tff(211,plain,
% 2.08/1.56 (((~hskp43) | c2_1(a1049)) <=> ((~hskp43) | c2_1(a1049))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(212,axiom,((~hskp43) | c2_1(a1049)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 2.08/1.56 tff(213,plain,
% 2.08/1.56 ((~hskp43) | c2_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[212, 211])).
% 2.08/1.56 tff(214,plain,
% 2.08/1.56 ((~hskp43) | c2_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[213, 211])).
% 2.08/1.56 tff(215,plain,
% 2.08/1.56 ((~hskp43) | c2_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[214, 211])).
% 2.08/1.56 tff(216,plain,
% 2.08/1.56 ((~hskp43) | c2_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[215, 211])).
% 2.08/1.56 tff(217,plain,
% 2.08/1.56 ((~hskp43) | c2_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[216, 211])).
% 2.08/1.56 tff(218,plain,
% 2.08/1.56 ((~hskp43) | c2_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[217, 211])).
% 2.08/1.56 tff(219,plain,
% 2.08/1.56 ((~hskp43) | c2_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[218, 211])).
% 2.08/1.56 tff(220,plain,
% 2.08/1.56 ((~hskp43) | c2_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[219, 211])).
% 2.08/1.56 tff(221,plain,
% 2.08/1.56 (c2_1(a1049)),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[220, 199])).
% 2.08/1.56 tff(222,plain,
% 2.08/1.56 (((~hskp43) | c0_1(a1049)) <=> ((~hskp43) | c0_1(a1049))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(223,axiom,((~hskp43) | c0_1(a1049)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 2.08/1.56 tff(224,plain,
% 2.08/1.56 ((~hskp43) | c0_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[223, 222])).
% 2.08/1.56 tff(225,plain,
% 2.08/1.56 ((~hskp43) | c0_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[224, 222])).
% 2.08/1.56 tff(226,plain,
% 2.08/1.56 ((~hskp43) | c0_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[225, 222])).
% 2.08/1.56 tff(227,plain,
% 2.08/1.56 ((~hskp43) | c0_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[226, 222])).
% 2.08/1.56 tff(228,plain,
% 2.08/1.56 ((~hskp43) | c0_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[227, 222])).
% 2.08/1.56 tff(229,plain,
% 2.08/1.56 ((~hskp43) | c0_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[228, 222])).
% 2.08/1.56 tff(230,plain,
% 2.08/1.56 ((~hskp43) | c0_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[229, 222])).
% 2.08/1.56 tff(231,plain,
% 2.08/1.56 ((~hskp43) | c0_1(a1049)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[230, 222])).
% 2.08/1.56 tff(232,plain,
% 2.08/1.56 (c0_1(a1049)),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[231, 199])).
% 2.08/1.56 tff(233,plain,
% 2.08/1.56 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))),
% 2.08/1.56 inference(bind,[status(th)],[])).
% 2.08/1.56 tff(234,plain,
% 2.08/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 2.08/1.56 inference(quant_intro,[status(thm)],[233])).
% 2.08/1.56 tff(235,plain,
% 2.08/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(236,plain,
% 2.08/1.56 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), (((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W))), (((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W)))), ((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W))), ((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W)))), (((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), ((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), ((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), (((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c1_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c1_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), ((((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), ((((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))), (((((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))), (((((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))))),
% 2.08/1.56 inference(bind,[status(th)],[])).
% 2.08/1.56 tff(237,plain,
% 2.08/1.56 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 2.08/1.56 inference(quant_intro,[status(thm)],[236])).
% 2.08/1.56 tff(238,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) | c3_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause313')).
% 2.08/1.56 tff(239,plain,
% 2.08/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[238, 237])).
% 2.08/1.56 tff(240,plain,
% 2.08/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[239, 235])).
% 2.08/1.56 tff(241,plain,(
% 2.08/1.56 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 2.08/1.56 inference(skolemize,[status(sab)],[240])).
% 2.08/1.56 tff(242,plain,
% 2.08/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[241, 234])).
% 2.08/1.56 tff(243,assumption,(hskp56), introduced(assumption)).
% 2.08/1.56 tff(244,plain,
% 2.08/1.56 (((~hskp56) | (~c1_1(a1084))) <=> ((~hskp56) | (~c1_1(a1084)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(245,plain,
% 2.08/1.56 (((~c1_1(a1084)) | (~hskp56)) <=> ((~hskp56) | (~c1_1(a1084)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(246,axiom,((~c1_1(a1084)) | (~hskp56)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 2.08/1.56 tff(247,plain,
% 2.08/1.56 ((~hskp56) | (~c1_1(a1084))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[246, 245])).
% 2.08/1.56 tff(248,plain,
% 2.08/1.56 ((~hskp56) | (~c1_1(a1084))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[247, 244])).
% 2.08/1.56 tff(249,plain,
% 2.08/1.56 (~c1_1(a1084)),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[248, 243])).
% 2.08/1.56 tff(250,plain,
% 2.08/1.56 (((~hskp56) | (~c3_1(a1084))) <=> ((~hskp56) | (~c3_1(a1084)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(251,plain,
% 2.08/1.56 (((~c3_1(a1084)) | (~hskp56)) <=> ((~hskp56) | (~c3_1(a1084)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(252,axiom,((~c3_1(a1084)) | (~hskp56)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 2.08/1.56 tff(253,plain,
% 2.08/1.56 ((~hskp56) | (~c3_1(a1084))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[252, 251])).
% 2.08/1.56 tff(254,plain,
% 2.08/1.56 ((~hskp56) | (~c3_1(a1084))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[253, 250])).
% 2.08/1.56 tff(255,plain,
% 2.08/1.56 (~c3_1(a1084)),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[254, 243])).
% 2.08/1.56 tff(256,plain,
% 2.08/1.56 (((~hskp56) | c0_1(a1084)) <=> ((~hskp56) | c0_1(a1084))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(257,axiom,((~hskp56) | c0_1(a1084)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 2.08/1.56 tff(258,plain,
% 2.08/1.56 ((~hskp56) | c0_1(a1084)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[257, 256])).
% 2.08/1.56 tff(259,plain,
% 2.08/1.56 ((~hskp56) | c0_1(a1084)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[258, 256])).
% 2.08/1.56 tff(260,plain,
% 2.08/1.56 ((~hskp56) | c0_1(a1084)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[259, 256])).
% 2.08/1.56 tff(261,plain,
% 2.08/1.56 ((~hskp56) | c0_1(a1084)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[260, 256])).
% 2.08/1.56 tff(262,plain,
% 2.08/1.56 ((~hskp56) | c0_1(a1084)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[261, 256])).
% 2.08/1.56 tff(263,plain,
% 2.08/1.56 ((~hskp56) | c0_1(a1084)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[262, 256])).
% 2.08/1.56 tff(264,plain,
% 2.08/1.56 ((~hskp56) | c0_1(a1084)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[263, 256])).
% 2.08/1.56 tff(265,plain,
% 2.08/1.56 ((~hskp56) | c0_1(a1084)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[264, 256])).
% 2.08/1.56 tff(266,plain,
% 2.08/1.56 (c0_1(a1084)),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[265, 243])).
% 2.08/1.56 tff(267,plain,
% 2.08/1.56 (^[V: $i, U: $i] : refl((hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 2.08/1.56 inference(bind,[status(th)],[])).
% 2.08/1.56 tff(268,plain,
% 2.08/1.56 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.56 inference(quant_intro,[status(thm)],[267])).
% 2.08/1.56 tff(269,plain,
% 2.08/1.56 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(270,plain,
% 2.08/1.56 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c1_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> (((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))))), rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) | hskp25) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp25))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 2.08/1.56 inference(bind,[status(th)],[])).
% 2.08/1.56 tff(271,plain,
% 2.08/1.56 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) | hskp25) <=> ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.56 inference(quant_intro,[status(thm)],[270])).
% 2.08/1.56 tff(272,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause305')).
% 2.08/1.56 tff(273,plain,
% 2.08/1.56 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[272, 271])).
% 2.08/1.56 tff(274,plain,
% 2.08/1.56 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[273, 269])).
% 2.08/1.56 tff(275,plain,(
% 2.08/1.56 ![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.56 inference(skolemize,[status(sab)],[274])).
% 2.08/1.56 tff(276,plain,
% 2.08/1.56 (![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[275, 268])).
% 2.08/1.56 tff(277,assumption,(c0_1(a1084)), introduced(assumption)).
% 2.08/1.56 tff(278,assumption,(~c3_1(a1084)), introduced(assumption)).
% 2.08/1.56 tff(279,assumption,(~c1_1(a1084)), introduced(assumption)).
% 2.08/1.56 tff(280,assumption,(~hskp1), introduced(assumption)).
% 2.08/1.56 tff(281,assumption,(~c2_1(a1084)), introduced(assumption)).
% 2.08/1.56 tff(282,assumption,(hskp33), introduced(assumption)).
% 2.08/1.56 tff(283,plain,
% 2.08/1.56 (((~hskp33) | (~c1_1(a1031))) <=> ((~hskp33) | (~c1_1(a1031)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(284,plain,
% 2.08/1.56 (((~c1_1(a1031)) | (~hskp33)) <=> ((~hskp33) | (~c1_1(a1031)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(285,axiom,((~c1_1(a1031)) | (~hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause202')).
% 2.08/1.56 tff(286,plain,
% 2.08/1.56 ((~hskp33) | (~c1_1(a1031))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[285, 284])).
% 2.08/1.56 tff(287,plain,
% 2.08/1.56 ((~hskp33) | (~c1_1(a1031))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[286, 283])).
% 2.08/1.56 tff(288,plain,
% 2.08/1.56 (~c1_1(a1031)),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[287, 282])).
% 2.08/1.56 tff(289,plain,
% 2.08/1.56 (((~hskp33) | c2_1(a1031)) <=> ((~hskp33) | c2_1(a1031))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(290,axiom,((~hskp33) | c2_1(a1031)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 2.08/1.56 tff(291,plain,
% 2.08/1.56 ((~hskp33) | c2_1(a1031)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[290, 289])).
% 2.08/1.56 tff(292,plain,
% 2.08/1.56 ((~hskp33) | c2_1(a1031)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[291, 289])).
% 2.08/1.56 tff(293,plain,
% 2.08/1.56 ((~hskp33) | c2_1(a1031)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[292, 289])).
% 2.08/1.56 tff(294,plain,
% 2.08/1.56 ((~hskp33) | c2_1(a1031)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[293, 289])).
% 2.08/1.56 tff(295,plain,
% 2.08/1.56 ((~hskp33) | c2_1(a1031)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[294, 289])).
% 2.08/1.56 tff(296,plain,
% 2.08/1.56 ((~hskp33) | c2_1(a1031)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[295, 289])).
% 2.08/1.56 tff(297,plain,
% 2.08/1.56 ((~hskp33) | c2_1(a1031)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[296, 289])).
% 2.08/1.56 tff(298,plain,
% 2.08/1.56 ((~hskp33) | c2_1(a1031)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[297, 289])).
% 2.08/1.56 tff(299,plain,
% 2.08/1.56 (c2_1(a1031)),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[298, 282])).
% 2.08/1.56 tff(300,assumption,(~c0_1(a1031)), introduced(assumption)).
% 2.08/1.56 tff(301,assumption,(~c1_1(a1031)), introduced(assumption)).
% 2.08/1.56 tff(302,assumption,(c2_1(a1031)), introduced(assumption)).
% 2.08/1.56 tff(303,plain,
% 2.08/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c1_1(a1031) | (~ndr1_0) | (~c2_1(a1031)) | c0_1(a1031) | c2_1(a1084) | (~c0_1(a1084)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1031) | (~ndr1_0) | (~c2_1(a1031)) | c0_1(a1031) | c2_1(a1084) | (~c0_1(a1084)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(304,plain,
% 2.08/1.56 (((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084)) <=> (c3_1(a1084) | c1_1(a1084) | c1_1(a1031) | (~ndr1_0) | (~c2_1(a1031)) | c0_1(a1031) | c2_1(a1084) | (~c0_1(a1084)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(305,plain,
% 2.08/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c1_1(a1031) | (~ndr1_0) | (~c2_1(a1031)) | c0_1(a1031) | c2_1(a1084) | (~c0_1(a1084))))),
% 2.08/1.56 inference(monotonicity,[status(thm)],[304])).
% 2.08/1.56 tff(306,plain,
% 2.08/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1031) | (~ndr1_0) | (~c2_1(a1031)) | c0_1(a1031) | c2_1(a1084) | (~c0_1(a1084)))),
% 2.08/1.56 inference(transitivity,[status(thm)],[305, 303])).
% 2.08/1.56 tff(307,plain,
% 2.08/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084))),
% 2.08/1.56 inference(quant_inst,[status(thm)],[])).
% 2.08/1.56 tff(308,plain,
% 2.08/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1031) | (~ndr1_0) | (~c2_1(a1031)) | c0_1(a1031) | c2_1(a1084) | (~c0_1(a1084))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[307, 306])).
% 2.08/1.56 tff(309,plain,
% 2.08/1.56 ($false),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[308, 126, 277, 302, 278, 279, 301, 242, 281, 300])).
% 2.08/1.56 tff(310,plain,(c0_1(a1031) | (~c0_1(a1084)) | (~c2_1(a1031)) | c3_1(a1084) | c1_1(a1084) | c1_1(a1031) | c2_1(a1084)), inference(lemma,lemma(discharge,[]))).
% 2.08/1.56 tff(311,plain,
% 2.08/1.56 (c0_1(a1031)),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[310, 299, 277, 278, 279, 288, 281])).
% 2.08/1.56 tff(312,plain,
% 2.08/1.56 (((~hskp33) | c3_1(a1031)) <=> ((~hskp33) | c3_1(a1031))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(313,axiom,((~hskp33) | c3_1(a1031)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 2.08/1.56 tff(314,plain,
% 2.08/1.56 ((~hskp33) | c3_1(a1031)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[313, 312])).
% 2.08/1.56 tff(315,plain,
% 2.08/1.56 ((~hskp33) | c3_1(a1031)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[314, 312])).
% 2.08/1.56 tff(316,plain,
% 2.08/1.56 ((~hskp33) | c3_1(a1031)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[315, 312])).
% 2.08/1.56 tff(317,plain,
% 2.08/1.56 ((~hskp33) | c3_1(a1031)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[316, 312])).
% 2.08/1.56 tff(318,plain,
% 2.08/1.56 ((~hskp33) | c3_1(a1031)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[317, 312])).
% 2.08/1.56 tff(319,plain,
% 2.08/1.56 ((~hskp33) | c3_1(a1031)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[318, 312])).
% 2.08/1.56 tff(320,plain,
% 2.08/1.56 ((~hskp33) | c3_1(a1031)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[319, 312])).
% 2.08/1.56 tff(321,plain,
% 2.08/1.56 ((~hskp33) | c3_1(a1031)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[320, 312])).
% 2.08/1.56 tff(322,plain,
% 2.08/1.56 (c3_1(a1031)),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[321, 282])).
% 2.08/1.56 tff(323,plain,
% 2.08/1.56 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(324,plain,
% 2.08/1.56 ((hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031))) <=> (hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(325,plain,
% 2.08/1.56 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031))))),
% 2.08/1.56 inference(monotonicity,[status(thm)],[324])).
% 2.08/1.56 tff(326,plain,
% 2.08/1.56 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))),
% 2.08/1.56 inference(transitivity,[status(thm)],[325, 323])).
% 2.08/1.56 tff(327,plain,
% 2.08/1.57 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031)))),
% 2.08/1.57 inference(quant_inst,[status(thm)],[])).
% 2.08/1.57 tff(328,plain,
% 2.08/1.57 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031))),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[327, 326])).
% 2.08/1.57 tff(329,plain,
% 2.08/1.57 (hskp53 | (~c0_1(a1031))),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[328, 126, 322, 299, 288, 20])).
% 2.08/1.57 tff(330,plain,
% 2.08/1.57 (hskp53),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[329, 311])).
% 2.08/1.57 tff(331,plain,
% 2.08/1.57 (((~hskp53) | c0_1(a1073)) <=> ((~hskp53) | c0_1(a1073))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(332,axiom,((~hskp53) | c0_1(a1073)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 2.08/1.57 tff(333,plain,
% 2.08/1.57 ((~hskp53) | c0_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[332, 331])).
% 2.08/1.57 tff(334,plain,
% 2.08/1.57 ((~hskp53) | c0_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[333, 331])).
% 2.08/1.57 tff(335,plain,
% 2.08/1.57 ((~hskp53) | c0_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[334, 331])).
% 2.08/1.57 tff(336,plain,
% 2.08/1.57 ((~hskp53) | c0_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[335, 331])).
% 2.08/1.57 tff(337,plain,
% 2.08/1.57 ((~hskp53) | c0_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[336, 331])).
% 2.08/1.57 tff(338,plain,
% 2.08/1.57 ((~hskp53) | c0_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[337, 331])).
% 2.08/1.57 tff(339,plain,
% 2.08/1.57 ((~hskp53) | c0_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[338, 331])).
% 2.08/1.57 tff(340,plain,
% 2.08/1.57 ((~hskp53) | c0_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[339, 331])).
% 2.08/1.57 tff(341,plain,
% 2.08/1.57 (c0_1(a1073)),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[340, 330])).
% 2.08/1.57 tff(342,plain,
% 2.08/1.57 (((~hskp53) | c2_1(a1073)) <=> ((~hskp53) | c2_1(a1073))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(343,axiom,((~hskp53) | c2_1(a1073)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 2.08/1.57 tff(344,plain,
% 2.08/1.57 ((~hskp53) | c2_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[343, 342])).
% 2.08/1.57 tff(345,plain,
% 2.08/1.57 ((~hskp53) | c2_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[344, 342])).
% 2.08/1.57 tff(346,plain,
% 2.08/1.57 ((~hskp53) | c2_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[345, 342])).
% 2.08/1.57 tff(347,plain,
% 2.08/1.57 ((~hskp53) | c2_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[346, 342])).
% 2.08/1.57 tff(348,plain,
% 2.08/1.57 ((~hskp53) | c2_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[347, 342])).
% 2.08/1.57 tff(349,plain,
% 2.08/1.57 ((~hskp53) | c2_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[348, 342])).
% 2.08/1.57 tff(350,plain,
% 2.08/1.57 ((~hskp53) | c2_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[349, 342])).
% 2.08/1.57 tff(351,plain,
% 2.08/1.57 ((~hskp53) | c2_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[350, 342])).
% 2.08/1.57 tff(352,plain,
% 2.08/1.57 (c2_1(a1073)),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[351, 330])).
% 2.08/1.57 tff(353,plain,
% 2.08/1.57 (((~hskp53) | c1_1(a1073)) <=> ((~hskp53) | c1_1(a1073))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(354,axiom,((~hskp53) | c1_1(a1073)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 2.08/1.57 tff(355,plain,
% 2.08/1.57 ((~hskp53) | c1_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[354, 353])).
% 2.08/1.57 tff(356,plain,
% 2.08/1.57 ((~hskp53) | c1_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[355, 353])).
% 2.08/1.57 tff(357,plain,
% 2.08/1.57 ((~hskp53) | c1_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[356, 353])).
% 2.08/1.57 tff(358,plain,
% 2.08/1.57 ((~hskp53) | c1_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[357, 353])).
% 2.08/1.57 tff(359,plain,
% 2.08/1.57 ((~hskp53) | c1_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[358, 353])).
% 2.08/1.57 tff(360,plain,
% 2.08/1.57 ((~hskp53) | c1_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[359, 353])).
% 2.08/1.57 tff(361,plain,
% 2.08/1.57 ((~hskp53) | c1_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[360, 353])).
% 2.08/1.57 tff(362,plain,
% 2.08/1.57 ((~hskp53) | c1_1(a1073)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[361, 353])).
% 2.08/1.57 tff(363,plain,
% 2.08/1.57 (c1_1(a1073)),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[362, 330])).
% 2.08/1.57 tff(364,plain,
% 2.08/1.57 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(365,plain,
% 2.08/1.57 (((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031))) <=> ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(366,plain,
% 2.08/1.57 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031))))),
% 2.08/1.57 inference(monotonicity,[status(thm)],[365])).
% 2.08/1.57 tff(367,plain,
% 2.08/1.57 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))),
% 2.08/1.57 inference(transitivity,[status(thm)],[366, 364])).
% 2.08/1.57 tff(368,plain,
% 2.08/1.57 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031)))),
% 2.08/1.57 inference(quant_inst,[status(thm)],[])).
% 2.08/1.57 tff(369,plain,
% 2.08/1.57 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031))),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[368, 367])).
% 2.08/1.57 tff(370,plain,
% 2.08/1.57 ($false),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[369, 126, 363, 352, 341, 322, 299, 10, 311])).
% 2.08/1.57 tff(371,plain,((~hskp33) | (~c0_1(a1084)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084)), inference(lemma,lemma(discharge,[]))).
% 2.08/1.57 tff(372,plain,
% 2.08/1.57 (~hskp33),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[371, 281, 278, 279, 277])).
% 2.08/1.57 tff(373,assumption,(hskp15), introduced(assumption)).
% 2.08/1.57 tff(374,plain,
% 2.08/1.57 (((~hskp15) | (~c1_1(a1059))) <=> ((~hskp15) | (~c1_1(a1059)))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(375,plain,
% 2.08/1.57 (((~c1_1(a1059)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a1059)))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(376,axiom,((~c1_1(a1059)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause232')).
% 2.08/1.57 tff(377,plain,
% 2.08/1.57 ((~hskp15) | (~c1_1(a1059))),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[376, 375])).
% 2.08/1.57 tff(378,plain,
% 2.08/1.57 ((~hskp15) | (~c1_1(a1059))),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[377, 374])).
% 2.08/1.57 tff(379,plain,
% 2.08/1.57 (~c1_1(a1059)),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[378, 373])).
% 2.08/1.57 tff(380,plain,
% 2.08/1.57 (((~hskp15) | c2_1(a1059)) <=> ((~hskp15) | c2_1(a1059))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(381,axiom,((~hskp15) | c2_1(a1059)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 2.08/1.57 tff(382,plain,
% 2.08/1.57 ((~hskp15) | c2_1(a1059)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[381, 380])).
% 2.08/1.57 tff(383,plain,
% 2.08/1.57 ((~hskp15) | c2_1(a1059)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[382, 380])).
% 2.08/1.57 tff(384,plain,
% 2.08/1.57 ((~hskp15) | c2_1(a1059)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[383, 380])).
% 2.08/1.57 tff(385,plain,
% 2.08/1.57 ((~hskp15) | c2_1(a1059)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[384, 380])).
% 2.08/1.57 tff(386,plain,
% 2.08/1.57 ((~hskp15) | c2_1(a1059)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[385, 380])).
% 2.08/1.57 tff(387,plain,
% 2.08/1.57 ((~hskp15) | c2_1(a1059)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[386, 380])).
% 2.08/1.57 tff(388,plain,
% 2.08/1.57 ((~hskp15) | c2_1(a1059)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[387, 380])).
% 2.08/1.57 tff(389,plain,
% 2.08/1.57 ((~hskp15) | c2_1(a1059)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[388, 380])).
% 2.08/1.57 tff(390,plain,
% 2.08/1.57 (c2_1(a1059)),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[389, 373])).
% 2.08/1.57 tff(391,assumption,(~c0_1(a1059)), introduced(assumption)).
% 2.08/1.57 tff(392,assumption,(~c1_1(a1059)), introduced(assumption)).
% 2.08/1.57 tff(393,assumption,(c2_1(a1059)), introduced(assumption)).
% 2.08/1.57 tff(394,plain,
% 2.08/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c1_1(a1059) | (~ndr1_0) | (~c2_1(a1059)) | c0_1(a1059) | c2_1(a1084) | (~c0_1(a1084)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1059) | (~ndr1_0) | (~c2_1(a1059)) | c0_1(a1059) | c2_1(a1084) | (~c0_1(a1084)))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(395,plain,
% 2.08/1.57 (((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1059) | c1_1(a1059) | (~c2_1(a1059)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084)) <=> (c3_1(a1084) | c1_1(a1084) | c1_1(a1059) | (~ndr1_0) | (~c2_1(a1059)) | c0_1(a1059) | c2_1(a1084) | (~c0_1(a1084)))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(396,plain,
% 2.08/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1059) | c1_1(a1059) | (~c2_1(a1059)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c1_1(a1059) | (~ndr1_0) | (~c2_1(a1059)) | c0_1(a1059) | c2_1(a1084) | (~c0_1(a1084))))),
% 2.08/1.57 inference(monotonicity,[status(thm)],[395])).
% 2.08/1.57 tff(397,plain,
% 2.08/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1059) | c1_1(a1059) | (~c2_1(a1059)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1059) | (~ndr1_0) | (~c2_1(a1059)) | c0_1(a1059) | c2_1(a1084) | (~c0_1(a1084)))),
% 2.08/1.57 inference(transitivity,[status(thm)],[396, 394])).
% 2.08/1.57 tff(398,plain,
% 2.08/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1059) | c1_1(a1059) | (~c2_1(a1059)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084))),
% 2.08/1.57 inference(quant_inst,[status(thm)],[])).
% 2.08/1.57 tff(399,plain,
% 2.08/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1059) | (~ndr1_0) | (~c2_1(a1059)) | c0_1(a1059) | c2_1(a1084) | (~c0_1(a1084))),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[398, 397])).
% 2.08/1.57 tff(400,plain,
% 2.08/1.57 ($false),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[399, 126, 277, 393, 278, 279, 392, 242, 281, 391])).
% 2.08/1.57 tff(401,plain,(c0_1(a1059) | (~c0_1(a1084)) | (~c2_1(a1059)) | c3_1(a1084) | c1_1(a1084) | c1_1(a1059) | c2_1(a1084)), inference(lemma,lemma(discharge,[]))).
% 2.08/1.57 tff(402,plain,
% 2.08/1.57 (c0_1(a1059)),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[401, 390, 281, 278, 279, 379, 277])).
% 2.08/1.57 tff(403,plain,
% 2.08/1.57 (((~hskp15) | c3_1(a1059)) <=> ((~hskp15) | c3_1(a1059))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(404,axiom,((~hskp15) | c3_1(a1059)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 2.08/1.57 tff(405,plain,
% 2.08/1.57 ((~hskp15) | c3_1(a1059)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[404, 403])).
% 2.08/1.57 tff(406,plain,
% 2.08/1.57 ((~hskp15) | c3_1(a1059)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[405, 403])).
% 2.08/1.57 tff(407,plain,
% 2.08/1.57 ((~hskp15) | c3_1(a1059)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[406, 403])).
% 2.08/1.57 tff(408,plain,
% 2.08/1.57 ((~hskp15) | c3_1(a1059)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[407, 403])).
% 2.08/1.57 tff(409,plain,
% 2.08/1.57 ((~hskp15) | c3_1(a1059)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[408, 403])).
% 2.08/1.57 tff(410,plain,
% 2.08/1.57 ((~hskp15) | c3_1(a1059)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[409, 403])).
% 2.08/1.57 tff(411,plain,
% 2.08/1.57 ((~hskp15) | c3_1(a1059)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[410, 403])).
% 2.08/1.57 tff(412,plain,
% 2.08/1.57 ((~hskp15) | c3_1(a1059)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[411, 403])).
% 2.08/1.57 tff(413,plain,
% 2.08/1.57 (c3_1(a1059)),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[412, 373])).
% 2.08/1.57 tff(414,plain,
% 2.08/1.57 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1059) | (~ndr1_0) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1059) | (~ndr1_0) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(415,plain,
% 2.08/1.57 ((hskp53 | (~ndr1_0) | c1_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059))) <=> (hskp53 | c1_1(a1059) | (~ndr1_0) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(416,plain,
% 2.08/1.57 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1059) | (~ndr1_0) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059))))),
% 2.08/1.57 inference(monotonicity,[status(thm)],[415])).
% 2.08/1.57 tff(417,plain,
% 2.08/1.57 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1059) | (~ndr1_0) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))),
% 2.08/1.57 inference(transitivity,[status(thm)],[416, 414])).
% 2.08/1.57 tff(418,plain,
% 2.08/1.57 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059)))),
% 2.08/1.57 inference(quant_inst,[status(thm)],[])).
% 2.08/1.57 tff(419,plain,
% 2.08/1.57 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1059) | (~ndr1_0) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059))),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[418, 417])).
% 2.08/1.57 tff(420,plain,
% 2.08/1.57 (hskp53),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[419, 126, 413, 390, 379, 20, 402])).
% 2.08/1.57 tff(421,plain,
% 2.08/1.57 (c0_1(a1073)),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[340, 420])).
% 2.08/1.57 tff(422,plain,
% 2.08/1.57 (c2_1(a1073)),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[351, 420])).
% 2.08/1.57 tff(423,plain,
% 2.08/1.57 (c1_1(a1073)),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[362, 420])).
% 2.08/1.57 tff(424,plain,
% 2.08/1.57 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(425,plain,
% 2.08/1.57 (((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059))) <=> ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(426,plain,
% 2.08/1.57 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059))))),
% 2.08/1.57 inference(monotonicity,[status(thm)],[425])).
% 2.08/1.57 tff(427,plain,
% 2.08/1.57 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))),
% 2.08/1.57 inference(transitivity,[status(thm)],[426, 424])).
% 2.08/1.57 tff(428,plain,
% 2.08/1.57 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059)))),
% 2.08/1.57 inference(quant_inst,[status(thm)],[])).
% 2.08/1.57 tff(429,plain,
% 2.08/1.57 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059))),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[428, 427])).
% 2.08/1.57 tff(430,plain,
% 2.08/1.57 ($false),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[429, 126, 423, 422, 421, 413, 390, 10, 402])).
% 2.08/1.57 tff(431,plain,((~hskp15) | c2_1(a1084) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084))), inference(lemma,lemma(discharge,[]))).
% 2.08/1.57 tff(432,plain,
% 2.08/1.57 (~hskp15),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[431, 281, 278, 279, 277])).
% 2.08/1.57 tff(433,assumption,(hskp10), introduced(assumption)).
% 2.08/1.57 tff(434,plain,
% 2.08/1.57 (((~hskp10) | (~c2_1(a1039))) <=> ((~hskp10) | (~c2_1(a1039)))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(435,plain,
% 2.08/1.57 (((~c2_1(a1039)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a1039)))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(436,axiom,((~c2_1(a1039)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause241')).
% 2.08/1.57 tff(437,plain,
% 2.08/1.57 ((~hskp10) | (~c2_1(a1039))),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[436, 435])).
% 2.08/1.57 tff(438,plain,
% 2.08/1.57 ((~hskp10) | (~c2_1(a1039))),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[437, 434])).
% 2.08/1.57 tff(439,plain,
% 2.08/1.57 (~c2_1(a1039)),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[438, 433])).
% 2.08/1.57 tff(440,plain,
% 2.08/1.57 (((~hskp10) | c1_1(a1039)) <=> ((~hskp10) | c1_1(a1039))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(441,axiom,((~hskp10) | c1_1(a1039)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 2.08/1.57 tff(442,plain,
% 2.08/1.57 ((~hskp10) | c1_1(a1039)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[441, 440])).
% 2.08/1.57 tff(443,plain,
% 2.08/1.57 ((~hskp10) | c1_1(a1039)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[442, 440])).
% 2.08/1.57 tff(444,plain,
% 2.08/1.57 ((~hskp10) | c1_1(a1039)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[443, 440])).
% 2.08/1.57 tff(445,plain,
% 2.08/1.57 ((~hskp10) | c1_1(a1039)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[444, 440])).
% 2.08/1.57 tff(446,plain,
% 2.08/1.57 ((~hskp10) | c1_1(a1039)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[445, 440])).
% 2.08/1.57 tff(447,plain,
% 2.08/1.57 ((~hskp10) | c1_1(a1039)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[446, 440])).
% 2.08/1.57 tff(448,plain,
% 2.08/1.57 ((~hskp10) | c1_1(a1039)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[447, 440])).
% 2.08/1.57 tff(449,plain,
% 2.08/1.57 ((~hskp10) | c1_1(a1039)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[448, 440])).
% 2.08/1.57 tff(450,plain,
% 2.08/1.57 (c1_1(a1039)),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[449, 433])).
% 2.08/1.57 tff(451,plain,
% 2.08/1.57 (((~hskp10) | (~c0_1(a1039))) <=> ((~hskp10) | (~c0_1(a1039)))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(452,plain,
% 2.08/1.57 (((~c0_1(a1039)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a1039)))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(453,axiom,((~c0_1(a1039)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause242')).
% 2.08/1.57 tff(454,plain,
% 2.08/1.57 ((~hskp10) | (~c0_1(a1039))),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[453, 452])).
% 2.08/1.57 tff(455,plain,
% 2.08/1.57 ((~hskp10) | (~c0_1(a1039))),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[454, 451])).
% 2.08/1.57 tff(456,plain,
% 2.08/1.57 (~c0_1(a1039)),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[455, 433])).
% 2.08/1.57 tff(457,assumption,(~c0_1(a1039)), introduced(assumption)).
% 2.08/1.57 tff(458,assumption,(~c2_1(a1039)), introduced(assumption)).
% 2.08/1.57 tff(459,assumption,(c1_1(a1039)), introduced(assumption)).
% 2.08/1.57 tff(460,assumption,(c2_1(a1084)), introduced(assumption)).
% 2.08/1.57 tff(461,plain,
% 2.08/1.57 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 2.08/1.57 inference(bind,[status(th)],[])).
% 2.08/1.57 tff(462,plain,
% 2.08/1.57 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.08/1.57 inference(quant_intro,[status(thm)],[461])).
% 2.08/1.57 tff(463,plain,
% 2.08/1.57 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(464,plain,
% 2.08/1.57 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | c1_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | c1_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 2.08/1.57 inference(bind,[status(th)],[])).
% 2.08/1.57 tff(465,plain,
% 2.08/1.57 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | c1_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.08/1.57 inference(quant_intro,[status(thm)],[464])).
% 2.08/1.57 tff(466,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | c1_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause292')).
% 2.08/1.57 tff(467,plain,
% 2.08/1.57 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[466, 465])).
% 2.08/1.57 tff(468,plain,
% 2.08/1.57 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[467, 463])).
% 2.08/1.57 tff(469,plain,(
% 2.08/1.57 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.08/1.57 inference(skolemize,[status(sab)],[468])).
% 2.08/1.57 tff(470,plain,
% 2.08/1.57 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[469, 462])).
% 2.08/1.57 tff(471,plain,
% 2.08/1.57 (^[V: $i, U: $i] : refl((hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 2.08/1.57 inference(bind,[status(th)],[])).
% 2.08/1.57 tff(472,plain,
% 2.08/1.57 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.57 inference(quant_intro,[status(thm)],[471])).
% 2.08/1.57 tff(473,plain,
% 2.08/1.57 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(474,plain,
% 2.08/1.57 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c0_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp47) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp47))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp47) <=> (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp47) <=> (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 2.08/1.57 inference(bind,[status(th)],[])).
% 2.08/1.57 tff(475,plain,
% 2.08/1.57 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp47) <=> ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.57 inference(quant_intro,[status(thm)],[474])).
% 2.08/1.57 tff(476,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp47)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause303')).
% 2.08/1.57 tff(477,plain,
% 2.08/1.57 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[476, 475])).
% 2.08/1.57 tff(478,plain,
% 2.08/1.57 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[477, 473])).
% 2.08/1.57 tff(479,plain,(
% 2.08/1.57 ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.57 inference(skolemize,[status(sab)],[478])).
% 2.08/1.57 tff(480,plain,
% 2.08/1.57 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[479, 472])).
% 2.08/1.57 tff(481,plain,
% 2.08/1.57 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c0_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp47 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(482,plain,
% 2.08/1.57 ((hskp47 | (~ndr1_0) | c3_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084))) <=> (hskp47 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(483,plain,
% 2.08/1.57 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c0_1(a1084))))),
% 2.08/1.57 inference(monotonicity,[status(thm)],[482])).
% 2.08/1.57 tff(484,plain,
% 2.08/1.57 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp47 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 2.08/1.57 inference(transitivity,[status(thm)],[483, 481])).
% 2.08/1.57 tff(485,plain,
% 2.08/1.57 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)))),
% 2.08/1.57 inference(quant_inst,[status(thm)],[])).
% 2.08/1.57 tff(486,plain,
% 2.08/1.57 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp47 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c2_1(a1084)) | (~c0_1(a1084))),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[485, 484])).
% 2.08/1.57 tff(487,plain,
% 2.08/1.57 (hskp47 | (~c2_1(a1084))),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[486, 126, 277, 278, 279, 480])).
% 2.08/1.57 tff(488,plain,
% 2.08/1.57 (hskp47),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[487, 460])).
% 2.08/1.57 tff(489,plain,
% 2.08/1.57 (((~hskp47) | c3_1(a1056)) <=> ((~hskp47) | c3_1(a1056))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(490,axiom,((~hskp47) | c3_1(a1056)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 2.08/1.57 tff(491,plain,
% 2.08/1.57 ((~hskp47) | c3_1(a1056)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[490, 489])).
% 2.08/1.57 tff(492,plain,
% 2.08/1.57 ((~hskp47) | c3_1(a1056)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[491, 489])).
% 2.08/1.57 tff(493,plain,
% 2.08/1.57 ((~hskp47) | c3_1(a1056)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[492, 489])).
% 2.08/1.57 tff(494,plain,
% 2.08/1.57 ((~hskp47) | c3_1(a1056)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[493, 489])).
% 2.08/1.57 tff(495,plain,
% 2.08/1.57 ((~hskp47) | c3_1(a1056)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[494, 489])).
% 2.08/1.57 tff(496,plain,
% 2.08/1.57 ((~hskp47) | c3_1(a1056)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[495, 489])).
% 2.08/1.57 tff(497,plain,
% 2.08/1.57 ((~hskp47) | c3_1(a1056)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[496, 489])).
% 2.08/1.57 tff(498,plain,
% 2.08/1.57 ((~hskp47) | c3_1(a1056)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[497, 489])).
% 2.08/1.57 tff(499,plain,
% 2.08/1.57 (c3_1(a1056)),
% 2.08/1.57 inference(unit_resolution,[status(thm)],[498, 488])).
% 2.08/1.57 tff(500,plain,
% 2.08/1.57 (((~hskp47) | c1_1(a1056)) <=> ((~hskp47) | c1_1(a1056))),
% 2.08/1.57 inference(rewrite,[status(thm)],[])).
% 2.08/1.57 tff(501,axiom,((~hskp47) | c1_1(a1056)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 2.08/1.57 tff(502,plain,
% 2.08/1.57 ((~hskp47) | c1_1(a1056)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[501, 500])).
% 2.08/1.57 tff(503,plain,
% 2.08/1.57 ((~hskp47) | c1_1(a1056)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[502, 500])).
% 2.08/1.57 tff(504,plain,
% 2.08/1.57 ((~hskp47) | c1_1(a1056)),
% 2.08/1.57 inference(modus_ponens,[status(thm)],[503, 500])).
% 2.08/1.57 tff(505,plain,
% 2.08/1.57 ((~hskp47) | c1_1(a1056)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[504, 500])).
% 2.08/1.58 tff(506,plain,
% 2.08/1.58 ((~hskp47) | c1_1(a1056)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[505, 500])).
% 2.08/1.58 tff(507,plain,
% 2.08/1.58 ((~hskp47) | c1_1(a1056)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[506, 500])).
% 2.08/1.58 tff(508,plain,
% 2.08/1.58 ((~hskp47) | c1_1(a1056)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[507, 500])).
% 2.08/1.58 tff(509,plain,
% 2.08/1.58 ((~hskp47) | c1_1(a1056)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[508, 500])).
% 2.08/1.58 tff(510,plain,
% 2.08/1.58 (c1_1(a1056)),
% 2.08/1.58 inference(unit_resolution,[status(thm)],[509, 488])).
% 2.08/1.58 tff(511,plain,
% 2.08/1.58 (((~hskp47) | c2_1(a1056)) <=> ((~hskp47) | c2_1(a1056))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(512,axiom,((~hskp47) | c2_1(a1056)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 2.08/1.58 tff(513,plain,
% 2.08/1.58 ((~hskp47) | c2_1(a1056)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[512, 511])).
% 2.08/1.58 tff(514,plain,
% 2.08/1.58 ((~hskp47) | c2_1(a1056)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[513, 511])).
% 2.08/1.58 tff(515,plain,
% 2.08/1.58 ((~hskp47) | c2_1(a1056)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[514, 511])).
% 2.08/1.58 tff(516,plain,
% 2.08/1.58 ((~hskp47) | c2_1(a1056)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[515, 511])).
% 2.08/1.58 tff(517,plain,
% 2.08/1.58 ((~hskp47) | c2_1(a1056)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[516, 511])).
% 2.08/1.58 tff(518,plain,
% 2.08/1.58 ((~hskp47) | c2_1(a1056)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[517, 511])).
% 2.08/1.58 tff(519,plain,
% 2.08/1.58 ((~hskp47) | c2_1(a1056)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[518, 511])).
% 2.08/1.58 tff(520,plain,
% 2.08/1.58 ((~hskp47) | c2_1(a1056)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[519, 511])).
% 2.08/1.58 tff(521,plain,
% 2.08/1.58 (c2_1(a1056)),
% 2.08/1.58 inference(unit_resolution,[status(thm)],[520, 488])).
% 2.08/1.58 tff(522,plain,
% 2.08/1.58 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c0_1(a1056)) | (~c1_1(a1056)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c0_1(a1056)) | (~c1_1(a1056)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(523,plain,
% 2.08/1.58 (((~ndr1_0) | (~c1_1(a1056)) | (~c0_1(a1056)) | (~c2_1(a1056)) | (~c3_1(a1056)) | (~c0_1(a1056)) | (~c2_1(a1056))) <=> ((~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c0_1(a1056)) | (~c1_1(a1056)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(524,plain,
% 2.08/1.58 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1056)) | (~c0_1(a1056)) | (~c2_1(a1056)) | (~c3_1(a1056)) | (~c0_1(a1056)) | (~c2_1(a1056)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c0_1(a1056)) | (~c1_1(a1056))))),
% 2.08/1.58 inference(monotonicity,[status(thm)],[523])).
% 2.08/1.58 tff(525,plain,
% 2.08/1.58 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1056)) | (~c0_1(a1056)) | (~c2_1(a1056)) | (~c3_1(a1056)) | (~c0_1(a1056)) | (~c2_1(a1056)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c0_1(a1056)) | (~c1_1(a1056)))),
% 2.08/1.58 inference(transitivity,[status(thm)],[524, 522])).
% 2.08/1.58 tff(526,plain,
% 2.08/1.58 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1056)) | (~c0_1(a1056)) | (~c2_1(a1056)) | (~c3_1(a1056)) | (~c0_1(a1056)) | (~c2_1(a1056)))),
% 2.08/1.58 inference(quant_inst,[status(thm)],[])).
% 2.08/1.58 tff(527,plain,
% 2.08/1.58 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c0_1(a1056)) | (~c1_1(a1056))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[526, 525])).
% 2.08/1.58 tff(528,plain,
% 2.08/1.58 (~c0_1(a1056)),
% 2.08/1.58 inference(unit_resolution,[status(thm)],[527, 126, 521, 510, 499, 10])).
% 2.08/1.58 tff(529,plain,
% 2.08/1.58 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_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)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)))),
% 2.08/1.58 inference(bind,[status(th)],[])).
% 2.08/1.58 tff(530,plain,
% 2.08/1.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_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)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))),
% 2.08/1.58 inference(quant_intro,[status(thm)],[529])).
% 2.08/1.58 tff(531,plain,
% 2.08/1.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_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)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(532,plain,
% 2.08/1.58 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), (((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W))), ((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)))), (((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W))), (((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W)))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)))), ((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)) | c1_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)) | c1_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))), ((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)))), (((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | 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(V)) | c0_1(W) | c1_1(W) | c2_1(W))), (((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))))),
% 2.08/1.58 inference(bind,[status(th)],[])).
% 2.08/1.58 tff(533,plain,
% 2.08/1.58 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))),
% 2.08/1.58 inference(quant_intro,[status(thm)],[532])).
% 2.08/1.58 tff(534,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c3_1(U)) | c1_1(U)) | c0_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause315')).
% 2.08/1.58 tff(535,plain,
% 2.08/1.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[534, 533])).
% 2.08/1.58 tff(536,plain,
% 2.08/1.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[535, 531])).
% 2.08/1.58 tff(537,plain,(
% 2.08/1.58 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))),
% 2.08/1.58 inference(skolemize,[status(sab)],[536])).
% 2.08/1.58 tff(538,plain,
% 2.08/1.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[537, 530])).
% 2.08/1.58 tff(539,plain,
% 2.08/1.58 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp25 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(540,plain,
% 2.08/1.58 ((hskp25 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039))) <=> (hskp25 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(541,plain,
% 2.08/1.58 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056))))),
% 2.08/1.58 inference(monotonicity,[status(thm)],[540])).
% 2.08/1.58 tff(542,plain,
% 2.08/1.58 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp25 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)))),
% 2.08/1.58 inference(transitivity,[status(thm)],[541, 539])).
% 2.08/1.58 tff(543,plain,
% 2.08/1.58 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039)))),
% 2.08/1.58 inference(quant_inst,[status(thm)],[])).
% 2.08/1.58 tff(544,plain,
% 2.08/1.58 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp25 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[543, 542])).
% 2.08/1.58 tff(545,plain,
% 2.08/1.58 (hskp25),
% 2.08/1.58 inference(unit_resolution,[status(thm)],[544, 126, 521, 510, 499, 459, 458, 457, 276])).
% 2.08/1.58 tff(546,plain,
% 2.08/1.58 (((~hskp25) | (~c2_1(a1091))) <=> ((~hskp25) | (~c2_1(a1091)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(547,plain,
% 2.08/1.58 (((~c2_1(a1091)) | (~hskp25)) <=> ((~hskp25) | (~c2_1(a1091)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(548,axiom,((~c2_1(a1091)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause215')).
% 2.08/1.58 tff(549,plain,
% 2.08/1.58 ((~hskp25) | (~c2_1(a1091))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[548, 547])).
% 2.08/1.58 tff(550,plain,
% 2.08/1.58 ((~hskp25) | (~c2_1(a1091))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[549, 546])).
% 2.08/1.58 tff(551,plain,
% 2.08/1.58 (~c2_1(a1091)),
% 2.08/1.58 inference(unit_resolution,[status(thm)],[550, 545])).
% 2.08/1.58 tff(552,plain,
% 2.08/1.58 (((~hskp25) | (~c0_1(a1091))) <=> ((~hskp25) | (~c0_1(a1091)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(553,plain,
% 2.08/1.58 (((~c0_1(a1091)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a1091)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(554,axiom,((~c0_1(a1091)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause214')).
% 2.08/1.58 tff(555,plain,
% 2.08/1.58 ((~hskp25) | (~c0_1(a1091))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[554, 553])).
% 2.08/1.58 tff(556,plain,
% 2.08/1.58 ((~hskp25) | (~c0_1(a1091))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[555, 552])).
% 2.08/1.58 tff(557,plain,
% 2.08/1.58 (~c0_1(a1091)),
% 2.08/1.58 inference(unit_resolution,[status(thm)],[556, 545])).
% 2.08/1.58 tff(558,plain,
% 2.08/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | c1_1(a1091) | (~c2_1(a1084)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | c1_1(a1091) | (~c2_1(a1084)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(559,plain,
% 2.08/1.58 (((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1056) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1091) | c1_1(a1091) | c2_1(a1091)) <=> (c3_1(a1084) | c1_1(a1084) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | c1_1(a1091) | (~c2_1(a1084)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(560,plain,
% 2.08/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1056) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1091) | c1_1(a1091) | c2_1(a1091))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | c1_1(a1091) | (~c2_1(a1084))))),
% 2.08/1.58 inference(monotonicity,[status(thm)],[559])).
% 2.08/1.58 tff(561,plain,
% 2.08/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1056) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1091) | c1_1(a1091) | c2_1(a1091))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | c1_1(a1091) | (~c2_1(a1084)))),
% 2.08/1.58 inference(transitivity,[status(thm)],[560, 558])).
% 2.08/1.58 tff(562,plain,
% 2.08/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1056) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1091) | c1_1(a1091) | c2_1(a1091))),
% 2.08/1.58 inference(quant_inst,[status(thm)],[])).
% 2.08/1.58 tff(563,plain,
% 2.08/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | c1_1(a1091) | (~c2_1(a1084))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[562, 561])).
% 2.08/1.58 tff(564,plain,
% 2.08/1.58 (c1_1(a1091)),
% 2.08/1.58 inference(unit_resolution,[status(thm)],[563, 126, 521, 499, 278, 279, 557, 551, 538, 460, 528])).
% 2.08/1.58 tff(565,plain,
% 2.08/1.58 (^[V: $i, U: $i] : refl((hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 2.08/1.58 inference(bind,[status(th)],[])).
% 2.08/1.58 tff(566,plain,
% 2.08/1.58 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.58 inference(quant_intro,[status(thm)],[565])).
% 2.08/1.58 tff(567,plain,
% 2.08/1.58 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(568,plain,
% 2.08/1.58 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) | c2_1(V)) | c3_1(V)) | hskp34) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp34))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp34) <=> (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) | c2_1(V)) | c3_1(V)) | hskp34) <=> (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 2.08/1.58 inference(bind,[status(th)],[])).
% 2.08/1.58 tff(569,plain,
% 2.08/1.58 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) | c2_1(V)) | c3_1(V)) | hskp34) <=> ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.58 inference(quant_intro,[status(thm)],[568])).
% 2.08/1.58 tff(570,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c1_1(U)) | c2_1(V)) | c3_1(V)) | hskp34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause289')).
% 2.08/1.58 tff(571,plain,
% 2.08/1.58 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[570, 569])).
% 2.08/1.58 tff(572,plain,
% 2.08/1.58 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[571, 567])).
% 2.08/1.58 tff(573,plain,(
% 2.08/1.58 ![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.58 inference(skolemize,[status(sab)],[572])).
% 2.08/1.58 tff(574,plain,
% 2.08/1.58 (![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[573, 566])).
% 2.08/1.58 tff(575,plain,
% 2.08/1.58 (((~hskp25) | (~c3_1(a1091))) <=> ((~hskp25) | (~c3_1(a1091)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(576,plain,
% 2.08/1.58 (((~c3_1(a1091)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a1091)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(577,axiom,((~c3_1(a1091)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause213')).
% 2.08/1.58 tff(578,plain,
% 2.08/1.58 ((~hskp25) | (~c3_1(a1091))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[577, 576])).
% 2.08/1.58 tff(579,plain,
% 2.08/1.58 ((~hskp25) | (~c3_1(a1091))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[578, 575])).
% 2.08/1.58 tff(580,plain,
% 2.08/1.58 (~c3_1(a1091)),
% 2.08/1.58 inference(unit_resolution,[status(thm)],[579, 545])).
% 2.08/1.58 tff(581,plain,
% 2.08/1.58 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c1_1(a1091)) | (~c0_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c1_1(a1091)) | (~c0_1(a1084)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(582,plain,
% 2.08/1.58 ((hskp34 | (~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c3_1(a1091) | c2_1(a1091) | (~c1_1(a1091))) <=> (hskp34 | c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c1_1(a1091)) | (~c0_1(a1084)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(583,plain,
% 2.08/1.58 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c3_1(a1091) | c2_1(a1091) | (~c1_1(a1091)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp34 | c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c1_1(a1091)) | (~c0_1(a1084))))),
% 2.08/1.58 inference(monotonicity,[status(thm)],[582])).
% 2.08/1.58 tff(584,plain,
% 2.08/1.58 (((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c3_1(a1091) | c2_1(a1091) | (~c1_1(a1091)))) <=> ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c1_1(a1091)) | (~c0_1(a1084)))),
% 2.08/1.58 inference(transitivity,[status(thm)],[583, 581])).
% 2.08/1.58 tff(585,plain,
% 2.08/1.58 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp34 | (~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c3_1(a1091) | c2_1(a1091) | (~c1_1(a1091)))),
% 2.08/1.58 inference(quant_inst,[status(thm)],[])).
% 2.08/1.58 tff(586,plain,
% 2.08/1.58 ((~![V: $i, U: $i] : (hskp34 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp34 | c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | (~ndr1_0) | (~c1_1(a1091)) | (~c0_1(a1084))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[585, 584])).
% 2.08/1.58 tff(587,plain,
% 2.08/1.58 (hskp34),
% 2.08/1.58 inference(unit_resolution,[status(thm)],[586, 126, 277, 278, 279, 580, 551, 574, 564])).
% 2.08/1.58 tff(588,plain,
% 2.08/1.58 (((~hskp34) | (~c1_1(a1032))) <=> ((~hskp34) | (~c1_1(a1032)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(589,plain,
% 2.08/1.58 (((~c1_1(a1032)) | (~hskp34)) <=> ((~hskp34) | (~c1_1(a1032)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(590,axiom,((~c1_1(a1032)) | (~hskp34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause201')).
% 2.08/1.58 tff(591,plain,
% 2.08/1.58 ((~hskp34) | (~c1_1(a1032))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[590, 589])).
% 2.08/1.58 tff(592,plain,
% 2.08/1.58 ((~hskp34) | (~c1_1(a1032))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[591, 588])).
% 2.08/1.58 tff(593,plain,
% 2.08/1.58 (~c1_1(a1032)),
% 2.08/1.58 inference(unit_resolution,[status(thm)],[592, 587])).
% 2.08/1.58 tff(594,plain,
% 2.08/1.58 (((~hskp34) | (~c2_1(a1032))) <=> ((~hskp34) | (~c2_1(a1032)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(595,plain,
% 2.08/1.58 (((~c2_1(a1032)) | (~hskp34)) <=> ((~hskp34) | (~c2_1(a1032)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(596,axiom,((~c2_1(a1032)) | (~hskp34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause200')).
% 2.08/1.58 tff(597,plain,
% 2.08/1.58 ((~hskp34) | (~c2_1(a1032))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[596, 595])).
% 2.08/1.58 tff(598,plain,
% 2.08/1.58 ((~hskp34) | (~c2_1(a1032))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[597, 594])).
% 2.08/1.58 tff(599,plain,
% 2.08/1.58 (~c2_1(a1032)),
% 2.08/1.58 inference(unit_resolution,[status(thm)],[598, 587])).
% 2.08/1.58 tff(600,plain,
% 2.08/1.58 (((~hskp34) | c3_1(a1032)) <=> ((~hskp34) | c3_1(a1032))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(601,axiom,((~hskp34) | c3_1(a1032)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 2.08/1.58 tff(602,plain,
% 2.08/1.58 ((~hskp34) | c3_1(a1032)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[601, 600])).
% 2.08/1.58 tff(603,plain,
% 2.08/1.58 ((~hskp34) | c3_1(a1032)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[602, 600])).
% 2.08/1.58 tff(604,plain,
% 2.08/1.58 ((~hskp34) | c3_1(a1032)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[603, 600])).
% 2.08/1.58 tff(605,plain,
% 2.08/1.58 ((~hskp34) | c3_1(a1032)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[604, 600])).
% 2.08/1.58 tff(606,plain,
% 2.08/1.58 ((~hskp34) | c3_1(a1032)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[605, 600])).
% 2.08/1.58 tff(607,plain,
% 2.08/1.58 ((~hskp34) | c3_1(a1032)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[606, 600])).
% 2.08/1.58 tff(608,plain,
% 2.08/1.58 ((~hskp34) | c3_1(a1032)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[607, 600])).
% 2.08/1.58 tff(609,plain,
% 2.08/1.58 ((~hskp34) | c3_1(a1032)),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[608, 600])).
% 2.08/1.58 tff(610,plain,
% 2.08/1.58 (c3_1(a1032)),
% 2.08/1.58 inference(unit_resolution,[status(thm)],[609, 587])).
% 2.08/1.58 tff(611,plain,
% 2.08/1.58 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a1084) | c2_1(a1032) | c1_1(a1032) | (~ndr1_0) | (~c3_1(a1032)) | (~c2_1(a1084)) | (~c0_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1084) | c2_1(a1032) | c1_1(a1032) | (~ndr1_0) | (~c3_1(a1032)) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(612,plain,
% 2.08/1.58 ((hskp1 | (~ndr1_0) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c2_1(a1032) | c1_1(a1032) | (~c3_1(a1032))) <=> (hskp1 | c1_1(a1084) | c2_1(a1032) | c1_1(a1032) | (~ndr1_0) | (~c3_1(a1032)) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(613,plain,
% 2.08/1.58 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c2_1(a1032) | c1_1(a1032) | (~c3_1(a1032)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a1084) | c2_1(a1032) | c1_1(a1032) | (~ndr1_0) | (~c3_1(a1032)) | (~c2_1(a1084)) | (~c0_1(a1084))))),
% 2.08/1.58 inference(monotonicity,[status(thm)],[612])).
% 2.08/1.58 tff(614,plain,
% 2.08/1.58 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c2_1(a1032) | c1_1(a1032) | (~c3_1(a1032)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1084) | c2_1(a1032) | c1_1(a1032) | (~ndr1_0) | (~c3_1(a1032)) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 2.08/1.58 inference(transitivity,[status(thm)],[613, 611])).
% 2.08/1.58 tff(615,plain,
% 2.08/1.58 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c2_1(a1032) | c1_1(a1032) | (~c3_1(a1032)))),
% 2.08/1.58 inference(quant_inst,[status(thm)],[])).
% 2.08/1.58 tff(616,plain,
% 2.08/1.58 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1084) | c2_1(a1032) | c1_1(a1032) | (~ndr1_0) | (~c3_1(a1032)) | (~c2_1(a1084)) | (~c0_1(a1084))),
% 2.08/1.58 inference(modus_ponens,[status(thm)],[615, 614])).
% 2.08/1.58 tff(617,plain,
% 2.08/1.58 ($false),
% 2.08/1.58 inference(unit_resolution,[status(thm)],[616, 126, 280, 277, 610, 279, 599, 593, 470, 460])).
% 2.08/1.58 tff(618,plain,((~c2_1(a1084)) | hskp1 | (~c0_1(a1084)) | c1_1(a1084) | c3_1(a1084) | (~c1_1(a1039)) | c2_1(a1039) | c0_1(a1039)), inference(lemma,lemma(discharge,[]))).
% 2.08/1.58 tff(619,plain,
% 2.08/1.58 (~c2_1(a1084)),
% 2.08/1.58 inference(unit_resolution,[status(thm)],[618, 280, 277, 279, 278, 459, 458, 457])).
% 2.08/1.58 tff(620,plain,
% 2.08/1.58 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)))),
% 2.08/1.58 inference(bind,[status(th)],[])).
% 2.08/1.58 tff(621,plain,
% 2.08/1.58 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 2.08/1.58 inference(quant_intro,[status(thm)],[620])).
% 2.08/1.58 tff(622,plain,
% 2.08/1.58 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 2.08/1.58 inference(rewrite,[status(thm)],[])).
% 2.08/1.58 tff(623,plain,
% 2.08/1.58 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) | c2_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V)) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) | c2_1(V)) | c0_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) | c2_1(V)) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))))),
% 2.08/1.59 inference(bind,[status(th)],[])).
% 2.08/1.59 tff(624,plain,
% 2.08/1.59 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) | c2_1(V)) | c0_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 2.08/1.59 inference(quant_intro,[status(thm)],[623])).
% 2.08/1.59 tff(625,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c3_1(V)) | c2_1(V)) | c0_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause288')).
% 2.08/1.59 tff(626,plain,
% 2.08/1.59 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[625, 624])).
% 2.08/1.59 tff(627,plain,
% 2.08/1.59 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[626, 622])).
% 2.08/1.59 tff(628,plain,(
% 2.08/1.59 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 2.08/1.59 inference(skolemize,[status(sab)],[627])).
% 2.08/1.59 tff(629,plain,
% 2.08/1.59 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[628, 621])).
% 2.08/1.59 tff(630,plain,
% 2.08/1.59 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | c1_1(a1084) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | c2_1(a1084) | (~c0_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp1 | c1_1(a1084) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | c2_1(a1084) | (~c0_1(a1084)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(631,plain,
% 2.08/1.59 ((hskp1 | (~ndr1_0) | c2_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1039) | c3_1(a1039) | c2_1(a1039)) <=> (hskp1 | c1_1(a1084) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | c2_1(a1084) | (~c0_1(a1084)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(632,plain,
% 2.08/1.59 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1039) | c3_1(a1039) | c2_1(a1039))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | c1_1(a1084) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | c2_1(a1084) | (~c0_1(a1084))))),
% 2.08/1.59 inference(monotonicity,[status(thm)],[631])).
% 2.08/1.59 tff(633,plain,
% 2.08/1.59 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1039) | c3_1(a1039) | c2_1(a1039))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp1 | c1_1(a1084) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | c2_1(a1084) | (~c0_1(a1084)))),
% 2.08/1.59 inference(transitivity,[status(thm)],[632, 630])).
% 2.08/1.59 tff(634,plain,
% 2.08/1.59 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1039) | c3_1(a1039) | c2_1(a1039))),
% 2.08/1.59 inference(quant_inst,[status(thm)],[])).
% 2.08/1.59 tff(635,plain,
% 2.08/1.59 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp1 | c1_1(a1084) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | c2_1(a1084) | (~c0_1(a1084))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[634, 633])).
% 2.08/1.59 tff(636,plain,
% 2.08/1.59 (c3_1(a1039)),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[635, 126, 280, 277, 279, 458, 457, 629, 619])).
% 2.08/1.59 tff(637,plain,
% 2.08/1.59 (~hskp33),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[371, 619, 278, 279, 277])).
% 2.08/1.59 tff(638,plain,
% 2.08/1.59 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(639,plain,
% 2.08/1.59 ((hskp33 | hskp15 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039))) <=> (hskp33 | hskp15 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(640,plain,
% 2.08/1.59 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039))))),
% 2.08/1.59 inference(monotonicity,[status(thm)],[639])).
% 2.08/1.59 tff(641,plain,
% 2.08/1.59 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)))),
% 2.08/1.59 inference(transitivity,[status(thm)],[640, 638])).
% 2.08/1.59 tff(642,plain,
% 2.08/1.59 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)))),
% 2.08/1.59 inference(quant_inst,[status(thm)],[])).
% 2.08/1.59 tff(643,plain,
% 2.08/1.59 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[642, 641])).
% 2.08/1.59 tff(644,plain,
% 2.08/1.59 (hskp33 | hskp15 | c2_1(a1039) | (~c3_1(a1039))),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[643, 126, 457, 52])).
% 2.08/1.59 tff(645,plain,
% 2.08/1.59 (hskp15),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[644, 637, 458, 636])).
% 2.08/1.59 tff(646,plain,
% 2.08/1.59 (~c1_1(a1059)),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[378, 645])).
% 2.08/1.59 tff(647,plain,
% 2.08/1.59 (c2_1(a1059)),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[389, 645])).
% 2.08/1.59 tff(648,plain,
% 2.08/1.59 (c0_1(a1059)),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[401, 647, 277, 278, 279, 646, 619])).
% 2.08/1.59 tff(649,plain,
% 2.08/1.59 (c3_1(a1059)),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[412, 645])).
% 2.08/1.59 tff(650,plain,
% 2.08/1.59 (hskp53 | (~c0_1(a1059))),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[419, 126, 649, 647, 646, 20])).
% 2.08/1.59 tff(651,plain,
% 2.08/1.59 (hskp53),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[650, 648])).
% 2.08/1.59 tff(652,plain,
% 2.08/1.59 (c0_1(a1073)),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[340, 651])).
% 2.08/1.59 tff(653,plain,
% 2.08/1.59 (c2_1(a1073)),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[351, 651])).
% 2.08/1.59 tff(654,plain,
% 2.08/1.59 (c1_1(a1073)),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[362, 651])).
% 2.08/1.59 tff(655,plain,
% 2.08/1.59 ($false),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[429, 126, 654, 653, 652, 649, 647, 10, 648])).
% 2.08/1.59 tff(656,plain,(hskp1 | (~c0_1(a1084)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1039) | c0_1(a1039) | (~c1_1(a1039))), inference(lemma,lemma(discharge,[]))).
% 2.08/1.59 tff(657,plain,
% 2.08/1.59 ($false),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[656, 456, 450, 278, 279, 277, 280, 439])).
% 2.08/1.59 tff(658,plain,((~hskp10) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | hskp1), inference(lemma,lemma(discharge,[]))).
% 2.08/1.59 tff(659,plain,
% 2.08/1.59 (~hskp10),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[658, 280, 279, 277, 278])).
% 2.08/1.59 tff(660,assumption,(~c0_1(a1079)), introduced(assumption)).
% 2.08/1.59 tff(661,assumption,(~c2_1(a1079)), introduced(assumption)).
% 2.08/1.59 tff(662,plain,
% 2.08/1.59 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1079)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1079)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(663,plain,
% 2.08/1.59 ((hskp33 | hskp15 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | (~c3_1(a1079))) <=> (hskp33 | hskp15 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1079)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(664,plain,
% 2.08/1.59 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | (~c3_1(a1079)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1079))))),
% 2.08/1.59 inference(monotonicity,[status(thm)],[663])).
% 2.08/1.59 tff(665,plain,
% 2.08/1.59 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | (~c3_1(a1079)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1079)))),
% 2.08/1.59 inference(transitivity,[status(thm)],[664, 662])).
% 2.08/1.59 tff(666,plain,
% 2.08/1.59 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1079) | c2_1(a1079) | (~c3_1(a1079)))),
% 2.08/1.59 inference(quant_inst,[status(thm)],[])).
% 2.08/1.59 tff(667,plain,
% 2.08/1.59 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1079))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[666, 665])).
% 2.08/1.59 tff(668,plain,
% 2.08/1.59 (c0_1(a1079) | (~c3_1(a1079))),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[667, 126, 21, 42, 661, 52])).
% 2.08/1.59 tff(669,plain,
% 2.08/1.59 (~c3_1(a1079)),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[668, 660])).
% 2.08/1.59 tff(670,plain,
% 2.08/1.59 (c0_1(a1079) | c3_1(a1079)),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[132, 126, 53, 661, 73])).
% 2.08/1.59 tff(671,plain,
% 2.08/1.59 ($false),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[670, 669, 660])).
% 2.08/1.59 tff(672,plain,(c0_1(a1079) | hskp10 | c2_1(a1079) | hskp33 | hskp15), inference(lemma,lemma(discharge,[]))).
% 2.08/1.59 tff(673,plain,
% 2.08/1.59 ($false),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[672, 80, 86, 53, 21, 42])).
% 2.08/1.59 tff(674,plain,((~hskp19) | hskp10 | hskp33 | hskp15), inference(lemma,lemma(discharge,[]))).
% 2.08/1.59 tff(675,plain,
% 2.08/1.59 (~hskp19),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[674, 21, 659, 42])).
% 2.08/1.59 tff(676,plain,
% 2.08/1.59 (^[U: $i] : refl((hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))),
% 2.08/1.59 inference(bind,[status(th)],[])).
% 2.08/1.59 tff(677,plain,
% 2.08/1.59 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.08/1.59 inference(quant_intro,[status(thm)],[676])).
% 2.08/1.59 tff(678,plain,
% 2.08/1.59 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(679,plain,
% 2.08/1.59 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp20) <=> ((hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp20))), rewrite(((hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp20) <=> (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp20) <=> (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))))),
% 2.08/1.59 inference(bind,[status(th)],[])).
% 2.08/1.59 tff(680,plain,
% 2.08/1.59 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp20) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.08/1.59 inference(quant_intro,[status(thm)],[679])).
% 2.08/1.59 tff(681,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause269')).
% 2.08/1.59 tff(682,plain,
% 2.08/1.59 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[681, 680])).
% 2.08/1.59 tff(683,plain,
% 2.08/1.59 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[682, 678])).
% 2.08/1.59 tff(684,plain,(
% 2.08/1.59 ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.08/1.59 inference(skolemize,[status(sab)],[683])).
% 2.08/1.59 tff(685,plain,
% 2.08/1.59 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[684, 677])).
% 2.08/1.59 tff(686,plain,
% 2.08/1.59 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(687,plain,
% 2.08/1.59 ((hskp20 | hskp19 | (~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084))) <=> (hskp20 | hskp19 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(688,plain,
% 2.08/1.59 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084))))),
% 2.08/1.59 inference(monotonicity,[status(thm)],[687])).
% 2.08/1.59 tff(689,plain,
% 2.08/1.59 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084)))),
% 2.08/1.59 inference(transitivity,[status(thm)],[688, 686])).
% 2.08/1.59 tff(690,plain,
% 2.08/1.59 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)))),
% 2.08/1.59 inference(quant_inst,[status(thm)],[])).
% 2.08/1.59 tff(691,plain,
% 2.08/1.59 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c3_1(a1084) | c1_1(a1084) | (~ndr1_0) | (~c0_1(a1084))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[690, 689])).
% 2.08/1.59 tff(692,plain,
% 2.08/1.59 (hskp20 | hskp19),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[691, 126, 277, 278, 279, 685])).
% 2.08/1.59 tff(693,plain,
% 2.08/1.59 (hskp20),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[692, 675])).
% 2.08/1.59 tff(694,assumption,(hskp20), introduced(assumption)).
% 2.08/1.59 tff(695,plain,
% 2.08/1.59 (((~hskp20) | (~c2_1(a1080))) <=> ((~hskp20) | (~c2_1(a1080)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(696,plain,
% 2.08/1.59 (((~c2_1(a1080)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a1080)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(697,axiom,((~c2_1(a1080)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause224')).
% 2.08/1.59 tff(698,plain,
% 2.08/1.59 ((~hskp20) | (~c2_1(a1080))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[697, 696])).
% 2.08/1.59 tff(699,plain,
% 2.08/1.59 ((~hskp20) | (~c2_1(a1080))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[698, 695])).
% 2.08/1.59 tff(700,plain,
% 2.08/1.59 (~c2_1(a1080)),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[699, 694])).
% 2.08/1.59 tff(701,plain,
% 2.08/1.59 (((~hskp20) | (~c0_1(a1080))) <=> ((~hskp20) | (~c0_1(a1080)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(702,plain,
% 2.08/1.59 (((~c0_1(a1080)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a1080)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(703,axiom,((~c0_1(a1080)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause223')).
% 2.08/1.59 tff(704,plain,
% 2.08/1.59 ((~hskp20) | (~c0_1(a1080))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[703, 702])).
% 2.08/1.59 tff(705,plain,
% 2.08/1.59 ((~hskp20) | (~c0_1(a1080))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[704, 701])).
% 2.08/1.59 tff(706,plain,
% 2.08/1.59 (~c0_1(a1080)),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[705, 694])).
% 2.08/1.59 tff(707,plain,
% 2.08/1.59 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | c2_1(a1084) | (~c0_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp1 | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | c2_1(a1084) | (~c0_1(a1084)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(708,plain,
% 2.08/1.59 ((hskp1 | (~ndr1_0) | c2_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1080) | c3_1(a1080) | c2_1(a1080)) <=> (hskp1 | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | c2_1(a1084) | (~c0_1(a1084)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(709,plain,
% 2.08/1.59 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1080) | c3_1(a1080) | c2_1(a1080))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | c2_1(a1084) | (~c0_1(a1084))))),
% 2.08/1.59 inference(monotonicity,[status(thm)],[708])).
% 2.08/1.59 tff(710,plain,
% 2.08/1.59 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1080) | c3_1(a1080) | c2_1(a1080))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp1 | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | c2_1(a1084) | (~c0_1(a1084)))),
% 2.08/1.59 inference(transitivity,[status(thm)],[709, 707])).
% 2.08/1.59 tff(711,plain,
% 2.08/1.59 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1080) | c3_1(a1080) | c2_1(a1080))),
% 2.08/1.59 inference(quant_inst,[status(thm)],[])).
% 2.08/1.59 tff(712,plain,
% 2.08/1.59 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp1 | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080) | c2_1(a1084) | (~c0_1(a1084))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[711, 710])).
% 2.08/1.59 tff(713,plain,
% 2.08/1.59 (c3_1(a1080)),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[712, 126, 280, 277, 279, 706, 700, 629, 281])).
% 2.08/1.59 tff(714,plain,
% 2.08/1.59 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(715,plain,
% 2.08/1.59 ((hskp33 | hskp15 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | (~c3_1(a1080))) <=> (hskp33 | hskp15 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(716,plain,
% 2.08/1.59 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | (~c3_1(a1080)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080))))),
% 2.08/1.59 inference(monotonicity,[status(thm)],[715])).
% 2.08/1.59 tff(717,plain,
% 2.08/1.59 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | (~c3_1(a1080)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)))),
% 2.08/1.59 inference(transitivity,[status(thm)],[716, 714])).
% 2.08/1.59 tff(718,plain,
% 2.08/1.59 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | (~c3_1(a1080)))),
% 2.08/1.59 inference(quant_inst,[status(thm)],[])).
% 2.08/1.59 tff(719,plain,
% 2.08/1.59 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[718, 717])).
% 2.08/1.59 tff(720,plain,
% 2.08/1.59 ($false),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[719, 126, 21, 42, 706, 700, 52, 713])).
% 2.08/1.59 tff(721,plain,((~hskp20) | hskp33 | hskp15 | hskp1 | (~c0_1(a1084)) | c1_1(a1084) | c2_1(a1084)), inference(lemma,lemma(discharge,[]))).
% 2.08/1.59 tff(722,plain,
% 2.08/1.59 (c2_1(a1084)),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[721, 693, 42, 280, 277, 279, 21])).
% 2.08/1.59 tff(723,plain,
% 2.08/1.59 (((~hskp20) | (~c1_1(a1080))) <=> ((~hskp20) | (~c1_1(a1080)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(724,plain,
% 2.08/1.59 (((~c1_1(a1080)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a1080)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(725,axiom,((~c1_1(a1080)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause225')).
% 2.08/1.59 tff(726,plain,
% 2.08/1.59 ((~hskp20) | (~c1_1(a1080))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[725, 724])).
% 2.08/1.59 tff(727,plain,
% 2.08/1.59 ((~hskp20) | (~c1_1(a1080))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[726, 723])).
% 2.08/1.59 tff(728,plain,
% 2.08/1.59 (~c1_1(a1080)),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[727, 693])).
% 2.08/1.59 tff(729,plain,
% 2.08/1.59 (~c2_1(a1080)),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[699, 693])).
% 2.08/1.59 tff(730,plain,
% 2.08/1.59 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a1084) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c2_1(a1084)) | (~c0_1(a1084)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1084) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(731,plain,
% 2.08/1.59 ((hskp1 | (~ndr1_0) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c2_1(a1080) | c1_1(a1080) | (~c3_1(a1080))) <=> (hskp1 | c1_1(a1084) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(732,plain,
% 2.08/1.59 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c2_1(a1080) | c1_1(a1080) | (~c3_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a1084) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c2_1(a1084)) | (~c0_1(a1084))))),
% 2.08/1.59 inference(monotonicity,[status(thm)],[731])).
% 2.08/1.59 tff(733,plain,
% 2.08/1.59 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c2_1(a1080) | c1_1(a1080) | (~c3_1(a1080)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1084) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c2_1(a1084)) | (~c0_1(a1084)))),
% 2.08/1.59 inference(transitivity,[status(thm)],[732, 730])).
% 2.08/1.59 tff(734,plain,
% 2.08/1.59 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a1084) | (~c0_1(a1084)) | (~c2_1(a1084)) | c2_1(a1080) | c1_1(a1080) | (~c3_1(a1080)))),
% 2.08/1.59 inference(quant_inst,[status(thm)],[])).
% 2.08/1.59 tff(735,plain,
% 2.08/1.59 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a1084) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c2_1(a1084)) | (~c0_1(a1084))),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[734, 733])).
% 2.08/1.59 tff(736,plain,
% 2.08/1.59 (~c3_1(a1080)),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[735, 126, 280, 277, 279, 729, 728, 470, 722])).
% 2.08/1.59 tff(737,plain,
% 2.08/1.59 (~c0_1(a1080)),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[705, 693])).
% 2.08/1.59 tff(738,plain,
% 2.08/1.59 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(739,plain,
% 2.08/1.59 ((hskp10 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | c3_1(a1080)) <=> (hskp10 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080))),
% 2.08/1.59 inference(rewrite,[status(thm)],[])).
% 2.08/1.59 tff(740,plain,
% 2.08/1.59 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | c3_1(a1080))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080)))),
% 2.08/1.59 inference(monotonicity,[status(thm)],[739])).
% 2.08/1.59 tff(741,plain,
% 2.08/1.59 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | c3_1(a1080))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080))),
% 2.08/1.59 inference(transitivity,[status(thm)],[740, 738])).
% 2.08/1.59 tff(742,plain,
% 2.08/1.59 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | c3_1(a1080))),
% 2.08/1.59 inference(quant_inst,[status(thm)],[])).
% 2.08/1.59 tff(743,plain,
% 2.08/1.59 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | c3_1(a1080)),
% 2.08/1.59 inference(modus_ponens,[status(thm)],[742, 741])).
% 2.08/1.59 tff(744,plain,
% 2.08/1.59 ($false),
% 2.08/1.59 inference(unit_resolution,[status(thm)],[743, 126, 659, 737, 729, 73, 736])).
% 2.08/1.59 tff(745,plain,(hskp33 | hskp1 | (~c0_1(a1084)) | c1_1(a1084) | hskp15 | c3_1(a1084)), inference(lemma,lemma(discharge,[]))).
% 2.08/1.60 tff(746,plain,
% 2.08/1.60 ($false),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[745, 432, 372, 277, 279, 280, 278])).
% 2.08/1.60 tff(747,plain,(c2_1(a1084) | (~c0_1(a1084)) | c1_1(a1084) | hskp1 | c3_1(a1084)), inference(lemma,lemma(discharge,[]))).
% 2.08/1.60 tff(748,plain,
% 2.08/1.60 (c2_1(a1084)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[747, 280, 279, 277, 278])).
% 2.08/1.60 tff(749,plain,
% 2.08/1.60 (^[V: $i, U: $i] : refl((hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 2.08/1.60 inference(bind,[status(th)],[])).
% 2.08/1.60 tff(750,plain,
% 2.08/1.60 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.60 inference(quant_intro,[status(thm)],[749])).
% 2.08/1.60 tff(751,plain,
% 2.08/1.60 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.60 inference(rewrite,[status(thm)],[])).
% 2.08/1.60 tff(752,plain,
% 2.08/1.60 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) | hskp33) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp33))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp33) <=> (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) | hskp33) <=> (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 2.08/1.60 inference(bind,[status(th)],[])).
% 2.08/1.60 tff(753,plain,
% 2.08/1.60 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) | hskp33) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.60 inference(quant_intro,[status(thm)],[752])).
% 2.08/1.60 tff(754,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c0_1(V)) | hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause300')).
% 2.08/1.60 tff(755,plain,
% 2.08/1.60 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[754, 753])).
% 2.08/1.60 tff(756,plain,
% 2.08/1.60 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[755, 751])).
% 2.08/1.60 tff(757,plain,(
% 2.08/1.60 ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.60 inference(skolemize,[status(sab)],[756])).
% 2.08/1.60 tff(758,plain,
% 2.08/1.60 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[757, 750])).
% 2.08/1.60 tff(759,plain,
% 2.08/1.60 (^[V: $i, U: $i] : refl((hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))))),
% 2.08/1.60 inference(bind,[status(th)],[])).
% 2.08/1.60 tff(760,plain,
% 2.08/1.60 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))),
% 2.08/1.60 inference(quant_intro,[status(thm)],[759])).
% 2.08/1.60 tff(761,plain,
% 2.08/1.60 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))),
% 2.08/1.60 inference(rewrite,[status(thm)],[])).
% 2.08/1.60 tff(762,plain,
% 2.08/1.60 (^[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(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(U)) | hskp36) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))) | hskp36))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V))) | hskp36) <=> (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(U)) | hskp36) <=> (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))))),
% 2.08/1.60 inference(bind,[status(th)],[])).
% 2.08/1.60 tff(763,plain,
% 2.08/1.60 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(U)) | hskp36) <=> ![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))),
% 2.08/1.60 inference(quant_intro,[status(thm)],[762])).
% 2.08/1.60 tff(764,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(V))) | c0_1(U)) | hskp36)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause310')).
% 2.08/1.60 tff(765,plain,
% 2.08/1.60 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[764, 763])).
% 2.08/1.60 tff(766,plain,
% 2.08/1.60 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[765, 761])).
% 2.08/1.60 tff(767,plain,(
% 2.08/1.60 ![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))),
% 2.08/1.60 inference(skolemize,[status(sab)],[766])).
% 2.08/1.60 tff(768,plain,
% 2.08/1.60 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[767, 760])).
% 2.08/1.60 tff(769,plain,
% 2.08/1.60 (((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056)))) <=> ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | hskp36 | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056)))),
% 2.08/1.60 inference(rewrite,[status(thm)],[])).
% 2.08/1.60 tff(770,plain,
% 2.08/1.60 ((hskp36 | (~ndr1_0) | c0_1(a1056) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056))) <=> (hskp36 | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056)))),
% 2.08/1.60 inference(rewrite,[status(thm)],[])).
% 2.08/1.60 tff(771,plain,
% 2.08/1.60 (((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | c0_1(a1056) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)))) <=> ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056))))),
% 2.08/1.60 inference(monotonicity,[status(thm)],[770])).
% 2.08/1.60 tff(772,plain,
% 2.08/1.60 (((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | c0_1(a1056) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)))) <=> ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | hskp36 | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056)))),
% 2.08/1.60 inference(transitivity,[status(thm)],[771, 769])).
% 2.08/1.60 tff(773,plain,
% 2.08/1.60 ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | c0_1(a1056) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)))),
% 2.08/1.60 inference(quant_inst,[status(thm)],[])).
% 2.08/1.60 tff(774,plain,
% 2.08/1.60 ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | hskp36 | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056))),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[773, 772])).
% 2.08/1.60 tff(775,plain,
% 2.08/1.60 (hskp36),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[774, 126, 521, 510, 499, 768, 528])).
% 2.08/1.60 tff(776,plain,
% 2.08/1.60 (((~hskp36) | (~c0_1(a1034))) <=> ((~hskp36) | (~c0_1(a1034)))),
% 2.08/1.60 inference(rewrite,[status(thm)],[])).
% 2.08/1.60 tff(777,plain,
% 2.08/1.60 (((~c0_1(a1034)) | (~hskp36)) <=> ((~hskp36) | (~c0_1(a1034)))),
% 2.08/1.60 inference(rewrite,[status(thm)],[])).
% 2.08/1.60 tff(778,axiom,((~c0_1(a1034)) | (~hskp36)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 2.08/1.60 tff(779,plain,
% 2.08/1.60 ((~hskp36) | (~c0_1(a1034))),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[778, 777])).
% 2.08/1.60 tff(780,plain,
% 2.08/1.60 ((~hskp36) | (~c0_1(a1034))),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[779, 776])).
% 2.08/1.60 tff(781,plain,
% 2.08/1.60 (~c0_1(a1034)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[780, 775])).
% 2.08/1.60 tff(782,plain,
% 2.08/1.60 (((~hskp36) | c1_1(a1034)) <=> ((~hskp36) | c1_1(a1034))),
% 2.08/1.60 inference(rewrite,[status(thm)],[])).
% 2.08/1.60 tff(783,axiom,((~hskp36) | c1_1(a1034)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 2.08/1.60 tff(784,plain,
% 2.08/1.60 ((~hskp36) | c1_1(a1034)),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[783, 782])).
% 2.08/1.60 tff(785,plain,
% 2.08/1.60 ((~hskp36) | c1_1(a1034)),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[784, 782])).
% 2.08/1.60 tff(786,plain,
% 2.08/1.60 ((~hskp36) | c1_1(a1034)),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[785, 782])).
% 2.08/1.60 tff(787,plain,
% 2.08/1.60 ((~hskp36) | c1_1(a1034)),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[786, 782])).
% 2.08/1.60 tff(788,plain,
% 2.08/1.60 ((~hskp36) | c1_1(a1034)),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[787, 782])).
% 2.08/1.60 tff(789,plain,
% 2.08/1.60 ((~hskp36) | c1_1(a1034)),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[788, 782])).
% 2.08/1.60 tff(790,plain,
% 2.08/1.60 ((~hskp36) | c1_1(a1034)),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[789, 782])).
% 2.08/1.60 tff(791,plain,
% 2.08/1.60 ((~hskp36) | c1_1(a1034)),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[790, 782])).
% 2.08/1.60 tff(792,plain,
% 2.08/1.60 (c1_1(a1034)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[791, 775])).
% 2.08/1.60 tff(793,plain,
% 2.08/1.60 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | c2_1(a1034) | (~c1_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp33 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | c2_1(a1034) | (~c1_1(a1034)))),
% 2.08/1.60 inference(rewrite,[status(thm)],[])).
% 2.08/1.60 tff(794,plain,
% 2.08/1.60 ((hskp33 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1034) | c2_1(a1034) | (~c1_1(a1034))) <=> (hskp33 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | c2_1(a1034) | (~c1_1(a1034)))),
% 2.08/1.60 inference(rewrite,[status(thm)],[])).
% 2.08/1.60 tff(795,plain,
% 2.08/1.60 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1034) | c2_1(a1034) | (~c1_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | c2_1(a1034) | (~c1_1(a1034))))),
% 2.08/1.60 inference(monotonicity,[status(thm)],[794])).
% 2.08/1.60 tff(796,plain,
% 2.08/1.60 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1034) | c2_1(a1034) | (~c1_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp33 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | c2_1(a1034) | (~c1_1(a1034)))),
% 2.08/1.60 inference(transitivity,[status(thm)],[795, 793])).
% 2.08/1.60 tff(797,plain,
% 2.08/1.60 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1034) | c2_1(a1034) | (~c1_1(a1034)))),
% 2.08/1.60 inference(quant_inst,[status(thm)],[])).
% 2.08/1.60 tff(798,plain,
% 2.08/1.60 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp33 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | c2_1(a1034) | (~c1_1(a1034))),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[797, 796])).
% 2.08/1.60 tff(799,plain,
% 2.08/1.60 (hskp33 | c2_1(a1034)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[798, 126, 521, 510, 499, 792, 781, 758])).
% 2.08/1.60 tff(800,plain,
% 2.08/1.60 (c2_1(a1034)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[799, 21])).
% 2.08/1.60 tff(801,assumption,(c3_1(a1056)), introduced(assumption)).
% 2.08/1.60 tff(802,assumption,(c1_1(a1056)), introduced(assumption)).
% 2.08/1.60 tff(803,assumption,(c2_1(a1056)), introduced(assumption)).
% 2.08/1.60 tff(804,plain,
% 2.08/1.60 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp33 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079)))),
% 2.08/1.60 inference(rewrite,[status(thm)],[])).
% 2.08/1.60 tff(805,plain,
% 2.08/1.60 ((hskp33 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1079) | c2_1(a1079) | (~c1_1(a1079))) <=> (hskp33 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079)))),
% 2.08/1.60 inference(rewrite,[status(thm)],[])).
% 2.08/1.60 tff(806,plain,
% 2.08/1.60 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1079) | c2_1(a1079) | (~c1_1(a1079)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079))))),
% 2.08/1.60 inference(monotonicity,[status(thm)],[805])).
% 2.08/1.60 tff(807,plain,
% 2.08/1.60 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1079) | c2_1(a1079) | (~c1_1(a1079)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp33 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079)))),
% 2.08/1.60 inference(transitivity,[status(thm)],[806, 804])).
% 2.08/1.60 tff(808,plain,
% 2.08/1.60 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1079) | c2_1(a1079) | (~c1_1(a1079)))),
% 2.08/1.60 inference(quant_inst,[status(thm)],[])).
% 2.08/1.60 tff(809,plain,
% 2.08/1.60 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp33 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079))),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[808, 807])).
% 2.08/1.60 tff(810,plain,
% 2.08/1.60 ($false),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[809, 126, 21, 803, 802, 801, 154, 86, 80, 758])).
% 2.08/1.60 tff(811,plain,((~hskp19) | hskp33 | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c3_1(a1056))), inference(lemma,lemma(discharge,[]))).
% 2.08/1.60 tff(812,plain,
% 2.08/1.60 (~hskp19),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[811, 21, 521, 510, 499])).
% 2.08/1.60 tff(813,plain,
% 2.08/1.60 (hskp20),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[692, 812])).
% 2.08/1.60 tff(814,plain,
% 2.08/1.60 (~c1_1(a1080)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[727, 813])).
% 2.08/1.60 tff(815,plain,
% 2.08/1.60 (~c2_1(a1080)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[699, 813])).
% 2.08/1.60 tff(816,plain,
% 2.08/1.60 (~c0_1(a1080)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[705, 813])).
% 2.08/1.60 tff(817,plain,
% 2.08/1.60 (((~hskp36) | c3_1(a1034)) <=> ((~hskp36) | c3_1(a1034))),
% 2.08/1.60 inference(rewrite,[status(thm)],[])).
% 2.08/1.60 tff(818,axiom,((~hskp36) | c3_1(a1034)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 2.08/1.60 tff(819,plain,
% 2.08/1.60 ((~hskp36) | c3_1(a1034)),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[818, 817])).
% 2.08/1.60 tff(820,plain,
% 2.08/1.60 ((~hskp36) | c3_1(a1034)),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[819, 817])).
% 2.08/1.60 tff(821,plain,
% 2.08/1.60 ((~hskp36) | c3_1(a1034)),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[820, 817])).
% 2.08/1.60 tff(822,plain,
% 2.08/1.60 ((~hskp36) | c3_1(a1034)),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[821, 817])).
% 2.08/1.60 tff(823,plain,
% 2.08/1.60 ((~hskp36) | c3_1(a1034)),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[822, 817])).
% 2.08/1.60 tff(824,plain,
% 2.08/1.60 ((~hskp36) | c3_1(a1034)),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[823, 817])).
% 2.08/1.60 tff(825,plain,
% 2.08/1.60 ((~hskp36) | c3_1(a1034)),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[824, 817])).
% 2.08/1.60 tff(826,plain,
% 2.08/1.60 ((~hskp36) | c3_1(a1034)),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[825, 817])).
% 2.08/1.60 tff(827,plain,
% 2.08/1.60 (c3_1(a1034)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[826, 775])).
% 2.08/1.60 tff(828,plain,
% 2.08/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c0_1(a1034) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c2_1(a1084)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c0_1(a1034) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c2_1(a1084)))),
% 2.08/1.60 inference(rewrite,[status(thm)],[])).
% 2.08/1.60 tff(829,plain,
% 2.08/1.60 (((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080)) <=> (c3_1(a1084) | c1_1(a1084) | c0_1(a1034) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c2_1(a1084)))),
% 2.08/1.60 inference(rewrite,[status(thm)],[])).
% 2.08/1.60 tff(830,plain,
% 2.08/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c0_1(a1034) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c2_1(a1084))))),
% 2.08/1.60 inference(monotonicity,[status(thm)],[829])).
% 2.08/1.60 tff(831,plain,
% 2.08/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c0_1(a1034) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c2_1(a1084)))),
% 2.08/1.60 inference(transitivity,[status(thm)],[830, 828])).
% 2.08/1.60 tff(832,plain,
% 2.08/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))),
% 2.08/1.60 inference(quant_inst,[status(thm)],[])).
% 2.08/1.60 tff(833,plain,
% 2.08/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c0_1(a1034) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c2_1(a1084))),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[832, 831])).
% 2.08/1.60 tff(834,plain,
% 2.08/1.60 ($false),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[833, 126, 827, 278, 279, 781, 816, 815, 814, 538, 460, 800])).
% 2.08/1.60 tff(835,plain,(hskp33 | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | (~c0_1(a1084))), inference(lemma,lemma(discharge,[]))).
% 2.08/1.60 tff(836,plain,
% 2.08/1.60 (hskp33),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[835, 748, 279, 278, 277])).
% 2.08/1.60 tff(837,plain,
% 2.08/1.60 (c2_1(a1031)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[298, 836])).
% 2.08/1.60 tff(838,plain,
% 2.08/1.60 (c3_1(a1031)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[321, 836])).
% 2.08/1.60 tff(839,plain,
% 2.08/1.60 (hskp47),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[487, 748])).
% 2.08/1.60 tff(840,plain,
% 2.08/1.60 (c3_1(a1056)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[498, 839])).
% 2.08/1.60 tff(841,plain,
% 2.08/1.60 (c1_1(a1056)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[509, 839])).
% 2.08/1.60 tff(842,plain,
% 2.08/1.60 (c2_1(a1056)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[520, 839])).
% 2.08/1.60 tff(843,plain,
% 2.08/1.60 (~c0_1(a1056)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[527, 126, 842, 841, 840, 10])).
% 2.08/1.60 tff(844,plain,
% 2.08/1.60 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | (~ndr1_0) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056)))),
% 2.08/1.60 inference(rewrite,[status(thm)],[])).
% 2.08/1.60 tff(845,plain,
% 2.08/1.60 ((hskp43 | hskp10 | (~ndr1_0) | c0_1(a1056) | (~c1_1(a1056)) | (~c2_1(a1056))) <=> (hskp43 | hskp10 | (~ndr1_0) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056)))),
% 2.08/1.60 inference(rewrite,[status(thm)],[])).
% 2.08/1.60 tff(846,plain,
% 2.08/1.60 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1056) | (~c1_1(a1056)) | (~c2_1(a1056)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056))))),
% 2.08/1.60 inference(monotonicity,[status(thm)],[845])).
% 2.08/1.60 tff(847,plain,
% 2.08/1.60 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1056) | (~c1_1(a1056)) | (~c2_1(a1056)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | (~ndr1_0) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056)))),
% 2.08/1.60 inference(transitivity,[status(thm)],[846, 844])).
% 2.08/1.60 tff(848,plain,
% 2.08/1.60 ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1056) | (~c1_1(a1056)) | (~c2_1(a1056)))),
% 2.08/1.60 inference(quant_inst,[status(thm)],[])).
% 2.08/1.60 tff(849,plain,
% 2.08/1.60 ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | (~ndr1_0) | (~c2_1(a1056)) | c0_1(a1056) | (~c1_1(a1056))),
% 2.08/1.60 inference(modus_ponens,[status(thm)],[848, 847])).
% 2.08/1.60 tff(850,plain,
% 2.08/1.60 (hskp43 | c0_1(a1056)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[849, 126, 659, 842, 841, 63])).
% 2.08/1.60 tff(851,plain,
% 2.08/1.60 (hskp43),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[850, 843])).
% 2.08/1.60 tff(852,plain,
% 2.08/1.60 (c1_1(a1049)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[209, 851])).
% 2.08/1.60 tff(853,plain,
% 2.08/1.60 (c2_1(a1049)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[220, 851])).
% 2.08/1.60 tff(854,plain,
% 2.08/1.60 (c0_1(a1049)),
% 2.08/1.60 inference(unit_resolution,[status(thm)],[231, 851])).
% 2.08/1.60 tff(855,plain,
% 2.08/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))),
% 2.08/1.60 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(856,plain,
% 2.08/1.61 (((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031))) <=> ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(857,plain,
% 2.08/1.61 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031))))),
% 2.08/1.61 inference(monotonicity,[status(thm)],[856])).
% 2.08/1.61 tff(858,plain,
% 2.08/1.61 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031)))),
% 2.08/1.61 inference(transitivity,[status(thm)],[857, 855])).
% 2.08/1.61 tff(859,plain,
% 2.08/1.61 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1031)) | (~c0_1(a1031)) | (~c2_1(a1031)))),
% 2.08/1.61 inference(quant_inst,[status(thm)],[])).
% 2.08/1.61 tff(860,plain,
% 2.08/1.61 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1031))),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[859, 858])).
% 2.08/1.61 tff(861,plain,
% 2.08/1.61 (~c0_1(a1031)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[860, 126, 854, 853, 852, 838, 837, 10])).
% 2.08/1.61 tff(862,plain,
% 2.08/1.61 (~c1_1(a1080)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[727, 694])).
% 2.08/1.61 tff(863,assumption,(c3_1(a1031)), introduced(assumption)).
% 2.08/1.61 tff(864,plain,
% 2.08/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | (~c2_1(a1084)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | (~c2_1(a1084)))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(865,plain,
% 2.08/1.61 (((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080)) <=> (c3_1(a1084) | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | (~c2_1(a1084)))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(866,plain,
% 2.08/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | (~c2_1(a1084))))),
% 2.08/1.61 inference(monotonicity,[status(thm)],[865])).
% 2.08/1.61 tff(867,plain,
% 2.08/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | (~c2_1(a1084)))),
% 2.08/1.61 inference(transitivity,[status(thm)],[866, 864])).
% 2.08/1.61 tff(868,plain,
% 2.08/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))),
% 2.08/1.61 inference(quant_inst,[status(thm)],[])).
% 2.08/1.61 tff(869,plain,
% 2.08/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | (~c2_1(a1084))),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[868, 867])).
% 2.08/1.61 tff(870,plain,
% 2.08/1.61 ($false),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[869, 126, 863, 302, 278, 279, 706, 700, 862, 538, 460, 300])).
% 2.08/1.61 tff(871,plain,((~hskp20) | (~c3_1(a1031)) | (~c2_1(a1031)) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1031)), inference(lemma,lemma(discharge,[]))).
% 2.08/1.61 tff(872,plain,
% 2.08/1.61 (~hskp20),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[871, 838, 837, 278, 279, 748, 861])).
% 2.08/1.61 tff(873,plain,
% 2.08/1.61 (hskp19),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[692, 872])).
% 2.08/1.61 tff(874,plain,
% 2.08/1.61 (~c2_1(a1079)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[79, 873])).
% 2.08/1.61 tff(875,plain,
% 2.08/1.61 (~c0_1(a1079)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[85, 873])).
% 2.08/1.61 tff(876,plain,
% 2.08/1.61 (c1_1(a1079)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[153, 873])).
% 2.08/1.61 tff(877,plain,
% 2.08/1.61 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp25 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079)))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(878,plain,
% 2.08/1.61 ((hskp25 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1079) | c2_1(a1079) | (~c1_1(a1079))) <=> (hskp25 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079)))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(879,plain,
% 2.08/1.61 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1079) | c2_1(a1079) | (~c1_1(a1079)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079))))),
% 2.08/1.61 inference(monotonicity,[status(thm)],[878])).
% 2.08/1.61 tff(880,plain,
% 2.08/1.61 (((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1079) | c2_1(a1079) | (~c1_1(a1079)))) <=> ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp25 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079)))),
% 2.08/1.61 inference(transitivity,[status(thm)],[879, 877])).
% 2.08/1.61 tff(881,plain,
% 2.08/1.61 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp25 | (~ndr1_0) | (~c1_1(a1056)) | (~c3_1(a1056)) | (~c2_1(a1056)) | c0_1(a1079) | c2_1(a1079) | (~c1_1(a1079)))),
% 2.08/1.61 inference(quant_inst,[status(thm)],[])).
% 2.08/1.61 tff(882,plain,
% 2.08/1.61 ((~![V: $i, U: $i] : (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp25 | c0_1(a1079) | c2_1(a1079) | (~ndr1_0) | (~c3_1(a1056)) | (~c2_1(a1056)) | (~c1_1(a1056)) | (~c1_1(a1079))),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[881, 880])).
% 2.08/1.61 tff(883,plain,
% 2.08/1.61 (hskp25),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[882, 126, 842, 841, 840, 876, 875, 874, 276])).
% 2.08/1.61 tff(884,plain,
% 2.08/1.61 (~c2_1(a1091)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[550, 883])).
% 2.08/1.61 tff(885,plain,
% 2.08/1.61 (~c0_1(a1091)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[556, 883])).
% 2.08/1.61 tff(886,plain,
% 2.08/1.61 (~c3_1(a1091)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[579, 883])).
% 2.08/1.61 tff(887,plain,
% 2.08/1.61 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c3_1(a1091) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c3_1(a1091) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(888,plain,
% 2.08/1.61 ((hskp10 | (~ndr1_0) | c0_1(a1091) | c2_1(a1091) | c3_1(a1091)) <=> (hskp10 | c3_1(a1091) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(889,plain,
% 2.08/1.61 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1091) | c2_1(a1091) | c3_1(a1091))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c3_1(a1091) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0)))),
% 2.08/1.61 inference(monotonicity,[status(thm)],[888])).
% 2.08/1.61 tff(890,plain,
% 2.08/1.61 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1091) | c2_1(a1091) | c3_1(a1091))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c3_1(a1091) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0))),
% 2.08/1.61 inference(transitivity,[status(thm)],[889, 887])).
% 2.08/1.61 tff(891,plain,
% 2.08/1.61 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1091) | c2_1(a1091) | c3_1(a1091))),
% 2.08/1.61 inference(quant_inst,[status(thm)],[])).
% 2.08/1.61 tff(892,plain,
% 2.08/1.61 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c3_1(a1091) | c0_1(a1091) | c2_1(a1091) | (~ndr1_0)),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[891, 890])).
% 2.08/1.61 tff(893,plain,
% 2.08/1.61 ($false),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[892, 126, 659, 886, 885, 884, 73])).
% 2.08/1.61 tff(894,plain,(hskp1 | (~c0_1(a1084)) | c3_1(a1084) | c1_1(a1084)), inference(lemma,lemma(discharge,[]))).
% 2.08/1.61 tff(895,plain,
% 2.08/1.61 (hskp1),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[894, 266, 255, 249])).
% 2.08/1.61 tff(896,plain,
% 2.08/1.61 (((~hskp1) | (~c0_1(a1023))) <=> ((~hskp1) | (~c0_1(a1023)))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(897,plain,
% 2.08/1.61 (((~c0_1(a1023)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a1023)))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(898,axiom,((~c0_1(a1023)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause259')).
% 2.08/1.61 tff(899,plain,
% 2.08/1.61 ((~hskp1) | (~c0_1(a1023))),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[898, 897])).
% 2.08/1.61 tff(900,plain,
% 2.08/1.61 ((~hskp1) | (~c0_1(a1023))),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[899, 896])).
% 2.08/1.61 tff(901,plain,
% 2.08/1.61 (~c0_1(a1023)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[900, 895])).
% 2.08/1.61 tff(902,plain,
% 2.08/1.61 (((~hskp1) | (~c1_1(a1023))) <=> ((~hskp1) | (~c1_1(a1023)))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(903,plain,
% 2.08/1.61 (((~c1_1(a1023)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a1023)))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(904,axiom,((~c1_1(a1023)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause258')).
% 2.08/1.61 tff(905,plain,
% 2.08/1.61 ((~hskp1) | (~c1_1(a1023))),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[904, 903])).
% 2.08/1.61 tff(906,plain,
% 2.08/1.61 ((~hskp1) | (~c1_1(a1023))),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[905, 902])).
% 2.08/1.61 tff(907,plain,
% 2.08/1.61 (~c1_1(a1023)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[906, 895])).
% 2.08/1.61 tff(908,plain,
% 2.08/1.61 (hskp1),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[894, 277, 278, 279])).
% 2.08/1.61 tff(909,plain,
% 2.08/1.61 (~c0_1(a1023)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[900, 908])).
% 2.08/1.61 tff(910,plain,
% 2.08/1.61 (~c1_1(a1023)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[906, 908])).
% 2.08/1.61 tff(911,plain,
% 2.08/1.61 (((~hskp1) | c2_1(a1023)) <=> ((~hskp1) | c2_1(a1023))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(912,axiom,((~hskp1) | c2_1(a1023)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 2.08/1.61 tff(913,plain,
% 2.08/1.61 ((~hskp1) | c2_1(a1023)),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[912, 911])).
% 2.08/1.61 tff(914,plain,
% 2.08/1.61 ((~hskp1) | c2_1(a1023)),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[913, 911])).
% 2.08/1.61 tff(915,plain,
% 2.08/1.61 ((~hskp1) | c2_1(a1023)),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[914, 911])).
% 2.08/1.61 tff(916,plain,
% 2.08/1.61 ((~hskp1) | c2_1(a1023)),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[915, 911])).
% 2.08/1.61 tff(917,plain,
% 2.08/1.61 ((~hskp1) | c2_1(a1023)),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[916, 911])).
% 2.08/1.61 tff(918,plain,
% 2.08/1.61 ((~hskp1) | c2_1(a1023)),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[917, 911])).
% 2.08/1.61 tff(919,plain,
% 2.08/1.61 ((~hskp1) | c2_1(a1023)),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[918, 911])).
% 2.08/1.61 tff(920,plain,
% 2.08/1.61 ((~hskp1) | c2_1(a1023)),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[919, 911])).
% 2.08/1.61 tff(921,plain,
% 2.08/1.61 (c2_1(a1023)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[920, 908])).
% 2.08/1.61 tff(922,plain,
% 2.08/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c2_1(a1084) | (~c0_1(a1084)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c2_1(a1084) | (~c0_1(a1084)))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(923,plain,
% 2.08/1.61 (((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084)) <=> (c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c2_1(a1084) | (~c0_1(a1084)))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(924,plain,
% 2.08/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c2_1(a1084) | (~c0_1(a1084))))),
% 2.08/1.61 inference(monotonicity,[status(thm)],[923])).
% 2.08/1.61 tff(925,plain,
% 2.08/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c2_1(a1084) | (~c0_1(a1084)))),
% 2.08/1.61 inference(transitivity,[status(thm)],[924, 922])).
% 2.08/1.61 tff(926,plain,
% 2.08/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c3_1(a1084) | c1_1(a1084) | c2_1(a1084))),
% 2.08/1.61 inference(quant_inst,[status(thm)],[])).
% 2.08/1.61 tff(927,plain,
% 2.08/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c2_1(a1084) | (~c0_1(a1084))),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[926, 925])).
% 2.08/1.61 tff(928,plain,
% 2.08/1.61 (c2_1(a1084)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[927, 126, 277, 921, 278, 279, 910, 909, 242])).
% 2.08/1.61 tff(929,plain,
% 2.08/1.61 (hskp33),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[835, 928, 279, 278, 277])).
% 2.08/1.61 tff(930,plain,
% 2.08/1.61 (c3_1(a1031)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[321, 929])).
% 2.08/1.61 tff(931,plain,
% 2.08/1.61 (c2_1(a1031)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[298, 929])).
% 2.08/1.61 tff(932,plain,
% 2.08/1.61 (hskp47),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[487, 928])).
% 2.08/1.61 tff(933,plain,
% 2.08/1.61 (c3_1(a1056)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[498, 932])).
% 2.08/1.61 tff(934,plain,
% 2.08/1.61 (c1_1(a1056)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[509, 932])).
% 2.08/1.61 tff(935,plain,
% 2.08/1.61 (c2_1(a1056)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[520, 932])).
% 2.08/1.61 tff(936,plain,
% 2.08/1.61 (~c0_1(a1056)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[527, 126, 935, 934, 933, 10])).
% 2.08/1.61 tff(937,plain,
% 2.08/1.61 (hskp43 | hskp10 | c0_1(a1056)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[849, 126, 935, 934, 63])).
% 2.08/1.61 tff(938,plain,
% 2.08/1.61 (hskp43),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[937, 53, 936])).
% 2.08/1.61 tff(939,plain,
% 2.08/1.61 (c1_1(a1049)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[209, 938])).
% 2.08/1.61 tff(940,plain,
% 2.08/1.61 (c2_1(a1049)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[220, 938])).
% 2.08/1.61 tff(941,plain,
% 2.08/1.61 (c0_1(a1049)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[231, 938])).
% 2.08/1.61 tff(942,plain,
% 2.08/1.61 (~c0_1(a1031)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[860, 126, 941, 940, 939, 930, 931, 10])).
% 2.08/1.61 tff(943,plain,
% 2.08/1.61 (~hskp20),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[871, 942, 931, 278, 279, 928, 930])).
% 2.08/1.61 tff(944,plain,
% 2.08/1.61 (hskp19),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[692, 943])).
% 2.08/1.61 tff(945,plain,
% 2.08/1.61 (~c2_1(a1079)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[79, 944])).
% 2.08/1.61 tff(946,plain,
% 2.08/1.61 (~c0_1(a1079)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[85, 944])).
% 2.08/1.61 tff(947,plain,
% 2.08/1.61 (c1_1(a1079)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[153, 944])).
% 2.08/1.61 tff(948,plain,
% 2.08/1.61 (hskp25),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[882, 126, 935, 934, 933, 947, 946, 945, 276])).
% 2.08/1.61 tff(949,plain,
% 2.08/1.61 (~c2_1(a1091)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[550, 948])).
% 2.08/1.61 tff(950,plain,
% 2.08/1.61 (~c0_1(a1091)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[556, 948])).
% 2.08/1.61 tff(951,plain,
% 2.08/1.61 (~c3_1(a1091)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[579, 948])).
% 2.08/1.61 tff(952,plain,
% 2.08/1.61 ($false),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[892, 126, 53, 951, 950, 949, 73])).
% 2.08/1.61 tff(953,plain,(hskp10 | (~c0_1(a1084)) | c3_1(a1084) | c1_1(a1084)), inference(lemma,lemma(discharge,[]))).
% 2.08/1.61 tff(954,plain,
% 2.08/1.61 (hskp10),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[953, 266, 255, 249])).
% 2.08/1.61 tff(955,plain,
% 2.08/1.61 (~c0_1(a1039)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[455, 954])).
% 2.08/1.61 tff(956,plain,
% 2.08/1.61 (~c2_1(a1039)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[438, 954])).
% 2.08/1.61 tff(957,plain,
% 2.08/1.61 (c1_1(a1039)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[449, 954])).
% 2.08/1.61 tff(958,plain,
% 2.08/1.61 (c2_1(a1023)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[920, 895])).
% 2.08/1.61 tff(959,plain,
% 2.08/1.61 (c2_1(a1084)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[927, 126, 266, 958, 255, 249, 907, 901, 242])).
% 2.08/1.61 tff(960,plain,
% 2.08/1.61 (hskp47 | (~c2_1(a1084))),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[486, 126, 266, 255, 249, 480])).
% 2.08/1.61 tff(961,plain,
% 2.08/1.61 (hskp47),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[960, 959])).
% 2.08/1.61 tff(962,plain,
% 2.08/1.61 (c3_1(a1056)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[498, 961])).
% 2.08/1.61 tff(963,plain,
% 2.08/1.61 (c1_1(a1056)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[509, 961])).
% 2.08/1.61 tff(964,plain,
% 2.08/1.61 (c2_1(a1056)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[520, 961])).
% 2.08/1.61 tff(965,plain,
% 2.08/1.61 (hskp25),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[544, 126, 964, 963, 962, 957, 956, 955, 276])).
% 2.08/1.61 tff(966,plain,
% 2.08/1.61 (~c2_1(a1091)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[550, 965])).
% 2.08/1.61 tff(967,plain,
% 2.08/1.61 (~c3_1(a1091)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[579, 965])).
% 2.08/1.61 tff(968,plain,
% 2.08/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c1_1(a1091) | (~c0_1(a1084)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c1_1(a1091) | (~c0_1(a1084)))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(969,plain,
% 2.08/1.61 (((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c3_1(a1091) | c1_1(a1091) | c2_1(a1091)) <=> (c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c1_1(a1091) | (~c0_1(a1084)))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(970,plain,
% 2.08/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c3_1(a1091) | c1_1(a1091) | c2_1(a1091))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c1_1(a1091) | (~c0_1(a1084))))),
% 2.08/1.61 inference(monotonicity,[status(thm)],[969])).
% 2.08/1.61 tff(971,plain,
% 2.08/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c3_1(a1091) | c1_1(a1091) | c2_1(a1091))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c1_1(a1091) | (~c0_1(a1084)))),
% 2.08/1.61 inference(transitivity,[status(thm)],[970, 968])).
% 2.08/1.61 tff(972,plain,
% 2.08/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c0_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c3_1(a1091) | c1_1(a1091) | c2_1(a1091))),
% 2.08/1.61 inference(quant_inst,[status(thm)],[])).
% 2.08/1.61 tff(973,plain,
% 2.08/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c3_1(a1084) | c1_1(a1084) | c3_1(a1091) | c2_1(a1091) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | (~c2_1(a1023)) | c1_1(a1091) | (~c0_1(a1084))),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[972, 971])).
% 2.08/1.61 tff(974,plain,
% 2.08/1.61 (c1_1(a1091)),
% 2.08/1.61 inference(unit_resolution,[status(thm)],[973, 126, 266, 958, 255, 249, 967, 966, 907, 901, 242])).
% 2.08/1.61 tff(975,plain,
% 2.08/1.61 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W)))),
% 2.08/1.61 inference(bind,[status(th)],[])).
% 2.08/1.61 tff(976,plain,
% 2.08/1.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_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)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))),
% 2.08/1.61 inference(quant_intro,[status(thm)],[975])).
% 2.08/1.61 tff(977,plain,
% 2.08/1.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_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)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(978,plain,
% 2.08/1.61 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c1_1(W)) | c3_1(W)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W)) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c1_1(W)) | c3_1(W)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))))),
% 2.08/1.61 inference(bind,[status(th)],[])).
% 2.08/1.61 tff(979,plain,
% 2.08/1.61 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c1_1(W)) | c3_1(W)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))),
% 2.08/1.61 inference(quant_intro,[status(thm)],[978])).
% 2.08/1.61 tff(980,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c1_1(W)) | c3_1(W)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause312')).
% 2.08/1.61 tff(981,plain,
% 2.08/1.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[980, 979])).
% 2.08/1.61 tff(982,plain,
% 2.08/1.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[981, 977])).
% 2.08/1.61 tff(983,plain,(
% 2.08/1.61 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))),
% 2.08/1.61 inference(skolemize,[status(sab)],[982])).
% 2.08/1.61 tff(984,plain,
% 2.08/1.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))),
% 2.08/1.61 inference(modus_ponens,[status(thm)],[983, 976])).
% 2.08/1.61 tff(985,plain,
% 2.08/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))) | (c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | c3_1(a1023) | (~c2_1(a1023)) | (~c2_1(a1084)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | c3_1(a1023) | (~c2_1(a1023)) | (~c2_1(a1084)))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(986,plain,
% 2.08/1.61 (((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c0_1(a1023) | c3_1(a1023) | c1_1(a1023)) <=> (c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | c3_1(a1023) | (~c2_1(a1023)) | (~c2_1(a1084)))),
% 2.08/1.61 inference(rewrite,[status(thm)],[])).
% 2.08/1.61 tff(987,plain,
% 2.08/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c0_1(a1023) | c3_1(a1023) | c1_1(a1023))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))) | (c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | c3_1(a1023) | (~c2_1(a1023)) | (~c2_1(a1084))))),
% 2.08/1.61 inference(monotonicity,[status(thm)],[986])).
% 2.08/1.61 tff(988,plain,
% 2.08/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c0_1(a1023) | c3_1(a1023) | c1_1(a1023))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | c3_1(a1023) | (~c2_1(a1023)) | (~c2_1(a1084)))),
% 2.08/1.61 inference(transitivity,[status(thm)],[987, 985])).
% 2.08/1.61 tff(989,plain,
% 2.08/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c3_1(a1084) | c1_1(a1084) | (~c2_1(a1084)) | c0_1(a1023) | c1_1(a1023) | (~c2_1(a1023)) | c0_1(a1023) | c3_1(a1023) | c1_1(a1023))),
% 2.08/1.61 inference(quant_inst,[status(thm)],[])).
% 2.08/1.61 tff(990,plain,
% 2.08/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | c1_1(W))) | c3_1(a1084) | c1_1(a1084) | c1_1(a1023) | c0_1(a1023) | (~ndr1_0) | c3_1(a1023) | (~c2_1(a1023)) | (~c2_1(a1084))),
% 2.08/1.62 inference(modus_ponens,[status(thm)],[989, 988])).
% 2.08/1.62 tff(991,plain,
% 2.08/1.62 (c3_1(a1023)),
% 2.08/1.62 inference(unit_resolution,[status(thm)],[990, 126, 958, 255, 249, 907, 901, 984, 959])).
% 2.08/1.62 tff(992,plain,
% 2.08/1.62 (^[V: $i, U: $i] : refl((hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 2.08/1.62 inference(bind,[status(th)],[])).
% 2.08/1.62 tff(993,plain,
% 2.08/1.62 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.08/1.62 inference(quant_intro,[status(thm)],[992])).
% 2.08/1.62 tff(994,plain,
% 2.08/1.62 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.08/1.62 inference(rewrite,[status(thm)],[])).
% 2.08/1.62 tff(995,plain,
% 2.08/1.62 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp35) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp35))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp35) <=> (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp35) <=> (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 2.08/1.62 inference(bind,[status(th)],[])).
% 2.08/1.62 tff(996,plain,
% 2.08/1.62 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp35) <=> ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.08/1.62 inference(quant_intro,[status(thm)],[995])).
% 2.08/1.62 tff(997,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp35)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause298')).
% 2.08/1.62 tff(998,plain,
% 2.08/1.62 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.08/1.62 inference(modus_ponens,[status(thm)],[997, 996])).
% 2.08/1.62 tff(999,plain,
% 2.08/1.62 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.08/1.62 inference(modus_ponens,[status(thm)],[998, 994])).
% 2.08/1.62 tff(1000,plain,(
% 2.08/1.62 ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.08/1.62 inference(skolemize,[status(sab)],[999])).
% 2.08/1.62 tff(1001,plain,
% 2.08/1.62 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.08/1.62 inference(modus_ponens,[status(thm)],[1000, 993])).
% 2.08/1.62 tff(1002,plain,
% 2.08/1.62 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c3_1(a1091) | c2_1(a1091) | c0_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c1_1(a1091)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a1091) | c2_1(a1091) | c0_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c1_1(a1091)))),
% 2.08/1.62 inference(rewrite,[status(thm)],[])).
% 2.08/1.62 tff(1003,plain,
% 2.08/1.62 ((hskp35 | (~ndr1_0) | c2_1(a1091) | c3_1(a1091) | (~c1_1(a1091)) | c0_1(a1023) | (~c3_1(a1023)) | (~c2_1(a1023))) <=> (hskp35 | c3_1(a1091) | c2_1(a1091) | c0_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c1_1(a1091)))),
% 2.08/1.62 inference(rewrite,[status(thm)],[])).
% 2.08/1.62 tff(1004,plain,
% 2.08/1.62 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1091) | c3_1(a1091) | (~c1_1(a1091)) | c0_1(a1023) | (~c3_1(a1023)) | (~c2_1(a1023)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c3_1(a1091) | c2_1(a1091) | c0_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c1_1(a1091))))),
% 2.08/1.62 inference(monotonicity,[status(thm)],[1003])).
% 2.08/1.62 tff(1005,plain,
% 2.08/1.62 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1091) | c3_1(a1091) | (~c1_1(a1091)) | c0_1(a1023) | (~c3_1(a1023)) | (~c2_1(a1023)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a1091) | c2_1(a1091) | c0_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c1_1(a1091)))),
% 2.08/1.62 inference(transitivity,[status(thm)],[1004, 1002])).
% 2.08/1.62 tff(1006,plain,
% 2.08/1.62 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1091) | c3_1(a1091) | (~c1_1(a1091)) | c0_1(a1023) | (~c3_1(a1023)) | (~c2_1(a1023)))),
% 2.08/1.62 inference(quant_inst,[status(thm)],[])).
% 2.08/1.62 tff(1007,plain,
% 2.08/1.62 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c3_1(a1091) | c2_1(a1091) | c0_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c1_1(a1091))),
% 2.08/1.62 inference(modus_ponens,[status(thm)],[1006, 1005])).
% 2.08/1.62 tff(1008,plain,
% 2.08/1.62 (hskp35),
% 2.08/1.62 inference(unit_resolution,[status(thm)],[1007, 126, 958, 967, 966, 901, 1001, 991, 974])).
% 2.08/1.62 tff(1009,plain,
% 2.08/1.62 (((~hskp35) | c3_1(a1033)) <=> ((~hskp35) | c3_1(a1033))),
% 2.08/1.62 inference(rewrite,[status(thm)],[])).
% 2.08/1.62 tff(1010,axiom,((~hskp35) | c3_1(a1033)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 2.16/1.62 tff(1011,plain,
% 2.16/1.62 ((~hskp35) | c3_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 2.16/1.62 tff(1012,plain,
% 2.16/1.62 ((~hskp35) | c3_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1011, 1009])).
% 2.16/1.62 tff(1013,plain,
% 2.16/1.62 ((~hskp35) | c3_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1012, 1009])).
% 2.16/1.62 tff(1014,plain,
% 2.16/1.62 ((~hskp35) | c3_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1013, 1009])).
% 2.16/1.62 tff(1015,plain,
% 2.16/1.62 ((~hskp35) | c3_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1014, 1009])).
% 2.16/1.62 tff(1016,plain,
% 2.16/1.62 ((~hskp35) | c3_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1015, 1009])).
% 2.16/1.62 tff(1017,plain,
% 2.16/1.62 ((~hskp35) | c3_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1016, 1009])).
% 2.16/1.62 tff(1018,plain,
% 2.16/1.62 ((~hskp35) | c3_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1017, 1009])).
% 2.16/1.62 tff(1019,plain,
% 2.16/1.62 (c3_1(a1033)),
% 2.16/1.62 inference(unit_resolution,[status(thm)],[1018, 1008])).
% 2.16/1.62 tff(1020,plain,
% 2.16/1.62 (((~hskp35) | c1_1(a1033)) <=> ((~hskp35) | c1_1(a1033))),
% 2.16/1.62 inference(rewrite,[status(thm)],[])).
% 2.16/1.62 tff(1021,axiom,((~hskp35) | c1_1(a1033)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 2.16/1.62 tff(1022,plain,
% 2.16/1.62 ((~hskp35) | c1_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 2.16/1.62 tff(1023,plain,
% 2.16/1.62 ((~hskp35) | c1_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1022, 1020])).
% 2.16/1.62 tff(1024,plain,
% 2.16/1.62 ((~hskp35) | c1_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1023, 1020])).
% 2.16/1.62 tff(1025,plain,
% 2.16/1.62 ((~hskp35) | c1_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1024, 1020])).
% 2.16/1.62 tff(1026,plain,
% 2.16/1.62 ((~hskp35) | c1_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1025, 1020])).
% 2.16/1.62 tff(1027,plain,
% 2.16/1.62 ((~hskp35) | c1_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1026, 1020])).
% 2.16/1.62 tff(1028,plain,
% 2.16/1.62 ((~hskp35) | c1_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1027, 1020])).
% 2.16/1.62 tff(1029,plain,
% 2.16/1.62 ((~hskp35) | c1_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1028, 1020])).
% 2.16/1.62 tff(1030,plain,
% 2.16/1.62 (c1_1(a1033)),
% 2.16/1.62 inference(unit_resolution,[status(thm)],[1029, 1008])).
% 2.16/1.62 tff(1031,plain,
% 2.16/1.62 (((~hskp35) | c0_1(a1033)) <=> ((~hskp35) | c0_1(a1033))),
% 2.16/1.62 inference(rewrite,[status(thm)],[])).
% 2.16/1.62 tff(1032,axiom,((~hskp35) | c0_1(a1033)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 2.16/1.62 tff(1033,plain,
% 2.16/1.62 ((~hskp35) | c0_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1032, 1031])).
% 2.16/1.62 tff(1034,plain,
% 2.16/1.62 ((~hskp35) | c0_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1033, 1031])).
% 2.16/1.62 tff(1035,plain,
% 2.16/1.62 ((~hskp35) | c0_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1034, 1031])).
% 2.16/1.62 tff(1036,plain,
% 2.16/1.62 ((~hskp35) | c0_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1035, 1031])).
% 2.16/1.62 tff(1037,plain,
% 2.16/1.62 ((~hskp35) | c0_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1036, 1031])).
% 2.16/1.62 tff(1038,plain,
% 2.16/1.62 ((~hskp35) | c0_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1037, 1031])).
% 2.16/1.62 tff(1039,plain,
% 2.16/1.62 ((~hskp35) | c0_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1038, 1031])).
% 2.16/1.62 tff(1040,plain,
% 2.16/1.62 ((~hskp35) | c0_1(a1033)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1039, 1031])).
% 2.16/1.62 tff(1041,plain,
% 2.16/1.62 (c0_1(a1033)),
% 2.16/1.62 inference(unit_resolution,[status(thm)],[1040, 1008])).
% 2.16/1.62 tff(1042,plain,
% 2.16/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c3_1(a1033)) | (~c2_1(a1033)) | (~c1_1(a1033)) | (~c0_1(a1033)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c3_1(a1033)) | (~c2_1(a1033)) | (~c1_1(a1033)) | (~c0_1(a1033)))),
% 2.16/1.62 inference(rewrite,[status(thm)],[])).
% 2.16/1.62 tff(1043,plain,
% 2.16/1.62 (((~ndr1_0) | (~c1_1(a1033)) | (~c0_1(a1033)) | (~c2_1(a1033)) | (~c3_1(a1033)) | (~c0_1(a1033)) | (~c2_1(a1033))) <=> ((~ndr1_0) | (~c3_1(a1033)) | (~c2_1(a1033)) | (~c1_1(a1033)) | (~c0_1(a1033)))),
% 2.16/1.62 inference(rewrite,[status(thm)],[])).
% 2.16/1.62 tff(1044,plain,
% 2.16/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1033)) | (~c0_1(a1033)) | (~c2_1(a1033)) | (~c3_1(a1033)) | (~c0_1(a1033)) | (~c2_1(a1033)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c3_1(a1033)) | (~c2_1(a1033)) | (~c1_1(a1033)) | (~c0_1(a1033))))),
% 2.16/1.62 inference(monotonicity,[status(thm)],[1043])).
% 2.16/1.62 tff(1045,plain,
% 2.16/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1033)) | (~c0_1(a1033)) | (~c2_1(a1033)) | (~c3_1(a1033)) | (~c0_1(a1033)) | (~c2_1(a1033)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c3_1(a1033)) | (~c2_1(a1033)) | (~c1_1(a1033)) | (~c0_1(a1033)))),
% 2.16/1.62 inference(transitivity,[status(thm)],[1044, 1042])).
% 2.16/1.62 tff(1046,plain,
% 2.16/1.62 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1033)) | (~c0_1(a1033)) | (~c2_1(a1033)) | (~c3_1(a1033)) | (~c0_1(a1033)) | (~c2_1(a1033)))),
% 2.16/1.62 inference(quant_inst,[status(thm)],[])).
% 2.16/1.62 tff(1047,plain,
% 2.16/1.62 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c3_1(a1033)) | (~c2_1(a1033)) | (~c1_1(a1033)) | (~c0_1(a1033))),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 2.16/1.62 tff(1048,plain,
% 2.16/1.62 (~c2_1(a1033)),
% 2.16/1.62 inference(unit_resolution,[status(thm)],[1047, 126, 1041, 1030, 1019, 10])).
% 2.16/1.62 tff(1049,plain,
% 2.16/1.62 (^[V: $i, U: $i] : refl((hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 2.16/1.62 inference(bind,[status(th)],[])).
% 2.16/1.62 tff(1050,plain,
% 2.16/1.62 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.16/1.62 inference(quant_intro,[status(thm)],[1049])).
% 2.16/1.62 tff(1051,plain,
% 2.16/1.62 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.16/1.62 inference(rewrite,[status(thm)],[])).
% 2.16/1.62 tff(1052,plain,
% 2.16/1.62 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | hskp57) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp57))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp57) <=> (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | hskp57) <=> (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 2.16/1.62 inference(bind,[status(th)],[])).
% 2.16/1.62 tff(1053,plain,
% 2.16/1.62 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | hskp57) <=> ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.16/1.62 inference(quant_intro,[status(thm)],[1052])).
% 2.16/1.62 tff(1054,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(V)) | hskp57)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause304')).
% 2.16/1.62 tff(1055,plain,
% 2.16/1.62 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1054, 1053])).
% 2.16/1.62 tff(1056,plain,
% 2.16/1.62 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1055, 1051])).
% 2.16/1.62 tff(1057,plain,(
% 2.16/1.62 ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.16/1.62 inference(skolemize,[status(sab)],[1056])).
% 2.16/1.62 tff(1058,plain,
% 2.16/1.62 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1057, 1050])).
% 2.16/1.62 tff(1059,plain,
% 2.16/1.62 (hskp33),
% 2.16/1.62 inference(unit_resolution,[status(thm)],[835, 959, 249, 255, 266])).
% 2.16/1.62 tff(1060,plain,
% 2.16/1.62 (~c1_1(a1031)),
% 2.16/1.62 inference(unit_resolution,[status(thm)],[287, 1059])).
% 2.16/1.62 tff(1061,plain,
% 2.16/1.62 (c2_1(a1031)),
% 2.16/1.62 inference(unit_resolution,[status(thm)],[298, 1059])).
% 2.16/1.62 tff(1062,plain,
% 2.16/1.62 (c3_1(a1031)),
% 2.16/1.62 inference(unit_resolution,[status(thm)],[321, 1059])).
% 2.16/1.62 tff(1063,assumption,(c3_1(a1023)), introduced(assumption)).
% 2.16/1.62 tff(1064,assumption,(~c1_1(a1023)), introduced(assumption)).
% 2.16/1.62 tff(1065,assumption,(c2_1(a1023)), introduced(assumption)).
% 2.16/1.62 tff(1066,assumption,(hskp57), introduced(assumption)).
% 2.16/1.62 tff(1067,plain,
% 2.16/1.62 (((~hskp57) | c3_1(a1085)) <=> ((~hskp57) | c3_1(a1085))),
% 2.16/1.62 inference(rewrite,[status(thm)],[])).
% 2.16/1.62 tff(1068,axiom,((~hskp57) | c3_1(a1085)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 2.16/1.62 tff(1069,plain,
% 2.16/1.62 ((~hskp57) | c3_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 2.16/1.62 tff(1070,plain,
% 2.16/1.62 ((~hskp57) | c3_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1069, 1067])).
% 2.16/1.62 tff(1071,plain,
% 2.16/1.62 ((~hskp57) | c3_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1070, 1067])).
% 2.16/1.62 tff(1072,plain,
% 2.16/1.62 ((~hskp57) | c3_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1071, 1067])).
% 2.16/1.62 tff(1073,plain,
% 2.16/1.62 ((~hskp57) | c3_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1072, 1067])).
% 2.16/1.62 tff(1074,plain,
% 2.16/1.62 ((~hskp57) | c3_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1073, 1067])).
% 2.16/1.62 tff(1075,plain,
% 2.16/1.62 ((~hskp57) | c3_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1074, 1067])).
% 2.16/1.62 tff(1076,plain,
% 2.16/1.62 ((~hskp57) | c3_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1075, 1067])).
% 2.16/1.62 tff(1077,plain,
% 2.16/1.62 (c3_1(a1085)),
% 2.16/1.62 inference(unit_resolution,[status(thm)],[1076, 1066])).
% 2.16/1.62 tff(1078,plain,
% 2.16/1.62 (((~hskp57) | c0_1(a1085)) <=> ((~hskp57) | c0_1(a1085))),
% 2.16/1.62 inference(rewrite,[status(thm)],[])).
% 2.16/1.62 tff(1079,axiom,((~hskp57) | c0_1(a1085)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 2.16/1.62 tff(1080,plain,
% 2.16/1.62 ((~hskp57) | c0_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 2.16/1.62 tff(1081,plain,
% 2.16/1.62 ((~hskp57) | c0_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1080, 1078])).
% 2.16/1.62 tff(1082,plain,
% 2.16/1.62 ((~hskp57) | c0_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1081, 1078])).
% 2.16/1.62 tff(1083,plain,
% 2.16/1.62 ((~hskp57) | c0_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1082, 1078])).
% 2.16/1.62 tff(1084,plain,
% 2.16/1.62 ((~hskp57) | c0_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1083, 1078])).
% 2.16/1.62 tff(1085,plain,
% 2.16/1.62 ((~hskp57) | c0_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1084, 1078])).
% 2.16/1.62 tff(1086,plain,
% 2.16/1.62 ((~hskp57) | c0_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1085, 1078])).
% 2.16/1.62 tff(1087,plain,
% 2.16/1.62 ((~hskp57) | c0_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1086, 1078])).
% 2.16/1.62 tff(1088,plain,
% 2.16/1.62 (c0_1(a1085)),
% 2.16/1.62 inference(unit_resolution,[status(thm)],[1087, 1066])).
% 2.16/1.62 tff(1089,plain,
% 2.16/1.62 (((~hskp57) | c2_1(a1085)) <=> ((~hskp57) | c2_1(a1085))),
% 2.16/1.62 inference(rewrite,[status(thm)],[])).
% 2.16/1.62 tff(1090,axiom,((~hskp57) | c2_1(a1085)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 2.16/1.62 tff(1091,plain,
% 2.16/1.62 ((~hskp57) | c2_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 2.16/1.62 tff(1092,plain,
% 2.16/1.62 ((~hskp57) | c2_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1091, 1089])).
% 2.16/1.62 tff(1093,plain,
% 2.16/1.62 ((~hskp57) | c2_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1092, 1089])).
% 2.16/1.62 tff(1094,plain,
% 2.16/1.62 ((~hskp57) | c2_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1093, 1089])).
% 2.16/1.62 tff(1095,plain,
% 2.16/1.62 ((~hskp57) | c2_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1094, 1089])).
% 2.16/1.62 tff(1096,plain,
% 2.16/1.62 ((~hskp57) | c2_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1095, 1089])).
% 2.16/1.62 tff(1097,plain,
% 2.16/1.62 ((~hskp57) | c2_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1096, 1089])).
% 2.16/1.62 tff(1098,plain,
% 2.16/1.62 ((~hskp57) | c2_1(a1085)),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1097, 1089])).
% 2.16/1.62 tff(1099,plain,
% 2.16/1.62 (c2_1(a1085)),
% 2.16/1.62 inference(unit_resolution,[status(thm)],[1098, 1066])).
% 2.16/1.62 tff(1100,plain,
% 2.16/1.62 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)))),
% 2.16/1.62 inference(rewrite,[status(thm)],[])).
% 2.16/1.62 tff(1101,plain,
% 2.16/1.62 ((hskp53 | (~ndr1_0) | c1_1(a1023) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085))) <=> (hskp53 | c1_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)))),
% 2.16/1.62 inference(rewrite,[status(thm)],[])).
% 2.16/1.62 tff(1102,plain,
% 2.16/1.62 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1023) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085))))),
% 2.16/1.62 inference(monotonicity,[status(thm)],[1101])).
% 2.16/1.62 tff(1103,plain,
% 2.16/1.62 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1023) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)))),
% 2.16/1.62 inference(transitivity,[status(thm)],[1102, 1100])).
% 2.16/1.62 tff(1104,plain,
% 2.16/1.62 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1023) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))),
% 2.16/1.62 inference(quant_inst,[status(thm)],[])).
% 2.16/1.62 tff(1105,plain,
% 2.16/1.62 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1023) | (~ndr1_0) | (~c3_1(a1023)) | (~c2_1(a1023)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085))),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1104, 1103])).
% 2.16/1.62 tff(1106,plain,
% 2.16/1.62 (hskp53),
% 2.16/1.62 inference(unit_resolution,[status(thm)],[1105, 126, 1099, 1088, 1077, 1065, 1064, 20, 1063])).
% 2.16/1.62 tff(1107,plain,
% 2.16/1.62 (c0_1(a1073)),
% 2.16/1.62 inference(unit_resolution,[status(thm)],[340, 1106])).
% 2.16/1.62 tff(1108,plain,
% 2.16/1.62 (c2_1(a1073)),
% 2.16/1.62 inference(unit_resolution,[status(thm)],[351, 1106])).
% 2.16/1.62 tff(1109,plain,
% 2.16/1.62 (c1_1(a1073)),
% 2.16/1.62 inference(unit_resolution,[status(thm)],[362, 1106])).
% 2.16/1.62 tff(1110,plain,
% 2.16/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 2.16/1.62 inference(rewrite,[status(thm)],[])).
% 2.16/1.62 tff(1111,plain,
% 2.16/1.62 (((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085))) <=> ((~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 2.16/1.62 inference(rewrite,[status(thm)],[])).
% 2.16/1.62 tff(1112,plain,
% 2.16/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073))))),
% 2.16/1.62 inference(monotonicity,[status(thm)],[1111])).
% 2.16/1.62 tff(1113,plain,
% 2.16/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 2.16/1.62 inference(transitivity,[status(thm)],[1112, 1110])).
% 2.16/1.62 tff(1114,plain,
% 2.16/1.62 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))),
% 2.16/1.62 inference(quant_inst,[status(thm)],[])).
% 2.16/1.62 tff(1115,plain,
% 2.16/1.62 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073))),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 2.16/1.62 tff(1116,plain,
% 2.16/1.62 ($false),
% 2.16/1.62 inference(unit_resolution,[status(thm)],[1115, 126, 1099, 1088, 1077, 1109, 1108, 1107, 10])).
% 2.16/1.62 tff(1117,plain,((~hskp57) | (~c2_1(a1023)) | c1_1(a1023) | (~c3_1(a1023))), inference(lemma,lemma(discharge,[]))).
% 2.16/1.62 tff(1118,plain,
% 2.16/1.62 (~hskp57),
% 2.16/1.62 inference(unit_resolution,[status(thm)],[1117, 991, 907, 958])).
% 2.16/1.62 tff(1119,plain,
% 2.16/1.62 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 2.16/1.62 inference(rewrite,[status(thm)],[])).
% 2.16/1.62 tff(1120,plain,
% 2.16/1.62 ((hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033))) <=> (hskp57 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 2.16/1.62 inference(rewrite,[status(thm)],[])).
% 2.16/1.62 tff(1121,plain,
% 2.16/1.62 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1031)) | (~c2_1(a1031))))),
% 2.16/1.62 inference(monotonicity,[status(thm)],[1120])).
% 2.16/1.62 tff(1122,plain,
% 2.16/1.62 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 2.16/1.62 inference(transitivity,[status(thm)],[1121, 1119])).
% 2.16/1.62 tff(1123,plain,
% 2.16/1.62 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)))),
% 2.16/1.62 inference(quant_inst,[status(thm)],[])).
% 2.16/1.62 tff(1124,plain,
% 2.16/1.62 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1031)) | (~c2_1(a1031))),
% 2.16/1.62 inference(modus_ponens,[status(thm)],[1123, 1122])).
% 2.16/1.62 tff(1125,plain,
% 2.16/1.62 ($false),
% 2.16/1.62 inference(unit_resolution,[status(thm)],[1124, 126, 1118, 1041, 1019, 1062, 1061, 1060, 1058, 1048])).
% 2.16/1.62 tff(1126,plain,(~hskp56), inference(lemma,lemma(discharge,[]))).
% 2.16/1.62 tff(1127,plain,
% 2.16/1.62 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)))),
% 2.16/1.62 inference(rewrite,[status(thm)],[])).
% 2.16/1.62 tff(1128,plain,
% 2.16/1.62 ((hskp56 | hskp22 | (~ndr1_0) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079))) <=> (hskp56 | hskp22 | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)))),
% 2.16/1.62 inference(rewrite,[status(thm)],[])).
% 2.16/1.62 tff(1129,plain,
% 2.16/1.62 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079))))),
% 2.16/1.62 inference(monotonicity,[status(thm)],[1128])).
% 2.16/1.62 tff(1130,plain,
% 2.16/1.62 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)))),
% 2.16/1.63 inference(transitivity,[status(thm)],[1129, 1127])).
% 2.16/1.63 tff(1131,plain,
% 2.16/1.63 ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)))),
% 2.16/1.63 inference(quant_inst,[status(thm)],[])).
% 2.16/1.63 tff(1132,plain,
% 2.16/1.63 ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079))),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 2.16/1.63 tff(1133,plain,
% 2.16/1.63 (hskp22 | (~c3_1(a1079))),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1132, 126, 1126, 154, 80, 31])).
% 2.16/1.63 tff(1134,plain,
% 2.16/1.63 (hskp22),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1133, 133])).
% 2.16/1.63 tff(1135,plain,
% 2.16/1.63 (((~hskp22) | c3_1(a1083)) <=> ((~hskp22) | c3_1(a1083))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1136,axiom,((~hskp22) | c3_1(a1083)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 2.16/1.63 tff(1137,plain,
% 2.16/1.63 ((~hskp22) | c3_1(a1083)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1136, 1135])).
% 2.16/1.63 tff(1138,plain,
% 2.16/1.63 ((~hskp22) | c3_1(a1083)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1137, 1135])).
% 2.16/1.63 tff(1139,plain,
% 2.16/1.63 ((~hskp22) | c3_1(a1083)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1138, 1135])).
% 2.16/1.63 tff(1140,plain,
% 2.16/1.63 ((~hskp22) | c3_1(a1083)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1139, 1135])).
% 2.16/1.63 tff(1141,plain,
% 2.16/1.63 ((~hskp22) | c3_1(a1083)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1140, 1135])).
% 2.16/1.63 tff(1142,plain,
% 2.16/1.63 ((~hskp22) | c3_1(a1083)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1141, 1135])).
% 2.16/1.63 tff(1143,plain,
% 2.16/1.63 ((~hskp22) | c3_1(a1083)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1142, 1135])).
% 2.16/1.63 tff(1144,plain,
% 2.16/1.63 ((~hskp22) | c3_1(a1083)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1143, 1135])).
% 2.16/1.63 tff(1145,plain,
% 2.16/1.63 (c3_1(a1083)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1144, 1134])).
% 2.16/1.63 tff(1146,plain,
% 2.16/1.63 (((~hskp22) | c2_1(a1083)) <=> ((~hskp22) | c2_1(a1083))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1147,axiom,((~hskp22) | c2_1(a1083)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 2.16/1.63 tff(1148,plain,
% 2.16/1.63 ((~hskp22) | c2_1(a1083)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1147, 1146])).
% 2.16/1.63 tff(1149,plain,
% 2.16/1.63 ((~hskp22) | c2_1(a1083)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1148, 1146])).
% 2.16/1.63 tff(1150,plain,
% 2.16/1.63 ((~hskp22) | c2_1(a1083)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1149, 1146])).
% 2.16/1.63 tff(1151,plain,
% 2.16/1.63 ((~hskp22) | c2_1(a1083)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1150, 1146])).
% 2.16/1.63 tff(1152,plain,
% 2.16/1.63 ((~hskp22) | c2_1(a1083)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1151, 1146])).
% 2.16/1.63 tff(1153,plain,
% 2.16/1.63 ((~hskp22) | c2_1(a1083)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1152, 1146])).
% 2.16/1.63 tff(1154,plain,
% 2.16/1.63 ((~hskp22) | c2_1(a1083)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1153, 1146])).
% 2.16/1.63 tff(1155,plain,
% 2.16/1.63 ((~hskp22) | c2_1(a1083)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1154, 1146])).
% 2.16/1.63 tff(1156,plain,
% 2.16/1.63 (c2_1(a1083)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1155, 1134])).
% 2.16/1.63 tff(1157,plain,
% 2.16/1.63 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c0_1(a1083)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c0_1(a1083)))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1158,plain,
% 2.16/1.63 (((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1083))) <=> ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c0_1(a1083)))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1159,plain,
% 2.16/1.63 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1083)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c0_1(a1083))))),
% 2.16/1.63 inference(monotonicity,[status(thm)],[1158])).
% 2.16/1.63 tff(1160,plain,
% 2.16/1.63 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1083)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c0_1(a1083)))),
% 2.16/1.63 inference(transitivity,[status(thm)],[1159, 1157])).
% 2.16/1.63 tff(1161,plain,
% 2.16/1.63 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1083)) | (~c0_1(a1083)) | (~c2_1(a1083)))),
% 2.16/1.63 inference(quant_inst,[status(thm)],[])).
% 2.16/1.63 tff(1162,plain,
% 2.16/1.63 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c0_1(a1083))),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1161, 1160])).
% 2.16/1.63 tff(1163,plain,
% 2.16/1.63 (~c0_1(a1083)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1162, 126, 232, 221, 210, 1156, 1145, 10])).
% 2.16/1.63 tff(1164,plain,
% 2.16/1.63 (^[V: $i, U: $i] : refl((hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))),
% 2.16/1.63 inference(bind,[status(th)],[])).
% 2.16/1.63 tff(1165,plain,
% 2.16/1.63 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.16/1.63 inference(quant_intro,[status(thm)],[1164])).
% 2.16/1.63 tff(1166,plain,
% 2.16/1.63 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1167,plain,
% 2.16/1.63 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(V)) | hskp42) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp42))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp42) <=> (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(V)) | hskp42) <=> (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))))),
% 2.16/1.63 inference(bind,[status(th)],[])).
% 2.16/1.63 tff(1168,plain,
% 2.16/1.63 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(V)) | hskp42) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.16/1.63 inference(quant_intro,[status(thm)],[1167])).
% 2.16/1.63 tff(1169,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c0_1(V)) | hskp42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause295')).
% 2.16/1.63 tff(1170,plain,
% 2.16/1.63 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1169, 1168])).
% 2.16/1.63 tff(1171,plain,
% 2.16/1.63 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1170, 1166])).
% 2.16/1.63 tff(1172,plain,(
% 2.16/1.63 ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.16/1.63 inference(skolemize,[status(sab)],[1171])).
% 2.16/1.63 tff(1173,plain,
% 2.16/1.63 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1172, 1165])).
% 2.16/1.63 tff(1174,plain,
% 2.16/1.63 (((~hskp22) | (~c1_1(a1083))) <=> ((~hskp22) | (~c1_1(a1083)))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1175,plain,
% 2.16/1.63 (((~c1_1(a1083)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a1083)))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1176,axiom,((~c1_1(a1083)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause219')).
% 2.16/1.63 tff(1177,plain,
% 2.16/1.63 ((~hskp22) | (~c1_1(a1083))),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1176, 1175])).
% 2.16/1.63 tff(1178,plain,
% 2.16/1.63 ((~hskp22) | (~c1_1(a1083))),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1177, 1174])).
% 2.16/1.63 tff(1179,plain,
% 2.16/1.63 (~c1_1(a1083)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1178, 1134])).
% 2.16/1.63 tff(1180,plain,
% 2.16/1.63 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | c1_1(a1083) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)) | (~c2_1(a1083)) | c0_1(a1083))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp42 | c1_1(a1083) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)) | (~c2_1(a1083)) | c0_1(a1083))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1181,plain,
% 2.16/1.63 ((hskp42 | (~ndr1_0) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)) | c0_1(a1083) | c1_1(a1083) | (~c2_1(a1083))) <=> (hskp42 | c1_1(a1083) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)) | (~c2_1(a1083)) | c0_1(a1083))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1182,plain,
% 2.16/1.63 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)) | c0_1(a1083) | c1_1(a1083) | (~c2_1(a1083)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | c1_1(a1083) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)) | (~c2_1(a1083)) | c0_1(a1083)))),
% 2.16/1.63 inference(monotonicity,[status(thm)],[1181])).
% 2.16/1.63 tff(1183,plain,
% 2.16/1.63 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)) | c0_1(a1083) | c1_1(a1083) | (~c2_1(a1083)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp42 | c1_1(a1083) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)) | (~c2_1(a1083)) | c0_1(a1083))),
% 2.16/1.63 inference(transitivity,[status(thm)],[1182, 1180])).
% 2.16/1.63 tff(1184,plain,
% 2.16/1.63 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a1079) | (~c1_1(a1079)) | (~c3_1(a1079)) | c0_1(a1083) | c1_1(a1083) | (~c2_1(a1083)))),
% 2.16/1.63 inference(quant_inst,[status(thm)],[])).
% 2.16/1.63 tff(1185,plain,
% 2.16/1.63 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp42 | c1_1(a1083) | c2_1(a1079) | (~ndr1_0) | (~c1_1(a1079)) | (~c3_1(a1079)) | (~c2_1(a1083)) | c0_1(a1083)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1184, 1183])).
% 2.16/1.63 tff(1186,plain,
% 2.16/1.63 (hskp42),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1185, 126, 1156, 154, 1179, 80, 1173, 133, 1163])).
% 2.16/1.63 tff(1187,plain,
% 2.16/1.63 (((~hskp42) | (~c2_1(a1046))) <=> ((~hskp42) | (~c2_1(a1046)))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1188,plain,
% 2.16/1.63 (((~c2_1(a1046)) | (~hskp42)) <=> ((~hskp42) | (~c2_1(a1046)))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1189,axiom,((~c2_1(a1046)) | (~hskp42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 2.16/1.63 tff(1190,plain,
% 2.16/1.63 ((~hskp42) | (~c2_1(a1046))),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 2.16/1.63 tff(1191,plain,
% 2.16/1.63 ((~hskp42) | (~c2_1(a1046))),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1190, 1187])).
% 2.16/1.63 tff(1192,plain,
% 2.16/1.63 (~c2_1(a1046)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1191, 1186])).
% 2.16/1.63 tff(1193,plain,
% 2.16/1.63 (((~hskp42) | c1_1(a1046)) <=> ((~hskp42) | c1_1(a1046))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1194,axiom,((~hskp42) | c1_1(a1046)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 2.16/1.63 tff(1195,plain,
% 2.16/1.63 ((~hskp42) | c1_1(a1046)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1194, 1193])).
% 2.16/1.63 tff(1196,plain,
% 2.16/1.63 ((~hskp42) | c1_1(a1046)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1195, 1193])).
% 2.16/1.63 tff(1197,plain,
% 2.16/1.63 ((~hskp42) | c1_1(a1046)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1196, 1193])).
% 2.16/1.63 tff(1198,plain,
% 2.16/1.63 ((~hskp42) | c1_1(a1046)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1197, 1193])).
% 2.16/1.63 tff(1199,plain,
% 2.16/1.63 ((~hskp42) | c1_1(a1046)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1198, 1193])).
% 2.16/1.63 tff(1200,plain,
% 2.16/1.63 ((~hskp42) | c1_1(a1046)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1199, 1193])).
% 2.16/1.63 tff(1201,plain,
% 2.16/1.63 ((~hskp42) | c1_1(a1046)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1200, 1193])).
% 2.16/1.63 tff(1202,plain,
% 2.16/1.63 ((~hskp42) | c1_1(a1046)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1201, 1193])).
% 2.16/1.63 tff(1203,plain,
% 2.16/1.63 (c1_1(a1046)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1202, 1186])).
% 2.16/1.63 tff(1204,assumption,(hskp35), introduced(assumption)).
% 2.16/1.63 tff(1205,plain,
% 2.16/1.63 (c3_1(a1033)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1018, 1204])).
% 2.16/1.63 tff(1206,plain,
% 2.16/1.63 (c1_1(a1033)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1029, 1204])).
% 2.16/1.63 tff(1207,plain,
% 2.16/1.63 (c0_1(a1033)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1040, 1204])).
% 2.16/1.63 tff(1208,plain,
% 2.16/1.63 (~c2_1(a1033)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1047, 126, 1207, 1206, 1205, 10])).
% 2.16/1.63 tff(1209,plain,
% 2.16/1.63 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c1_1(a1033)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c1_1(a1033)))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1210,plain,
% 2.16/1.63 ((hskp56 | hskp22 | (~ndr1_0) | c2_1(a1033) | (~c1_1(a1033)) | (~c3_1(a1033))) <=> (hskp56 | hskp22 | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c1_1(a1033)))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1211,plain,
% 2.16/1.63 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1033) | (~c1_1(a1033)) | (~c3_1(a1033)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c1_1(a1033))))),
% 2.16/1.63 inference(monotonicity,[status(thm)],[1210])).
% 2.16/1.63 tff(1212,plain,
% 2.16/1.63 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1033) | (~c1_1(a1033)) | (~c3_1(a1033)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c1_1(a1033)))),
% 2.16/1.63 inference(transitivity,[status(thm)],[1211, 1209])).
% 2.16/1.63 tff(1213,plain,
% 2.16/1.63 ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1033) | (~c1_1(a1033)) | (~c3_1(a1033)))),
% 2.16/1.63 inference(quant_inst,[status(thm)],[])).
% 2.16/1.63 tff(1214,plain,
% 2.16/1.63 ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c1_1(a1033))),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1213, 1212])).
% 2.16/1.63 tff(1215,plain,
% 2.16/1.63 (hskp22),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1214, 126, 1126, 1206, 1205, 31, 1208])).
% 2.16/1.63 tff(1216,plain,
% 2.16/1.63 (~c1_1(a1083)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1178, 1215])).
% 2.16/1.63 tff(1217,plain,
% 2.16/1.63 (c3_1(a1083)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1144, 1215])).
% 2.16/1.63 tff(1218,plain,
% 2.16/1.63 (c2_1(a1083)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1155, 1215])).
% 2.16/1.63 tff(1219,plain,
% 2.16/1.63 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1083)) | (~c2_1(a1083)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1220,plain,
% 2.16/1.63 ((hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033))) <=> (hskp57 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1221,plain,
% 2.16/1.63 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1083)) | (~c2_1(a1083))))),
% 2.16/1.63 inference(monotonicity,[status(thm)],[1220])).
% 2.16/1.63 tff(1222,plain,
% 2.16/1.63 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 2.16/1.63 inference(transitivity,[status(thm)],[1221, 1219])).
% 2.16/1.63 tff(1223,plain,
% 2.16/1.63 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)))),
% 2.16/1.63 inference(quant_inst,[status(thm)],[])).
% 2.16/1.63 tff(1224,plain,
% 2.16/1.63 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)) | (~c3_1(a1083)) | (~c2_1(a1083))),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 2.16/1.63 tff(1225,plain,
% 2.16/1.63 (hskp57),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1224, 126, 1207, 1205, 1218, 1217, 1216, 1058, 1208])).
% 2.16/1.63 tff(1226,plain,
% 2.16/1.63 (c3_1(a1085)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1076, 1225])).
% 2.16/1.63 tff(1227,plain,
% 2.16/1.63 (c0_1(a1085)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1087, 1225])).
% 2.16/1.63 tff(1228,plain,
% 2.16/1.63 (c2_1(a1085)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1098, 1225])).
% 2.16/1.63 tff(1229,plain,
% 2.16/1.63 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1083)) | (~c2_1(a1083)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1230,plain,
% 2.16/1.63 ((hskp53 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085))) <=> (hskp53 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1231,plain,
% 2.16/1.63 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1083)) | (~c2_1(a1083))))),
% 2.16/1.63 inference(monotonicity,[status(thm)],[1230])).
% 2.16/1.63 tff(1232,plain,
% 2.16/1.63 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 2.16/1.63 inference(transitivity,[status(thm)],[1231, 1229])).
% 2.16/1.63 tff(1233,plain,
% 2.16/1.63 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))),
% 2.16/1.63 inference(quant_inst,[status(thm)],[])).
% 2.16/1.63 tff(1234,plain,
% 2.16/1.63 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1083)) | (~c2_1(a1083))),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1233, 1232])).
% 2.16/1.63 tff(1235,plain,
% 2.16/1.63 (hskp53),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1234, 126, 1228, 1227, 1226, 1218, 1217, 1216, 20])).
% 2.16/1.63 tff(1236,plain,
% 2.16/1.63 (c0_1(a1073)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[340, 1235])).
% 2.16/1.63 tff(1237,plain,
% 2.16/1.63 (c2_1(a1073)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[351, 1235])).
% 2.16/1.63 tff(1238,plain,
% 2.16/1.63 (c1_1(a1073)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[362, 1235])).
% 2.16/1.63 tff(1239,plain,
% 2.16/1.63 ($false),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1115, 126, 1228, 1227, 1226, 1238, 1237, 1236, 10])).
% 2.16/1.63 tff(1240,plain,(~hskp35), inference(lemma,lemma(discharge,[]))).
% 2.16/1.63 tff(1241,plain,
% 2.16/1.63 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | c0_1(a1083) | c3_1(a1046) | (~c1_1(a1046)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | c0_1(a1083) | c3_1(a1046) | (~c1_1(a1046)))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1242,plain,
% 2.16/1.63 ((hskp35 | (~ndr1_0) | c2_1(a1046) | c3_1(a1046) | (~c1_1(a1046)) | c0_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083))) <=> (hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | c0_1(a1083) | c3_1(a1046) | (~c1_1(a1046)))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1243,plain,
% 2.16/1.63 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1046) | c3_1(a1046) | (~c1_1(a1046)) | c0_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | c0_1(a1083) | c3_1(a1046) | (~c1_1(a1046))))),
% 2.16/1.63 inference(monotonicity,[status(thm)],[1242])).
% 2.16/1.63 tff(1244,plain,
% 2.16/1.63 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1046) | c3_1(a1046) | (~c1_1(a1046)) | c0_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | c0_1(a1083) | c3_1(a1046) | (~c1_1(a1046)))),
% 2.16/1.63 inference(transitivity,[status(thm)],[1243, 1241])).
% 2.16/1.63 tff(1245,plain,
% 2.16/1.63 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1046) | c3_1(a1046) | (~c1_1(a1046)) | c0_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 2.16/1.63 inference(quant_inst,[status(thm)],[])).
% 2.16/1.63 tff(1246,plain,
% 2.16/1.63 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | c0_1(a1083) | c3_1(a1046) | (~c1_1(a1046))),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 2.16/1.63 tff(1247,plain,
% 2.16/1.63 (c3_1(a1046)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1246, 126, 1240, 1203, 1156, 1145, 1192, 1001, 1163])).
% 2.16/1.63 tff(1248,plain,
% 2.16/1.63 (((~hskp42) | c0_1(a1046)) <=> ((~hskp42) | c0_1(a1046))),
% 2.16/1.63 inference(rewrite,[status(thm)],[])).
% 2.16/1.63 tff(1249,axiom,((~hskp42) | c0_1(a1046)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 2.16/1.63 tff(1250,plain,
% 2.16/1.63 ((~hskp42) | c0_1(a1046)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1249, 1248])).
% 2.16/1.63 tff(1251,plain,
% 2.16/1.63 ((~hskp42) | c0_1(a1046)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1250, 1248])).
% 2.16/1.63 tff(1252,plain,
% 2.16/1.63 ((~hskp42) | c0_1(a1046)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1251, 1248])).
% 2.16/1.63 tff(1253,plain,
% 2.16/1.63 ((~hskp42) | c0_1(a1046)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1252, 1248])).
% 2.16/1.63 tff(1254,plain,
% 2.16/1.63 ((~hskp42) | c0_1(a1046)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1253, 1248])).
% 2.16/1.63 tff(1255,plain,
% 2.16/1.63 ((~hskp42) | c0_1(a1046)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1254, 1248])).
% 2.16/1.63 tff(1256,plain,
% 2.16/1.63 ((~hskp42) | c0_1(a1046)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1255, 1248])).
% 2.16/1.63 tff(1257,plain,
% 2.16/1.63 ((~hskp42) | c0_1(a1046)),
% 2.16/1.63 inference(modus_ponens,[status(thm)],[1256, 1248])).
% 2.16/1.63 tff(1258,plain,
% 2.16/1.63 (c0_1(a1046)),
% 2.16/1.63 inference(unit_resolution,[status(thm)],[1257, 1186])).
% 2.16/1.63 tff(1259,plain,
% 2.16/1.63 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c2_1(a1046) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1046)) | (~c0_1(a1046)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c2_1(a1046) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1046)) | (~c0_1(a1046)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1260,plain,
% 2.16/1.64 ((hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1046) | (~c3_1(a1046)) | (~c0_1(a1046))) <=> (hskp57 | c2_1(a1046) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1046)) | (~c0_1(a1046)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1261,plain,
% 2.16/1.64 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1046) | (~c3_1(a1046)) | (~c0_1(a1046)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c2_1(a1046) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1046)) | (~c0_1(a1046))))),
% 2.16/1.64 inference(monotonicity,[status(thm)],[1260])).
% 2.16/1.64 tff(1262,plain,
% 2.16/1.64 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1046) | (~c3_1(a1046)) | (~c0_1(a1046)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c2_1(a1046) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1046)) | (~c0_1(a1046)))),
% 2.16/1.64 inference(transitivity,[status(thm)],[1261, 1259])).
% 2.16/1.64 tff(1263,plain,
% 2.16/1.64 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1046) | (~c3_1(a1046)) | (~c0_1(a1046)))),
% 2.16/1.64 inference(quant_inst,[status(thm)],[])).
% 2.16/1.64 tff(1264,plain,
% 2.16/1.64 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c2_1(a1046) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1046)) | (~c0_1(a1046))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1263, 1262])).
% 2.16/1.64 tff(1265,plain,
% 2.16/1.64 (hskp57 | (~c3_1(a1046))),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1264, 126, 1258, 1156, 1145, 1192, 1179, 1058])).
% 2.16/1.64 tff(1266,plain,
% 2.16/1.64 (hskp57),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1265, 1247])).
% 2.16/1.64 tff(1267,plain,
% 2.16/1.64 (c3_1(a1085)),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1076, 1266])).
% 2.16/1.64 tff(1268,plain,
% 2.16/1.64 (c0_1(a1085)),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1087, 1266])).
% 2.16/1.64 tff(1269,plain,
% 2.16/1.64 (c2_1(a1085)),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1098, 1266])).
% 2.16/1.64 tff(1270,plain,
% 2.16/1.64 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1271,plain,
% 2.16/1.64 (((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085))) <=> ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1272,plain,
% 2.16/1.64 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085))))),
% 2.16/1.64 inference(monotonicity,[status(thm)],[1271])).
% 2.16/1.64 tff(1273,plain,
% 2.16/1.64 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)))),
% 2.16/1.64 inference(transitivity,[status(thm)],[1272, 1270])).
% 2.16/1.64 tff(1274,plain,
% 2.16/1.64 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))),
% 2.16/1.64 inference(quant_inst,[status(thm)],[])).
% 2.16/1.64 tff(1275,plain,
% 2.16/1.64 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1274, 1273])).
% 2.16/1.64 tff(1276,plain,
% 2.16/1.64 ($false),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1275, 126, 1269, 1268, 1267, 232, 221, 210, 10])).
% 2.16/1.64 tff(1277,plain,((~hskp19) | hskp10), inference(lemma,lemma(discharge,[]))).
% 2.16/1.64 tff(1278,plain,
% 2.16/1.64 (~hskp19),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1277, 53])).
% 2.16/1.64 tff(1279,plain,
% 2.16/1.64 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))))),
% 2.16/1.64 inference(bind,[status(th)],[])).
% 2.16/1.64 tff(1280,plain,
% 2.16/1.64 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.16/1.64 inference(quant_intro,[status(thm)],[1279])).
% 2.16/1.64 tff(1281,plain,
% 2.16/1.64 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1282,plain,
% 2.16/1.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c0_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))))),
% 2.16/1.64 inference(bind,[status(th)],[])).
% 2.16/1.64 tff(1283,plain,
% 2.16/1.64 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.16/1.64 inference(quant_intro,[status(thm)],[1282])).
% 2.16/1.64 tff(1284,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause307')).
% 2.16/1.64 tff(1285,plain,
% 2.16/1.64 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 2.16/1.64 tff(1286,plain,
% 2.16/1.64 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1285, 1281])).
% 2.16/1.64 tff(1287,plain,(
% 2.16/1.64 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.16/1.64 inference(skolemize,[status(sab)],[1286])).
% 2.16/1.64 tff(1288,plain,
% 2.16/1.64 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1287, 1280])).
% 2.16/1.64 tff(1289,assumption,(~hskp20), introduced(assumption)).
% 2.16/1.64 tff(1290,assumption,(~hskp19), introduced(assumption)).
% 2.16/1.64 tff(1291,assumption,(~hskp43), introduced(assumption)).
% 2.16/1.64 tff(1292,assumption,(hskp38), introduced(assumption)).
% 2.16/1.64 tff(1293,plain,
% 2.16/1.64 (((~hskp38) | c2_1(a1040)) <=> ((~hskp38) | c2_1(a1040))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1294,axiom,((~hskp38) | c2_1(a1040)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 2.16/1.64 tff(1295,plain,
% 2.16/1.64 ((~hskp38) | c2_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1294, 1293])).
% 2.16/1.64 tff(1296,plain,
% 2.16/1.64 ((~hskp38) | c2_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1295, 1293])).
% 2.16/1.64 tff(1297,plain,
% 2.16/1.64 ((~hskp38) | c2_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1296, 1293])).
% 2.16/1.64 tff(1298,plain,
% 2.16/1.64 ((~hskp38) | c2_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1297, 1293])).
% 2.16/1.64 tff(1299,plain,
% 2.16/1.64 ((~hskp38) | c2_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1298, 1293])).
% 2.16/1.64 tff(1300,plain,
% 2.16/1.64 ((~hskp38) | c2_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1299, 1293])).
% 2.16/1.64 tff(1301,plain,
% 2.16/1.64 ((~hskp38) | c2_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1300, 1293])).
% 2.16/1.64 tff(1302,plain,
% 2.16/1.64 ((~hskp38) | c2_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1301, 1293])).
% 2.16/1.64 tff(1303,plain,
% 2.16/1.64 (c2_1(a1040)),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1302, 1292])).
% 2.16/1.64 tff(1304,plain,
% 2.16/1.64 (((~hskp38) | c3_1(a1040)) <=> ((~hskp38) | c3_1(a1040))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1305,axiom,((~hskp38) | c3_1(a1040)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 2.16/1.64 tff(1306,plain,
% 2.16/1.64 ((~hskp38) | c3_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 2.16/1.64 tff(1307,plain,
% 2.16/1.64 ((~hskp38) | c3_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1306, 1304])).
% 2.16/1.64 tff(1308,plain,
% 2.16/1.64 ((~hskp38) | c3_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1307, 1304])).
% 2.16/1.64 tff(1309,plain,
% 2.16/1.64 ((~hskp38) | c3_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1308, 1304])).
% 2.16/1.64 tff(1310,plain,
% 2.16/1.64 ((~hskp38) | c3_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1309, 1304])).
% 2.16/1.64 tff(1311,plain,
% 2.16/1.64 ((~hskp38) | c3_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1310, 1304])).
% 2.16/1.64 tff(1312,plain,
% 2.16/1.64 ((~hskp38) | c3_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1311, 1304])).
% 2.16/1.64 tff(1313,plain,
% 2.16/1.64 ((~hskp38) | c3_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1312, 1304])).
% 2.16/1.64 tff(1314,plain,
% 2.16/1.64 (c3_1(a1040)),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1313, 1292])).
% 2.16/1.64 tff(1315,plain,
% 2.16/1.64 (((~hskp38) | c1_1(a1040)) <=> ((~hskp38) | c1_1(a1040))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1316,axiom,((~hskp38) | c1_1(a1040)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 2.16/1.64 tff(1317,plain,
% 2.16/1.64 ((~hskp38) | c1_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 2.16/1.64 tff(1318,plain,
% 2.16/1.64 ((~hskp38) | c1_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1317, 1315])).
% 2.16/1.64 tff(1319,plain,
% 2.16/1.64 ((~hskp38) | c1_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1318, 1315])).
% 2.16/1.64 tff(1320,plain,
% 2.16/1.64 ((~hskp38) | c1_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1319, 1315])).
% 2.16/1.64 tff(1321,plain,
% 2.16/1.64 ((~hskp38) | c1_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1320, 1315])).
% 2.16/1.64 tff(1322,plain,
% 2.16/1.64 ((~hskp38) | c1_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1321, 1315])).
% 2.16/1.64 tff(1323,plain,
% 2.16/1.64 ((~hskp38) | c1_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1322, 1315])).
% 2.16/1.64 tff(1324,plain,
% 2.16/1.64 ((~hskp38) | c1_1(a1040)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1323, 1315])).
% 2.16/1.64 tff(1325,plain,
% 2.16/1.64 (c1_1(a1040)),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1324, 1292])).
% 2.16/1.64 tff(1326,plain,
% 2.16/1.64 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1327,plain,
% 2.16/1.64 (((~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040))) <=> ((~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1328,plain,
% 2.16/1.64 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040))))),
% 2.16/1.64 inference(monotonicity,[status(thm)],[1327])).
% 2.16/1.64 tff(1329,plain,
% 2.16/1.64 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)))),
% 2.16/1.64 inference(transitivity,[status(thm)],[1328, 1326])).
% 2.16/1.64 tff(1330,plain,
% 2.16/1.64 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)))),
% 2.16/1.64 inference(quant_inst,[status(thm)],[])).
% 2.16/1.64 tff(1331,plain,
% 2.16/1.64 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c1_1(a1040)) | (~c0_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 2.16/1.64 tff(1332,plain,
% 2.16/1.64 (~c0_1(a1040)),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1331, 126, 1325, 1314, 1303, 10])).
% 2.16/1.64 tff(1333,plain,
% 2.16/1.64 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1334,plain,
% 2.16/1.64 ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040)))),
% 2.16/1.64 inference(quant_inst,[status(thm)],[])).
% 2.16/1.64 tff(1335,plain,
% 2.16/1.64 ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1334, 1333])).
% 2.16/1.64 tff(1336,plain,
% 2.16/1.64 ($false),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1335, 126, 1291, 53, 1325, 1303, 63, 1332])).
% 2.16/1.64 tff(1337,plain,((~hskp38) | hskp43 | hskp10), inference(lemma,lemma(discharge,[]))).
% 2.16/1.64 tff(1338,plain,
% 2.16/1.64 (~hskp38),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1337, 1291, 53])).
% 2.16/1.64 tff(1339,assumption,(~hskp38), introduced(assumption)).
% 2.16/1.64 tff(1340,assumption,(~hskp14), introduced(assumption)).
% 2.16/1.64 tff(1341,plain,
% 2.16/1.64 ((hskp46 | hskp38 | hskp14) <=> (hskp46 | hskp38 | hskp14)),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1342,plain,
% 2.16/1.64 (((hskp46 | hskp38) | hskp14) <=> (hskp46 | hskp38 | hskp14)),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1343,plain,
% 2.16/1.64 ((hskp46 | hskp38) <=> (hskp46 | hskp38)),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1344,plain,
% 2.16/1.64 (((hskp46 | hskp38) | hskp14) <=> ((hskp46 | hskp38) | hskp14)),
% 2.16/1.64 inference(monotonicity,[status(thm)],[1343])).
% 2.16/1.64 tff(1345,plain,
% 2.16/1.64 (((hskp46 | hskp38) | hskp14) <=> (hskp46 | hskp38 | hskp14)),
% 2.16/1.64 inference(transitivity,[status(thm)],[1344, 1342])).
% 2.16/1.64 tff(1346,axiom,((hskp46 | hskp38) | hskp14), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 2.16/1.64 tff(1347,plain,
% 2.16/1.64 (hskp46 | hskp38 | hskp14),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1346, 1345])).
% 2.16/1.64 tff(1348,plain,
% 2.16/1.64 (hskp46 | hskp38 | hskp14),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1347, 1341])).
% 2.16/1.64 tff(1349,plain,
% 2.16/1.64 (hskp46 | hskp38 | hskp14),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1348, 1341])).
% 2.16/1.64 tff(1350,plain,
% 2.16/1.64 (hskp46 | hskp38 | hskp14),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1349, 1341])).
% 2.16/1.64 tff(1351,plain,
% 2.16/1.64 (hskp46 | hskp38 | hskp14),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1350, 1341])).
% 2.16/1.64 tff(1352,plain,
% 2.16/1.64 (hskp46 | hskp38 | hskp14),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1351, 1341])).
% 2.16/1.64 tff(1353,plain,
% 2.16/1.64 (hskp46 | hskp38 | hskp14),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1352, 1341])).
% 2.16/1.64 tff(1354,plain,
% 2.16/1.64 (hskp46 | hskp38 | hskp14),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1353, 1341])).
% 2.16/1.64 tff(1355,plain,
% 2.16/1.64 (hskp46),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1354, 1339, 1340])).
% 2.16/1.64 tff(1356,assumption,(hskp46), introduced(assumption)).
% 2.16/1.64 tff(1357,plain,
% 2.16/1.64 (((~hskp46) | (~c1_1(a1053))) <=> ((~hskp46) | (~c1_1(a1053)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1358,plain,
% 2.16/1.64 (((~c1_1(a1053)) | (~hskp46)) <=> ((~hskp46) | (~c1_1(a1053)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1359,axiom,((~c1_1(a1053)) | (~hskp46)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 2.16/1.64 tff(1360,plain,
% 2.16/1.64 ((~hskp46) | (~c1_1(a1053))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 2.16/1.64 tff(1361,plain,
% 2.16/1.64 ((~hskp46) | (~c1_1(a1053))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1360, 1357])).
% 2.16/1.64 tff(1362,plain,
% 2.16/1.64 (~c1_1(a1053)),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1361, 1356])).
% 2.16/1.64 tff(1363,plain,
% 2.16/1.64 (((~hskp46) | c0_1(a1053)) <=> ((~hskp46) | c0_1(a1053))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1364,axiom,((~hskp46) | c0_1(a1053)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 2.16/1.64 tff(1365,plain,
% 2.16/1.64 ((~hskp46) | c0_1(a1053)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1364, 1363])).
% 2.16/1.64 tff(1366,plain,
% 2.16/1.64 ((~hskp46) | c0_1(a1053)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1365, 1363])).
% 2.16/1.64 tff(1367,plain,
% 2.16/1.64 ((~hskp46) | c0_1(a1053)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1366, 1363])).
% 2.16/1.64 tff(1368,plain,
% 2.16/1.64 ((~hskp46) | c0_1(a1053)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1367, 1363])).
% 2.16/1.64 tff(1369,plain,
% 2.16/1.64 ((~hskp46) | c0_1(a1053)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1368, 1363])).
% 2.16/1.64 tff(1370,plain,
% 2.16/1.64 ((~hskp46) | c0_1(a1053)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1369, 1363])).
% 2.16/1.64 tff(1371,plain,
% 2.16/1.64 ((~hskp46) | c0_1(a1053)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1370, 1363])).
% 2.16/1.64 tff(1372,plain,
% 2.16/1.64 ((~hskp46) | c0_1(a1053)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1371, 1363])).
% 2.16/1.64 tff(1373,plain,
% 2.16/1.64 (c0_1(a1053)),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1372, 1356])).
% 2.16/1.64 tff(1374,plain,
% 2.16/1.64 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | c1_1(a1053) | (~ndr1_0) | c3_1(a1053) | (~c0_1(a1053)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c1_1(a1053) | (~ndr1_0) | c3_1(a1053) | (~c0_1(a1053)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1375,plain,
% 2.16/1.64 ((hskp20 | hskp19 | (~ndr1_0) | c3_1(a1053) | c1_1(a1053) | (~c0_1(a1053))) <=> (hskp20 | hskp19 | c1_1(a1053) | (~ndr1_0) | c3_1(a1053) | (~c0_1(a1053)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1376,plain,
% 2.16/1.64 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a1053) | c1_1(a1053) | (~c0_1(a1053)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | c1_1(a1053) | (~ndr1_0) | c3_1(a1053) | (~c0_1(a1053))))),
% 2.16/1.64 inference(monotonicity,[status(thm)],[1375])).
% 2.16/1.64 tff(1377,plain,
% 2.16/1.64 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a1053) | c1_1(a1053) | (~c0_1(a1053)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c1_1(a1053) | (~ndr1_0) | c3_1(a1053) | (~c0_1(a1053)))),
% 2.16/1.64 inference(transitivity,[status(thm)],[1376, 1374])).
% 2.16/1.64 tff(1378,plain,
% 2.16/1.64 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a1053) | c1_1(a1053) | (~c0_1(a1053)))),
% 2.16/1.64 inference(quant_inst,[status(thm)],[])).
% 2.16/1.64 tff(1379,plain,
% 2.16/1.64 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c1_1(a1053) | (~ndr1_0) | c3_1(a1053) | (~c0_1(a1053))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1378, 1377])).
% 2.16/1.64 tff(1380,plain,
% 2.16/1.64 (c3_1(a1053)),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1379, 126, 1289, 1290, 1373, 1362, 685])).
% 2.16/1.64 tff(1381,plain,
% 2.16/1.64 (^[V: $i, U: $i] : refl((hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 2.16/1.64 inference(bind,[status(th)],[])).
% 2.16/1.64 tff(1382,plain,
% 2.16/1.64 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.16/1.64 inference(quant_intro,[status(thm)],[1381])).
% 2.16/1.64 tff(1383,plain,
% 2.16/1.64 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1384,plain,
% 2.16/1.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) | hskp38) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp38))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp38) <=> (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) | hskp38) <=> (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 2.16/1.64 inference(bind,[status(th)],[])).
% 2.16/1.64 tff(1385,plain,
% 2.16/1.64 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) | hskp38) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.16/1.64 inference(quant_intro,[status(thm)],[1384])).
% 2.16/1.64 tff(1386,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) | hskp38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause301')).
% 2.16/1.64 tff(1387,plain,
% 2.16/1.64 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 2.16/1.64 tff(1388,plain,
% 2.16/1.64 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1387, 1383])).
% 2.16/1.64 tff(1389,plain,(
% 2.16/1.64 ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.16/1.64 inference(skolemize,[status(sab)],[1388])).
% 2.16/1.64 tff(1390,plain,
% 2.16/1.64 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1389, 1382])).
% 2.16/1.64 tff(1391,plain,
% 2.16/1.64 (((~hskp46) | (~c2_1(a1053))) <=> ((~hskp46) | (~c2_1(a1053)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1392,plain,
% 2.16/1.64 (((~c2_1(a1053)) | (~hskp46)) <=> ((~hskp46) | (~c2_1(a1053)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1393,axiom,((~c2_1(a1053)) | (~hskp46)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 2.16/1.64 tff(1394,plain,
% 2.16/1.64 ((~hskp46) | (~c2_1(a1053))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1393, 1392])).
% 2.16/1.64 tff(1395,plain,
% 2.16/1.64 ((~hskp46) | (~c2_1(a1053))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1394, 1391])).
% 2.16/1.64 tff(1396,plain,
% 2.16/1.64 (~c2_1(a1053)),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1395, 1356])).
% 2.16/1.64 tff(1397,plain,
% 2.16/1.64 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp38 | c1_1(a1053) | c2_1(a1053) | (~ndr1_0) | (~c3_1(a1053)) | (~c0_1(a1053)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp38 | c1_1(a1053) | c2_1(a1053) | (~ndr1_0) | (~c3_1(a1053)) | (~c0_1(a1053)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1398,plain,
% 2.16/1.64 ((hskp38 | (~ndr1_0) | c1_1(a1053) | (~c3_1(a1053)) | (~c0_1(a1053)) | c2_1(a1053) | (~c3_1(a1053)) | (~c0_1(a1053))) <=> (hskp38 | c1_1(a1053) | c2_1(a1053) | (~ndr1_0) | (~c3_1(a1053)) | (~c0_1(a1053)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1399,plain,
% 2.16/1.64 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp38 | (~ndr1_0) | c1_1(a1053) | (~c3_1(a1053)) | (~c0_1(a1053)) | c2_1(a1053) | (~c3_1(a1053)) | (~c0_1(a1053)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp38 | c1_1(a1053) | c2_1(a1053) | (~ndr1_0) | (~c3_1(a1053)) | (~c0_1(a1053))))),
% 2.16/1.64 inference(monotonicity,[status(thm)],[1398])).
% 2.16/1.64 tff(1400,plain,
% 2.16/1.64 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp38 | (~ndr1_0) | c1_1(a1053) | (~c3_1(a1053)) | (~c0_1(a1053)) | c2_1(a1053) | (~c3_1(a1053)) | (~c0_1(a1053)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp38 | c1_1(a1053) | c2_1(a1053) | (~ndr1_0) | (~c3_1(a1053)) | (~c0_1(a1053)))),
% 2.16/1.64 inference(transitivity,[status(thm)],[1399, 1397])).
% 2.16/1.64 tff(1401,plain,
% 2.16/1.64 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp38 | (~ndr1_0) | c1_1(a1053) | (~c3_1(a1053)) | (~c0_1(a1053)) | c2_1(a1053) | (~c3_1(a1053)) | (~c0_1(a1053)))),
% 2.16/1.64 inference(quant_inst,[status(thm)],[])).
% 2.16/1.64 tff(1402,plain,
% 2.16/1.64 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp38 | c1_1(a1053) | c2_1(a1053) | (~ndr1_0) | (~c3_1(a1053)) | (~c0_1(a1053))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 2.16/1.64 tff(1403,plain,
% 2.16/1.64 ($false),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1402, 126, 1339, 1373, 1362, 1396, 1390, 1380])).
% 2.16/1.64 tff(1404,plain,((~hskp46) | hskp38 | hskp20 | hskp19), inference(lemma,lemma(discharge,[]))).
% 2.16/1.64 tff(1405,plain,
% 2.16/1.64 ($false),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1404, 1355, 1339, 1289, 1290])).
% 2.16/1.64 tff(1406,plain,(hskp38 | hskp20 | hskp19 | hskp14), inference(lemma,lemma(discharge,[]))).
% 2.16/1.64 tff(1407,plain,
% 2.16/1.64 (hskp14),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1406, 1338, 1289, 1290])).
% 2.16/1.64 tff(1408,plain,
% 2.16/1.64 (((~hskp14) | (~c2_1(a1055))) <=> ((~hskp14) | (~c2_1(a1055)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1409,plain,
% 2.16/1.64 (((~c2_1(a1055)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a1055)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1410,axiom,((~c2_1(a1055)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause235')).
% 2.16/1.64 tff(1411,plain,
% 2.16/1.64 ((~hskp14) | (~c2_1(a1055))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1410, 1409])).
% 2.16/1.64 tff(1412,plain,
% 2.16/1.64 ((~hskp14) | (~c2_1(a1055))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1411, 1408])).
% 2.16/1.64 tff(1413,plain,
% 2.16/1.64 (~c2_1(a1055)),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1412, 1407])).
% 2.16/1.64 tff(1414,plain,
% 2.16/1.64 (((~hskp14) | (~c0_1(a1055))) <=> ((~hskp14) | (~c0_1(a1055)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1415,plain,
% 2.16/1.64 (((~c0_1(a1055)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a1055)))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1416,axiom,((~c0_1(a1055)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause233')).
% 2.16/1.64 tff(1417,plain,
% 2.16/1.64 ((~hskp14) | (~c0_1(a1055))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 2.16/1.64 tff(1418,plain,
% 2.16/1.64 ((~hskp14) | (~c0_1(a1055))),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1417, 1414])).
% 2.16/1.64 tff(1419,plain,
% 2.16/1.64 (~c0_1(a1055)),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1418, 1407])).
% 2.16/1.64 tff(1420,plain,
% 2.16/1.64 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | c3_1(a1055))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | c3_1(a1055))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1421,plain,
% 2.16/1.64 ((hskp10 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | c3_1(a1055)) <=> (hskp10 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | c3_1(a1055))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1422,plain,
% 2.16/1.64 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | c3_1(a1055))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | c3_1(a1055)))),
% 2.16/1.64 inference(monotonicity,[status(thm)],[1421])).
% 2.16/1.64 tff(1423,plain,
% 2.16/1.64 (((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | c3_1(a1055))) <=> ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | c3_1(a1055))),
% 2.16/1.64 inference(transitivity,[status(thm)],[1422, 1420])).
% 2.16/1.64 tff(1424,plain,
% 2.16/1.64 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | (hskp10 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | c3_1(a1055))),
% 2.16/1.64 inference(quant_inst,[status(thm)],[])).
% 2.16/1.64 tff(1425,plain,
% 2.16/1.64 ((~![U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | c3_1(U))) | hskp10 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | c3_1(a1055)),
% 2.16/1.64 inference(modus_ponens,[status(thm)],[1424, 1423])).
% 2.16/1.64 tff(1426,plain,
% 2.16/1.64 (c3_1(a1055)),
% 2.16/1.64 inference(unit_resolution,[status(thm)],[1425, 126, 53, 1419, 1413, 73])).
% 2.16/1.64 tff(1427,plain,
% 2.16/1.64 (^[V: $i, U: $i] : refl((hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) <=> (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)))),
% 2.16/1.64 inference(bind,[status(th)],[])).
% 2.16/1.64 tff(1428,plain,
% 2.16/1.64 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 2.16/1.64 inference(quant_intro,[status(thm)],[1427])).
% 2.16/1.64 tff(1429,plain,
% 2.16/1.64 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 2.16/1.64 inference(rewrite,[status(thm)],[])).
% 2.16/1.64 tff(1430,plain,
% 2.16/1.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V)) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c3_1(V)) | hskp35) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) | hskp35))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V)) | hskp35) <=> (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c3_1(V)) | hskp35) <=> (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))))),
% 2.16/1.65 inference(bind,[status(th)],[])).
% 2.16/1.65 tff(1431,plain,
% 2.16/1.65 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c3_1(V)) | hskp35) <=> ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 2.16/1.65 inference(quant_intro,[status(thm)],[1430])).
% 2.16/1.65 tff(1432,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c2_1(V)) | c0_1(V)) | c3_1(V)) | hskp35)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause286')).
% 2.16/1.65 tff(1433,plain,
% 2.16/1.65 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 2.16/1.65 tff(1434,plain,
% 2.16/1.65 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1433, 1429])).
% 2.16/1.65 tff(1435,plain,(
% 2.16/1.65 ![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 2.16/1.65 inference(skolemize,[status(sab)],[1434])).
% 2.16/1.65 tff(1436,plain,
% 2.16/1.65 (![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1435, 1428])).
% 2.16/1.65 tff(1437,assumption,(hskp62), introduced(assumption)).
% 2.16/1.65 tff(1438,plain,
% 2.16/1.65 (((~hskp62) | c1_1(a1103)) <=> ((~hskp62) | c1_1(a1103))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1439,axiom,((~hskp62) | c1_1(a1103)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 2.16/1.65 tff(1440,plain,
% 2.16/1.65 ((~hskp62) | c1_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1439, 1438])).
% 2.16/1.65 tff(1441,plain,
% 2.16/1.65 ((~hskp62) | c1_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1440, 1438])).
% 2.16/1.65 tff(1442,plain,
% 2.16/1.65 ((~hskp62) | c1_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1441, 1438])).
% 2.16/1.65 tff(1443,plain,
% 2.16/1.65 ((~hskp62) | c1_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1442, 1438])).
% 2.16/1.65 tff(1444,plain,
% 2.16/1.65 ((~hskp62) | c1_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1443, 1438])).
% 2.16/1.65 tff(1445,plain,
% 2.16/1.65 ((~hskp62) | c1_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1444, 1438])).
% 2.16/1.65 tff(1446,plain,
% 2.16/1.65 ((~hskp62) | c1_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1445, 1438])).
% 2.16/1.65 tff(1447,plain,
% 2.16/1.65 ((~hskp62) | c1_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1446, 1438])).
% 2.16/1.65 tff(1448,plain,
% 2.16/1.65 (c1_1(a1103)),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1447, 1437])).
% 2.16/1.65 tff(1449,plain,
% 2.16/1.65 (((~hskp62) | c2_1(a1103)) <=> ((~hskp62) | c2_1(a1103))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1450,axiom,((~hskp62) | c2_1(a1103)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 2.16/1.65 tff(1451,plain,
% 2.16/1.65 ((~hskp62) | c2_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1450, 1449])).
% 2.16/1.65 tff(1452,plain,
% 2.16/1.65 ((~hskp62) | c2_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1451, 1449])).
% 2.16/1.65 tff(1453,plain,
% 2.16/1.65 ((~hskp62) | c2_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1452, 1449])).
% 2.16/1.65 tff(1454,plain,
% 2.16/1.65 ((~hskp62) | c2_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1453, 1449])).
% 2.16/1.65 tff(1455,plain,
% 2.16/1.65 ((~hskp62) | c2_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1454, 1449])).
% 2.16/1.65 tff(1456,plain,
% 2.16/1.65 ((~hskp62) | c2_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1455, 1449])).
% 2.16/1.65 tff(1457,plain,
% 2.16/1.65 ((~hskp62) | c2_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1456, 1449])).
% 2.16/1.65 tff(1458,plain,
% 2.16/1.65 ((~hskp62) | c2_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1457, 1449])).
% 2.16/1.65 tff(1459,plain,
% 2.16/1.65 (c2_1(a1103)),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1458, 1437])).
% 2.16/1.65 tff(1460,plain,
% 2.16/1.65 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c2_1(a1103)) | (~c1_1(a1103)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c2_1(a1103)) | (~c1_1(a1103)))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1461,plain,
% 2.16/1.65 ((hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c1_1(a1103)) | (~c2_1(a1103))) <=> (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c2_1(a1103)) | (~c1_1(a1103)))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1462,plain,
% 2.16/1.65 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c1_1(a1103)) | (~c2_1(a1103)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c2_1(a1103)) | (~c1_1(a1103))))),
% 2.16/1.65 inference(monotonicity,[status(thm)],[1461])).
% 2.16/1.65 tff(1463,plain,
% 2.16/1.65 (((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c1_1(a1103)) | (~c2_1(a1103)))) <=> ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c2_1(a1103)) | (~c1_1(a1103)))),
% 2.16/1.65 inference(transitivity,[status(thm)],[1462, 1460])).
% 2.16/1.65 tff(1464,plain,
% 2.16/1.65 ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c1_1(a1103)) | (~c2_1(a1103)))),
% 2.16/1.65 inference(quant_inst,[status(thm)],[])).
% 2.16/1.65 tff(1465,plain,
% 2.16/1.65 ((~![U: $i] : (hskp43 | hskp10 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp43 | hskp10 | (~ndr1_0) | c0_1(a1103) | (~c2_1(a1103)) | (~c1_1(a1103))),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1464, 1463])).
% 2.16/1.65 tff(1466,plain,
% 2.16/1.65 (c0_1(a1103)),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1465, 126, 1291, 53, 1459, 1448, 63])).
% 2.16/1.65 tff(1467,plain,
% 2.16/1.65 (((~hskp62) | c3_1(a1103)) <=> ((~hskp62) | c3_1(a1103))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1468,axiom,((~hskp62) | c3_1(a1103)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 2.16/1.65 tff(1469,plain,
% 2.16/1.65 ((~hskp62) | c3_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1468, 1467])).
% 2.16/1.65 tff(1470,plain,
% 2.16/1.65 ((~hskp62) | c3_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1469, 1467])).
% 2.16/1.65 tff(1471,plain,
% 2.16/1.65 ((~hskp62) | c3_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1470, 1467])).
% 2.16/1.65 tff(1472,plain,
% 2.16/1.65 ((~hskp62) | c3_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1471, 1467])).
% 2.16/1.65 tff(1473,plain,
% 2.16/1.65 ((~hskp62) | c3_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1472, 1467])).
% 2.16/1.65 tff(1474,plain,
% 2.16/1.65 ((~hskp62) | c3_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1473, 1467])).
% 2.16/1.65 tff(1475,plain,
% 2.16/1.65 ((~hskp62) | c3_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1474, 1467])).
% 2.16/1.65 tff(1476,plain,
% 2.16/1.65 ((~hskp62) | c3_1(a1103)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1475, 1467])).
% 2.16/1.65 tff(1477,plain,
% 2.16/1.65 (c3_1(a1103)),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1476, 1437])).
% 2.16/1.65 tff(1478,plain,
% 2.16/1.65 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c1_1(a1103)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c1_1(a1103)))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1479,plain,
% 2.16/1.65 (((~ndr1_0) | (~c1_1(a1103)) | (~c0_1(a1103)) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c2_1(a1103))) <=> ((~ndr1_0) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c1_1(a1103)))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1480,plain,
% 2.16/1.65 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1103)) | (~c0_1(a1103)) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c2_1(a1103)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c1_1(a1103))))),
% 2.16/1.65 inference(monotonicity,[status(thm)],[1479])).
% 2.16/1.65 tff(1481,plain,
% 2.16/1.65 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1103)) | (~c0_1(a1103)) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c2_1(a1103)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c1_1(a1103)))),
% 2.16/1.65 inference(transitivity,[status(thm)],[1480, 1478])).
% 2.16/1.65 tff(1482,plain,
% 2.16/1.65 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1103)) | (~c0_1(a1103)) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c2_1(a1103)))),
% 2.16/1.65 inference(quant_inst,[status(thm)],[])).
% 2.16/1.65 tff(1483,plain,
% 2.16/1.65 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c2_1(a1103)) | (~c3_1(a1103)) | (~c0_1(a1103)) | (~c1_1(a1103))),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1482, 1481])).
% 2.16/1.65 tff(1484,plain,
% 2.16/1.65 ($false),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1483, 126, 1459, 1477, 1448, 10, 1466])).
% 2.16/1.65 tff(1485,plain,((~hskp62) | hskp43 | hskp10), inference(lemma,lemma(discharge,[]))).
% 2.16/1.65 tff(1486,plain,
% 2.16/1.65 (~hskp62),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1485, 1291, 53])).
% 2.16/1.65 tff(1487,plain,
% 2.16/1.65 (hskp63 | hskp62),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[124, 1126])).
% 2.16/1.65 tff(1488,plain,
% 2.16/1.65 (hskp63),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1487, 1486])).
% 2.16/1.65 tff(1489,plain,
% 2.16/1.65 (((~hskp63) | (~c2_1(a1105))) <=> ((~hskp63) | (~c2_1(a1105)))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1490,plain,
% 2.16/1.65 (((~c2_1(a1105)) | (~hskp63)) <=> ((~hskp63) | (~c2_1(a1105)))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1491,axiom,((~c2_1(a1105)) | (~hskp63)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 2.16/1.65 tff(1492,plain,
% 2.16/1.65 ((~hskp63) | (~c2_1(a1105))),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1491, 1490])).
% 2.16/1.65 tff(1493,plain,
% 2.16/1.65 ((~hskp63) | (~c2_1(a1105))),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1492, 1489])).
% 2.16/1.65 tff(1494,plain,
% 2.16/1.65 (~c2_1(a1105)),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1493, 1488])).
% 2.16/1.65 tff(1495,plain,
% 2.16/1.65 (((~hskp63) | c3_1(a1105)) <=> ((~hskp63) | c3_1(a1105))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1496,axiom,((~hskp63) | c3_1(a1105)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 2.16/1.65 tff(1497,plain,
% 2.16/1.65 ((~hskp63) | c3_1(a1105)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1496, 1495])).
% 2.16/1.65 tff(1498,plain,
% 2.16/1.65 ((~hskp63) | c3_1(a1105)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1497, 1495])).
% 2.16/1.65 tff(1499,plain,
% 2.16/1.65 ((~hskp63) | c3_1(a1105)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1498, 1495])).
% 2.16/1.65 tff(1500,plain,
% 2.16/1.65 ((~hskp63) | c3_1(a1105)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1499, 1495])).
% 2.16/1.65 tff(1501,plain,
% 2.16/1.65 ((~hskp63) | c3_1(a1105)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1500, 1495])).
% 2.16/1.65 tff(1502,plain,
% 2.16/1.65 ((~hskp63) | c3_1(a1105)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1501, 1495])).
% 2.16/1.65 tff(1503,plain,
% 2.16/1.65 ((~hskp63) | c3_1(a1105)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1502, 1495])).
% 2.16/1.65 tff(1504,plain,
% 2.16/1.65 ((~hskp63) | c3_1(a1105)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1503, 1495])).
% 2.16/1.65 tff(1505,plain,
% 2.16/1.65 (c3_1(a1105)),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1504, 1488])).
% 2.16/1.65 tff(1506,plain,
% 2.16/1.65 (((~hskp63) | c1_1(a1105)) <=> ((~hskp63) | c1_1(a1105))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1507,axiom,((~hskp63) | c1_1(a1105)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 2.16/1.65 tff(1508,plain,
% 2.16/1.65 ((~hskp63) | c1_1(a1105)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1507, 1506])).
% 2.16/1.65 tff(1509,plain,
% 2.16/1.65 ((~hskp63) | c1_1(a1105)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1508, 1506])).
% 2.16/1.65 tff(1510,plain,
% 2.16/1.65 ((~hskp63) | c1_1(a1105)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1509, 1506])).
% 2.16/1.65 tff(1511,plain,
% 2.16/1.65 ((~hskp63) | c1_1(a1105)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1510, 1506])).
% 2.16/1.65 tff(1512,plain,
% 2.16/1.65 ((~hskp63) | c1_1(a1105)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1511, 1506])).
% 2.16/1.65 tff(1513,plain,
% 2.16/1.65 ((~hskp63) | c1_1(a1105)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1512, 1506])).
% 2.16/1.65 tff(1514,plain,
% 2.16/1.65 ((~hskp63) | c1_1(a1105)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1513, 1506])).
% 2.16/1.65 tff(1515,plain,
% 2.16/1.65 ((~hskp63) | c1_1(a1105)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1514, 1506])).
% 2.16/1.65 tff(1516,plain,
% 2.16/1.65 (c1_1(a1105)),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1515, 1488])).
% 2.16/1.65 tff(1517,plain,
% 2.16/1.65 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | c2_1(a1105) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | (~c1_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c2_1(a1105) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | (~c1_1(a1105)) | (~c3_1(a1105)))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1518,plain,
% 2.16/1.65 ((hskp59 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)) | c2_1(a1105) | (~c1_1(a1105)) | (~c3_1(a1105))) <=> (hskp59 | c2_1(a1105) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | (~c1_1(a1105)) | (~c3_1(a1105)))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1519,plain,
% 2.16/1.65 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)) | c2_1(a1105) | (~c1_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | c2_1(a1105) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | (~c1_1(a1105)) | (~c3_1(a1105))))),
% 2.16/1.65 inference(monotonicity,[status(thm)],[1518])).
% 2.16/1.65 tff(1520,plain,
% 2.16/1.65 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)) | c2_1(a1105) | (~c1_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c2_1(a1105) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | (~c1_1(a1105)) | (~c3_1(a1105)))),
% 2.16/1.65 inference(transitivity,[status(thm)],[1519, 1517])).
% 2.16/1.65 tff(1521,plain,
% 2.16/1.65 ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)) | c2_1(a1105) | (~c1_1(a1105)) | (~c3_1(a1105)))),
% 2.16/1.65 inference(quant_inst,[status(thm)],[])).
% 2.16/1.65 tff(1522,plain,
% 2.16/1.65 ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c2_1(a1105) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | (~c1_1(a1105)) | (~c3_1(a1105))),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1521, 1520])).
% 2.16/1.65 tff(1523,plain,
% 2.16/1.65 (hskp59),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1522, 126, 1516, 1505, 1494, 1419, 1413, 143, 1426])).
% 2.16/1.65 tff(1524,plain,
% 2.16/1.65 (~c3_1(a1095)),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[167, 1523])).
% 2.16/1.65 tff(1525,plain,
% 2.16/1.65 (~c0_1(a1095)),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[173, 1523])).
% 2.16/1.65 tff(1526,assumption,(~hskp35), introduced(assumption)).
% 2.16/1.65 tff(1527,plain,
% 2.16/1.65 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | c2_1(a1095))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | c2_1(a1095))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1528,plain,
% 2.16/1.65 ((hskp35 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095)) <=> (hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | c2_1(a1095))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1529,plain,
% 2.16/1.65 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | c2_1(a1095)))),
% 2.16/1.65 inference(monotonicity,[status(thm)],[1528])).
% 2.16/1.65 tff(1530,plain,
% 2.16/1.65 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | c2_1(a1095))),
% 2.16/1.65 inference(transitivity,[status(thm)],[1529, 1527])).
% 2.16/1.65 tff(1531,plain,
% 2.16/1.65 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095))),
% 2.16/1.65 inference(quant_inst,[status(thm)],[])).
% 2.16/1.65 tff(1532,plain,
% 2.16/1.65 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)) | c2_1(a1095)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1531, 1530])).
% 2.16/1.65 tff(1533,plain,
% 2.16/1.65 (c2_1(a1095)),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1532, 126, 1526, 1525, 1524, 1419, 1413, 1436, 1426])).
% 2.16/1.65 tff(1534,plain,
% 2.16/1.65 (c1_1(a1095)),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[191, 1523])).
% 2.16/1.65 tff(1535,plain,
% 2.16/1.65 ($false),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[198, 126, 1291, 53, 1534, 1525, 63, 1533])).
% 2.16/1.65 tff(1536,plain,(hskp43 | hskp10 | hskp35 | hskp20 | hskp19), inference(lemma,lemma(discharge,[]))).
% 2.16/1.65 tff(1537,plain,
% 2.16/1.65 (hskp43 | hskp10 | hskp20 | hskp19),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1536, 1240])).
% 2.16/1.65 tff(1538,plain,
% 2.16/1.65 (hskp43),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1537, 1290, 53, 1289])).
% 2.16/1.65 tff(1539,plain,
% 2.16/1.65 (c0_1(a1049)),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[231, 1538])).
% 2.16/1.65 tff(1540,plain,
% 2.16/1.65 (c2_1(a1049)),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[220, 1538])).
% 2.16/1.65 tff(1541,plain,
% 2.16/1.65 (c1_1(a1049)),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[209, 1538])).
% 2.16/1.65 tff(1542,assumption,(c3_1(a1049)), introduced(assumption)).
% 2.16/1.65 tff(1543,assumption,(c1_1(a1049)), introduced(assumption)).
% 2.16/1.65 tff(1544,assumption,(c2_1(a1049)), introduced(assumption)).
% 2.16/1.65 tff(1545,assumption,(c0_1(a1049)), introduced(assumption)).
% 2.16/1.65 tff(1546,plain,
% 2.16/1.65 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1049)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1049)))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1547,plain,
% 2.16/1.65 (((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049))) <=> ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1049)))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1548,plain,
% 2.16/1.65 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1049))))),
% 2.16/1.65 inference(monotonicity,[status(thm)],[1547])).
% 2.16/1.65 tff(1549,plain,
% 2.16/1.65 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1049)))),
% 2.16/1.65 inference(transitivity,[status(thm)],[1548, 1546])).
% 2.16/1.65 tff(1550,plain,
% 2.16/1.65 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)))),
% 2.16/1.65 inference(quant_inst,[status(thm)],[])).
% 2.16/1.65 tff(1551,plain,
% 2.16/1.65 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1049))),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1550, 1549])).
% 2.16/1.65 tff(1552,plain,
% 2.16/1.65 ($false),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1551, 126, 1545, 1544, 1543, 10, 1542])).
% 2.16/1.65 tff(1553,plain,((~c3_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049))), inference(lemma,lemma(discharge,[]))).
% 2.16/1.65 tff(1554,plain,
% 2.16/1.65 (~c3_1(a1049)),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1553, 1541, 1540, 1539])).
% 2.16/1.65 tff(1555,plain,
% 2.16/1.65 (^[U: $i] : refl((hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 2.16/1.65 inference(bind,[status(th)],[])).
% 2.16/1.65 tff(1556,plain,
% 2.16/1.65 (![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.16/1.65 inference(quant_intro,[status(thm)],[1555])).
% 2.16/1.65 tff(1557,plain,
% 2.16/1.65 (![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1558,plain,
% 2.16/1.65 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c1_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp12) <=> ((hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp12))), rewrite(((hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp12) <=> (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp12) <=> (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 2.16/1.65 inference(bind,[status(th)],[])).
% 2.16/1.65 tff(1559,plain,
% 2.16/1.65 (![U: $i] : ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp12) <=> ![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.16/1.65 inference(quant_intro,[status(thm)],[1558])).
% 2.16/1.65 tff(1560,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause278')).
% 2.16/1.65 tff(1561,plain,
% 2.16/1.65 (![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1560, 1559])).
% 2.16/1.65 tff(1562,plain,
% 2.16/1.65 (![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1561, 1557])).
% 2.16/1.65 tff(1563,plain,(
% 2.16/1.65 ![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.16/1.65 inference(skolemize,[status(sab)],[1562])).
% 2.16/1.65 tff(1564,plain,
% 2.16/1.65 (![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1563, 1556])).
% 2.16/1.65 tff(1565,assumption,(hskp12), introduced(assumption)).
% 2.16/1.65 tff(1566,plain,
% 2.16/1.65 (((~hskp12) | (~c3_1(a1043))) <=> ((~hskp12) | (~c3_1(a1043)))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1567,plain,
% 2.16/1.65 (((~c3_1(a1043)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a1043)))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1568,axiom,((~c3_1(a1043)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause238')).
% 2.16/1.65 tff(1569,plain,
% 2.16/1.65 ((~hskp12) | (~c3_1(a1043))),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1568, 1567])).
% 2.16/1.65 tff(1570,plain,
% 2.16/1.65 ((~hskp12) | (~c3_1(a1043))),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1569, 1566])).
% 2.16/1.65 tff(1571,plain,
% 2.16/1.65 (~c3_1(a1043)),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1570, 1565])).
% 2.16/1.65 tff(1572,plain,
% 2.16/1.65 (((~hskp12) | (~c1_1(a1043))) <=> ((~hskp12) | (~c1_1(a1043)))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1573,plain,
% 2.16/1.65 (((~c1_1(a1043)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a1043)))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1574,axiom,((~c1_1(a1043)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause237')).
% 2.16/1.65 tff(1575,plain,
% 2.16/1.65 ((~hskp12) | (~c1_1(a1043))),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1574, 1573])).
% 2.16/1.65 tff(1576,plain,
% 2.16/1.65 ((~hskp12) | (~c1_1(a1043))),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1575, 1572])).
% 2.16/1.65 tff(1577,plain,
% 2.16/1.65 (~c1_1(a1043)),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1576, 1565])).
% 2.16/1.65 tff(1578,plain,
% 2.16/1.65 (((~hskp12) | c0_1(a1043)) <=> ((~hskp12) | c0_1(a1043))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1579,axiom,((~hskp12) | c0_1(a1043)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 2.16/1.65 tff(1580,plain,
% 2.16/1.65 ((~hskp12) | c0_1(a1043)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1579, 1578])).
% 2.16/1.65 tff(1581,plain,
% 2.16/1.65 ((~hskp12) | c0_1(a1043)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1580, 1578])).
% 2.16/1.65 tff(1582,plain,
% 2.16/1.65 ((~hskp12) | c0_1(a1043)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1581, 1578])).
% 2.16/1.65 tff(1583,plain,
% 2.16/1.65 ((~hskp12) | c0_1(a1043)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1582, 1578])).
% 2.16/1.65 tff(1584,plain,
% 2.16/1.65 ((~hskp12) | c0_1(a1043)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1583, 1578])).
% 2.16/1.65 tff(1585,plain,
% 2.16/1.65 ((~hskp12) | c0_1(a1043)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1584, 1578])).
% 2.16/1.65 tff(1586,plain,
% 2.16/1.65 ((~hskp12) | c0_1(a1043)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1585, 1578])).
% 2.16/1.65 tff(1587,plain,
% 2.16/1.65 ((~hskp12) | c0_1(a1043)),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1586, 1578])).
% 2.16/1.65 tff(1588,plain,
% 2.16/1.65 (c0_1(a1043)),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1587, 1565])).
% 2.16/1.65 tff(1589,plain,
% 2.16/1.65 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c0_1(a1043)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c0_1(a1043)))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1590,plain,
% 2.16/1.65 ((hskp20 | hskp19 | (~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043))) <=> (hskp20 | hskp19 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c0_1(a1043)))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1591,plain,
% 2.16/1.65 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c0_1(a1043))))),
% 2.16/1.65 inference(monotonicity,[status(thm)],[1590])).
% 2.16/1.65 tff(1592,plain,
% 2.16/1.65 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c0_1(a1043)))),
% 2.16/1.65 inference(transitivity,[status(thm)],[1591, 1589])).
% 2.16/1.65 tff(1593,plain,
% 2.16/1.65 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)))),
% 2.16/1.65 inference(quant_inst,[status(thm)],[])).
% 2.16/1.65 tff(1594,plain,
% 2.16/1.65 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp19 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c0_1(a1043))),
% 2.16/1.65 inference(modus_ponens,[status(thm)],[1593, 1592])).
% 2.16/1.65 tff(1595,plain,
% 2.16/1.65 ($false),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1594, 126, 1289, 1290, 1588, 1577, 1571, 685])).
% 2.16/1.65 tff(1596,plain,((~hskp12) | hskp20 | hskp19), inference(lemma,lemma(discharge,[]))).
% 2.16/1.65 tff(1597,plain,
% 2.16/1.65 (~hskp12),
% 2.16/1.65 inference(unit_resolution,[status(thm)],[1596, 1290, 1289])).
% 2.16/1.65 tff(1598,plain,
% 2.16/1.65 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | (~c2_1(a1049)) | (~c1_1(a1049)) | c3_1(a1049))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp12 | hskp7 | (~ndr1_0) | (~c2_1(a1049)) | (~c1_1(a1049)) | c3_1(a1049))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1599,plain,
% 2.16/1.65 ((hskp12 | hskp7 | (~ndr1_0) | c3_1(a1049) | (~c1_1(a1049)) | (~c2_1(a1049))) <=> (hskp12 | hskp7 | (~ndr1_0) | (~c2_1(a1049)) | (~c1_1(a1049)) | c3_1(a1049))),
% 2.16/1.65 inference(rewrite,[status(thm)],[])).
% 2.16/1.65 tff(1600,plain,
% 2.16/1.65 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c3_1(a1049) | (~c1_1(a1049)) | (~c2_1(a1049)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | (~c2_1(a1049)) | (~c1_1(a1049)) | c3_1(a1049)))),
% 2.16/1.65 inference(monotonicity,[status(thm)],[1599])).
% 2.16/1.65 tff(1601,plain,
% 2.16/1.65 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c3_1(a1049) | (~c1_1(a1049)) | (~c2_1(a1049)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp12 | hskp7 | (~ndr1_0) | (~c2_1(a1049)) | (~c1_1(a1049)) | c3_1(a1049))),
% 2.16/1.66 inference(transitivity,[status(thm)],[1600, 1598])).
% 2.16/1.66 tff(1602,plain,
% 2.16/1.66 ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c3_1(a1049) | (~c1_1(a1049)) | (~c2_1(a1049)))),
% 2.16/1.66 inference(quant_inst,[status(thm)],[])).
% 2.16/1.66 tff(1603,plain,
% 2.16/1.66 ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp12 | hskp7 | (~ndr1_0) | (~c2_1(a1049)) | (~c1_1(a1049)) | c3_1(a1049)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1602, 1601])).
% 2.16/1.66 tff(1604,plain,
% 2.16/1.66 (hskp7),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1603, 126, 1597, 1540, 1541, 1564, 1554])).
% 2.16/1.66 tff(1605,plain,
% 2.16/1.66 (((~hskp7) | (~c2_1(a1035))) <=> ((~hskp7) | (~c2_1(a1035)))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1606,plain,
% 2.16/1.66 (((~c2_1(a1035)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a1035)))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1607,axiom,((~c2_1(a1035)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause247')).
% 2.16/1.66 tff(1608,plain,
% 2.16/1.66 ((~hskp7) | (~c2_1(a1035))),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1607, 1606])).
% 2.16/1.66 tff(1609,plain,
% 2.16/1.66 ((~hskp7) | (~c2_1(a1035))),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1608, 1605])).
% 2.16/1.66 tff(1610,plain,
% 2.16/1.66 (~c2_1(a1035)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1609, 1604])).
% 2.16/1.66 tff(1611,plain,
% 2.16/1.66 (((~hskp7) | c0_1(a1035)) <=> ((~hskp7) | c0_1(a1035))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1612,axiom,((~hskp7) | c0_1(a1035)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 2.16/1.66 tff(1613,plain,
% 2.16/1.66 ((~hskp7) | c0_1(a1035)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1612, 1611])).
% 2.16/1.66 tff(1614,plain,
% 2.16/1.66 ((~hskp7) | c0_1(a1035)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1613, 1611])).
% 2.16/1.66 tff(1615,plain,
% 2.16/1.66 ((~hskp7) | c0_1(a1035)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1614, 1611])).
% 2.16/1.66 tff(1616,plain,
% 2.16/1.66 ((~hskp7) | c0_1(a1035)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1615, 1611])).
% 2.16/1.66 tff(1617,plain,
% 2.16/1.66 ((~hskp7) | c0_1(a1035)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1616, 1611])).
% 2.16/1.66 tff(1618,plain,
% 2.16/1.66 ((~hskp7) | c0_1(a1035)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1617, 1611])).
% 2.16/1.66 tff(1619,plain,
% 2.16/1.66 ((~hskp7) | c0_1(a1035)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1618, 1611])).
% 2.16/1.66 tff(1620,plain,
% 2.16/1.66 ((~hskp7) | c0_1(a1035)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1619, 1611])).
% 2.16/1.66 tff(1621,plain,
% 2.16/1.66 (c0_1(a1035)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1620, 1604])).
% 2.16/1.66 tff(1622,plain,
% 2.16/1.66 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | c2_1(a1035) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1035)) | (~c0_1(a1035)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1035) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1035)) | (~c0_1(a1035)))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1623,plain,
% 2.16/1.66 ((hskp12 | (~ndr1_0) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049))) <=> (hskp12 | c2_1(a1035) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1035)) | (~c0_1(a1035)))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1624,plain,
% 2.16/1.66 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | c2_1(a1035) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1035)) | (~c0_1(a1035))))),
% 2.16/1.66 inference(monotonicity,[status(thm)],[1623])).
% 2.16/1.66 tff(1625,plain,
% 2.16/1.66 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1035) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1035)) | (~c0_1(a1035)))),
% 2.16/1.66 inference(transitivity,[status(thm)],[1624, 1622])).
% 2.16/1.66 tff(1626,plain,
% 2.16/1.66 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)))),
% 2.16/1.66 inference(quant_inst,[status(thm)],[])).
% 2.16/1.66 tff(1627,plain,
% 2.16/1.66 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1035) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1035)) | (~c0_1(a1035))),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1626, 1625])).
% 2.16/1.66 tff(1628,plain,
% 2.16/1.66 (~c3_1(a1035)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1627, 126, 1597, 1539, 1540, 1541, 1621, 1610, 1288])).
% 2.16/1.66 tff(1629,assumption,(c3_1(a1059)), introduced(assumption)).
% 2.16/1.66 tff(1630,plain,
% 2.16/1.66 (hskp43),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1536, 1526, 53, 1289, 1290])).
% 2.16/1.66 tff(1631,plain,
% 2.16/1.66 (c1_1(a1049)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[209, 1630])).
% 2.16/1.66 tff(1632,plain,
% 2.16/1.66 (c2_1(a1049)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[220, 1630])).
% 2.16/1.66 tff(1633,plain,
% 2.16/1.66 (c0_1(a1049)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[231, 1630])).
% 2.16/1.66 tff(1634,plain,
% 2.16/1.66 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1635,plain,
% 2.16/1.66 (((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059))) <=> ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1636,plain,
% 2.16/1.66 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059))))),
% 2.16/1.66 inference(monotonicity,[status(thm)],[1635])).
% 2.16/1.66 tff(1637,plain,
% 2.16/1.66 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059)))),
% 2.16/1.66 inference(transitivity,[status(thm)],[1636, 1634])).
% 2.16/1.66 tff(1638,plain,
% 2.16/1.66 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c3_1(a1059)) | (~c0_1(a1059)) | (~c2_1(a1059)))),
% 2.16/1.66 inference(quant_inst,[status(thm)],[])).
% 2.16/1.66 tff(1639,plain,
% 2.16/1.66 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1059))),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1638, 1637])).
% 2.16/1.66 tff(1640,plain,
% 2.16/1.66 (~c0_1(a1059)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1639, 126, 1633, 1632, 1631, 1629, 393, 10])).
% 2.16/1.66 tff(1641,plain,
% 2.16/1.66 (~c3_1(a1049)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1553, 1631, 1632, 1633])).
% 2.16/1.66 tff(1642,plain,
% 2.16/1.66 (hskp7),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1603, 126, 1597, 1632, 1631, 1564, 1641])).
% 2.16/1.66 tff(1643,plain,
% 2.16/1.66 (~c2_1(a1035)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1609, 1642])).
% 2.16/1.66 tff(1644,plain,
% 2.16/1.66 (((~hskp7) | c1_1(a1035)) <=> ((~hskp7) | c1_1(a1035))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1645,axiom,((~hskp7) | c1_1(a1035)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 2.16/1.66 tff(1646,plain,
% 2.16/1.66 ((~hskp7) | c1_1(a1035)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1645, 1644])).
% 2.16/1.66 tff(1647,plain,
% 2.16/1.66 ((~hskp7) | c1_1(a1035)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1646, 1644])).
% 2.16/1.66 tff(1648,plain,
% 2.16/1.66 ((~hskp7) | c1_1(a1035)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1647, 1644])).
% 2.16/1.66 tff(1649,plain,
% 2.16/1.66 ((~hskp7) | c1_1(a1035)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1648, 1644])).
% 2.16/1.66 tff(1650,plain,
% 2.16/1.66 ((~hskp7) | c1_1(a1035)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1649, 1644])).
% 2.16/1.66 tff(1651,plain,
% 2.16/1.66 ((~hskp7) | c1_1(a1035)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1650, 1644])).
% 2.16/1.66 tff(1652,plain,
% 2.16/1.66 ((~hskp7) | c1_1(a1035)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1651, 1644])).
% 2.16/1.66 tff(1653,plain,
% 2.16/1.66 ((~hskp7) | c1_1(a1035)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1652, 1644])).
% 2.16/1.66 tff(1654,plain,
% 2.16/1.66 (c1_1(a1035)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1653, 1642])).
% 2.16/1.66 tff(1655,plain,
% 2.16/1.66 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1656,plain,
% 2.16/1.66 ((hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059))) <=> (hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1657,plain,
% 2.16/1.66 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059)))),
% 2.16/1.66 inference(monotonicity,[status(thm)],[1656])).
% 2.16/1.66 tff(1658,plain,
% 2.16/1.66 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))),
% 2.16/1.66 inference(transitivity,[status(thm)],[1657, 1655])).
% 2.16/1.66 tff(1659,plain,
% 2.16/1.66 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)))),
% 2.16/1.66 inference(quant_inst,[status(thm)],[])).
% 2.16/1.66 tff(1660,plain,
% 2.16/1.66 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1659, 1658])).
% 2.16/1.66 tff(1661,plain,
% 2.16/1.66 (c3_1(a1035)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1660, 126, 1526, 1629, 393, 1654, 1643, 1001, 1640])).
% 2.16/1.66 tff(1662,plain,
% 2.16/1.66 (c0_1(a1035)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1620, 1642])).
% 2.16/1.66 tff(1663,plain,
% 2.16/1.66 ($false),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1627, 126, 1597, 1633, 1632, 1631, 1662, 1643, 1288, 1661])).
% 2.16/1.66 tff(1664,plain,(hskp35 | (~c3_1(a1059)) | (~c2_1(a1059)) | hskp10 | hskp20 | hskp19), inference(lemma,lemma(discharge,[]))).
% 2.16/1.66 tff(1665,plain,
% 2.16/1.66 ((~c3_1(a1059)) | (~c2_1(a1059)) | hskp10 | hskp20 | hskp19),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1664, 1240])).
% 2.16/1.66 tff(1666,plain,
% 2.16/1.66 ($false),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1665, 390, 413, 53, 1289, 1290])).
% 2.16/1.66 tff(1667,plain,((~hskp15) | hskp10 | hskp20 | hskp19), inference(lemma,lemma(discharge,[]))).
% 2.16/1.66 tff(1668,plain,
% 2.16/1.66 (~hskp15),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1667, 1290, 1289, 53])).
% 2.16/1.66 tff(1669,assumption,(hskp14), introduced(assumption)).
% 2.16/1.66 tff(1670,plain,
% 2.16/1.66 (~c0_1(a1055)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1418, 1669])).
% 2.16/1.66 tff(1671,plain,
% 2.16/1.66 (~c2_1(a1055)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1412, 1669])).
% 2.16/1.66 tff(1672,assumption,(~c0_1(a1055)), introduced(assumption)).
% 2.16/1.66 tff(1673,assumption,(~c2_1(a1055)), introduced(assumption)).
% 2.16/1.66 tff(1674,plain,
% 2.16/1.66 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1675,plain,
% 2.16/1.66 ((hskp33 | hskp15 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055))) <=> (hskp33 | hskp15 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1676,plain,
% 2.16/1.66 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055))))),
% 2.16/1.66 inference(monotonicity,[status(thm)],[1675])).
% 2.16/1.66 tff(1677,plain,
% 2.16/1.66 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055)))),
% 2.16/1.66 inference(transitivity,[status(thm)],[1676, 1674])).
% 2.16/1.66 tff(1678,plain,
% 2.16/1.66 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1055) | c2_1(a1055) | (~c3_1(a1055)))),
% 2.16/1.66 inference(quant_inst,[status(thm)],[])).
% 2.16/1.66 tff(1679,plain,
% 2.16/1.66 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1055) | c2_1(a1055) | (~ndr1_0) | (~c3_1(a1055))),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1678, 1677])).
% 2.16/1.66 tff(1680,plain,
% 2.16/1.66 (c0_1(a1055) | (~c3_1(a1055))),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1679, 126, 21, 42, 1673, 52])).
% 2.16/1.66 tff(1681,plain,
% 2.16/1.66 (~c3_1(a1055)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1680, 1672])).
% 2.16/1.66 tff(1682,plain,
% 2.16/1.66 (c0_1(a1055) | c3_1(a1055)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1425, 126, 53, 1673, 73])).
% 2.16/1.66 tff(1683,plain,
% 2.16/1.66 ($false),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1682, 1681, 1672])).
% 2.16/1.66 tff(1684,plain,(c0_1(a1055) | hskp10 | c2_1(a1055) | hskp33 | hskp15), inference(lemma,lemma(discharge,[]))).
% 2.16/1.66 tff(1685,plain,
% 2.16/1.66 ($false),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1684, 1671, 1670, 53, 21, 42])).
% 2.16/1.66 tff(1686,plain,((~hskp14) | hskp10 | hskp33 | hskp15), inference(lemma,lemma(discharge,[]))).
% 2.16/1.66 tff(1687,plain,
% 2.16/1.66 (~hskp14),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1686, 42, 21, 53])).
% 2.16/1.66 tff(1688,plain,
% 2.16/1.66 (~hskp19),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[674, 42, 21, 53])).
% 2.16/1.66 tff(1689,plain,
% 2.16/1.66 (hskp38),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1406, 1289, 1688, 1687])).
% 2.16/1.66 tff(1690,plain,
% 2.16/1.66 (hskp43),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1337, 1689, 53])).
% 2.16/1.66 tff(1691,plain,
% 2.16/1.66 (c1_1(a1049)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[209, 1690])).
% 2.16/1.66 tff(1692,plain,
% 2.16/1.66 (c2_1(a1049)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[220, 1690])).
% 2.16/1.66 tff(1693,plain,
% 2.16/1.66 (c0_1(a1049)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[231, 1690])).
% 2.16/1.66 tff(1694,plain,
% 2.16/1.66 (~hskp12),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1596, 1289, 1688])).
% 2.16/1.66 tff(1695,plain,
% 2.16/1.66 (c2_1(a1040)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1302, 1689])).
% 2.16/1.66 tff(1696,plain,
% 2.16/1.66 (c3_1(a1040)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1313, 1689])).
% 2.16/1.66 tff(1697,plain,
% 2.16/1.66 (c1_1(a1040)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1324, 1689])).
% 2.16/1.66 tff(1698,plain,
% 2.16/1.66 (~c0_1(a1040)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1331, 126, 1697, 1696, 1695, 10])).
% 2.16/1.66 tff(1699,plain,
% 2.16/1.66 (((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)))) <=> ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1700,plain,
% 2.16/1.66 ((hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c3_1(a1040)) | (~c2_1(a1040))) <=> (hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1701,plain,
% 2.16/1.66 (((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c3_1(a1040)) | (~c2_1(a1040)))) <=> ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040))))),
% 2.16/1.66 inference(monotonicity,[status(thm)],[1700])).
% 2.16/1.66 tff(1702,plain,
% 2.16/1.66 (((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c3_1(a1040)) | (~c2_1(a1040)))) <=> ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040)))),
% 2.16/1.66 inference(transitivity,[status(thm)],[1701, 1699])).
% 2.16/1.66 tff(1703,plain,
% 2.16/1.66 ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | (hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c3_1(a1040)) | (~c1_1(a1040)) | (~c3_1(a1040)) | (~c2_1(a1040)))),
% 2.16/1.66 inference(quant_inst,[status(thm)],[])).
% 2.16/1.66 tff(1704,plain,
% 2.16/1.66 ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(V)))) | hskp36 | (~ndr1_0) | c0_1(a1040) | (~c1_1(a1040)) | (~c2_1(a1040)) | (~c3_1(a1040))),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1703, 1702])).
% 2.16/1.66 tff(1705,plain,
% 2.16/1.66 (hskp36),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1704, 126, 1697, 1696, 1695, 768, 1698])).
% 2.16/1.66 tff(1706,plain,
% 2.16/1.66 (~c0_1(a1034)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[780, 1705])).
% 2.16/1.66 tff(1707,plain,
% 2.16/1.66 (c3_1(a1034)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[826, 1705])).
% 2.16/1.66 tff(1708,plain,
% 2.16/1.66 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1709,plain,
% 2.16/1.66 ((hskp33 | hskp15 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034))) <=> (hskp33 | hskp15 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1710,plain,
% 2.16/1.66 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034)))),
% 2.16/1.66 inference(monotonicity,[status(thm)],[1709])).
% 2.16/1.66 tff(1711,plain,
% 2.16/1.66 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034))),
% 2.16/1.66 inference(transitivity,[status(thm)],[1710, 1708])).
% 2.16/1.66 tff(1712,plain,
% 2.16/1.66 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)))),
% 2.16/1.66 inference(quant_inst,[status(thm)],[])).
% 2.16/1.66 tff(1713,plain,
% 2.16/1.66 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034)),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1712, 1711])).
% 2.16/1.66 tff(1714,plain,
% 2.16/1.66 (c2_1(a1034)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1713, 126, 21, 42, 1707, 1706, 52])).
% 2.16/1.66 tff(1715,assumption,(hskp7), introduced(assumption)).
% 2.16/1.66 tff(1716,plain,
% 2.16/1.66 (~c2_1(a1035)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1609, 1715])).
% 2.16/1.66 tff(1717,plain,
% 2.16/1.66 (c0_1(a1035)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1620, 1715])).
% 2.16/1.66 tff(1718,assumption,(~hskp12), introduced(assumption)).
% 2.16/1.66 tff(1719,plain,
% 2.16/1.66 (~c3_1(a1035)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1627, 126, 1718, 1545, 1544, 1543, 1717, 1716, 1288])).
% 2.16/1.66 tff(1720,assumption,(c2_1(a1034)), introduced(assumption)).
% 2.16/1.66 tff(1721,assumption,(~c0_1(a1034)), introduced(assumption)).
% 2.16/1.66 tff(1722,plain,
% 2.16/1.66 (c1_1(a1035)),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1653, 1715])).
% 2.16/1.66 tff(1723,assumption,(c3_1(a1034)), introduced(assumption)).
% 2.16/1.66 tff(1724,plain,
% 2.16/1.66 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1725,plain,
% 2.16/1.66 ((hskp12 | (~ndr1_0) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049))) <=> (hskp12 | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1726,plain,
% 2.16/1.66 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033))))),
% 2.16/1.66 inference(monotonicity,[status(thm)],[1725])).
% 2.16/1.66 tff(1727,plain,
% 2.16/1.66 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033)))),
% 2.16/1.66 inference(transitivity,[status(thm)],[1726, 1724])).
% 2.16/1.66 tff(1728,plain,
% 2.16/1.66 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1033) | (~c3_1(a1033)) | (~c0_1(a1033)) | (~c1_1(a1049)) | (~c0_1(a1049)) | (~c2_1(a1049)))),
% 2.16/1.66 inference(quant_inst,[status(thm)],[])).
% 2.16/1.66 tff(1729,plain,
% 2.16/1.66 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049)) | (~c3_1(a1033)) | c2_1(a1033) | (~c0_1(a1033))),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1728, 1727])).
% 2.16/1.66 tff(1730,plain,
% 2.16/1.66 ($false),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1729, 126, 1718, 1545, 1544, 1543, 1207, 1205, 1288, 1208])).
% 2.16/1.66 tff(1731,plain,((~hskp35) | hskp12 | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049))), inference(lemma,lemma(discharge,[]))).
% 2.16/1.66 tff(1732,plain,
% 2.16/1.66 (~hskp35),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1731, 1545, 1718, 1544, 1543])).
% 2.16/1.66 tff(1733,plain,
% 2.16/1.66 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c0_1(a1034) | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1034)) | (~c2_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c0_1(a1034) | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1034)) | (~c2_1(a1034)))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1734,plain,
% 2.16/1.66 ((hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034))) <=> (hskp35 | c0_1(a1034) | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1034)) | (~c2_1(a1034)))),
% 2.16/1.66 inference(rewrite,[status(thm)],[])).
% 2.16/1.66 tff(1735,plain,
% 2.16/1.66 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c0_1(a1034) | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1034)) | (~c2_1(a1034))))),
% 2.16/1.66 inference(monotonicity,[status(thm)],[1734])).
% 2.16/1.66 tff(1736,plain,
% 2.16/1.66 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c0_1(a1034) | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1034)) | (~c2_1(a1034)))),
% 2.16/1.66 inference(transitivity,[status(thm)],[1735, 1733])).
% 2.16/1.66 tff(1737,plain,
% 2.16/1.66 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)))),
% 2.16/1.66 inference(quant_inst,[status(thm)],[])).
% 2.16/1.66 tff(1738,plain,
% 2.16/1.66 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c0_1(a1034) | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1034)) | (~c2_1(a1034))),
% 2.16/1.66 inference(modus_ponens,[status(thm)],[1737, 1736])).
% 2.16/1.66 tff(1739,plain,
% 2.16/1.66 ($false),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1738, 126, 1732, 1723, 1722, 1721, 1716, 1001, 1720, 1719])).
% 2.16/1.66 tff(1740,plain,((~hskp7) | (~c3_1(a1034)) | c0_1(a1034) | (~c2_1(a1034)) | hskp12 | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049))), inference(lemma,lemma(discharge,[]))).
% 2.16/1.66 tff(1741,plain,
% 2.16/1.66 (~hskp7),
% 2.16/1.66 inference(unit_resolution,[status(thm)],[1740, 1707, 1706, 1714, 1694, 1693, 1692, 1691])).
% 2.16/1.67 tff(1742,plain,
% 2.16/1.67 (hskp7 | c3_1(a1049)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1603, 126, 1694, 1692, 1691, 1564])).
% 2.16/1.67 tff(1743,plain,
% 2.16/1.67 (c3_1(a1049)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1742, 1741])).
% 2.16/1.67 tff(1744,plain,
% 2.16/1.67 ($false),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1551, 126, 1693, 1692, 1691, 10, 1743])).
% 2.16/1.67 tff(1745,plain,(hskp20 | hskp33 | hskp15 | hskp10), inference(lemma,lemma(discharge,[]))).
% 2.16/1.67 tff(1746,plain,
% 2.16/1.67 (hskp33),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1745, 1668, 1289, 53])).
% 2.16/1.67 tff(1747,plain,
% 2.16/1.67 (c2_1(a1031)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[298, 1746])).
% 2.16/1.67 tff(1748,plain,
% 2.16/1.67 (c3_1(a1031)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[321, 1746])).
% 2.16/1.67 tff(1749,plain,
% 2.16/1.67 (~c0_1(a1031)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[860, 126, 1539, 1540, 1541, 1748, 1747, 10])).
% 2.16/1.67 tff(1750,plain,
% 2.16/1.67 (c1_1(a1035)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1653, 1604])).
% 2.16/1.67 tff(1751,plain,
% 2.16/1.67 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031))),
% 2.16/1.67 inference(rewrite,[status(thm)],[])).
% 2.16/1.67 tff(1752,plain,
% 2.16/1.67 ((hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031))) <=> (hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031))),
% 2.16/1.67 inference(rewrite,[status(thm)],[])).
% 2.16/1.67 tff(1753,plain,
% 2.16/1.67 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031)))),
% 2.16/1.67 inference(monotonicity,[status(thm)],[1752])).
% 2.16/1.67 tff(1754,plain,
% 2.16/1.67 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031))),
% 2.16/1.67 inference(transitivity,[status(thm)],[1753, 1751])).
% 2.16/1.67 tff(1755,plain,
% 2.16/1.67 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1035) | c3_1(a1035) | (~c1_1(a1035)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 2.16/1.67 inference(quant_inst,[status(thm)],[])).
% 2.16/1.67 tff(1756,plain,
% 2.16/1.67 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1035) | (~ndr1_0) | c3_1(a1035) | (~c1_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031)),
% 2.16/1.67 inference(modus_ponens,[status(thm)],[1755, 1754])).
% 2.16/1.67 tff(1757,plain,
% 2.16/1.67 ($false),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1756, 126, 1240, 1748, 1747, 1750, 1610, 1001, 1749, 1628])).
% 2.16/1.67 tff(1758,plain,(hskp19 | hskp20 | hskp10), inference(lemma,lemma(discharge,[]))).
% 2.16/1.67 tff(1759,plain,
% 2.16/1.67 (hskp20),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1758, 1278, 53])).
% 2.16/1.67 tff(1760,plain,
% 2.16/1.67 (~c2_1(a1080)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[699, 1759])).
% 2.16/1.67 tff(1761,plain,
% 2.16/1.67 (~c0_1(a1080)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[705, 1759])).
% 2.16/1.67 tff(1762,plain,
% 2.16/1.67 (c3_1(a1080)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[743, 126, 53, 1761, 1760, 73])).
% 2.16/1.67 tff(1763,plain,
% 2.16/1.67 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | c2_1(a1105) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c2_1(a1105) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1105)) | (~c3_1(a1105)))),
% 2.16/1.67 inference(rewrite,[status(thm)],[])).
% 2.16/1.67 tff(1764,plain,
% 2.16/1.67 ((hskp59 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | (~c3_1(a1080)) | c2_1(a1105) | (~c1_1(a1105)) | (~c3_1(a1105))) <=> (hskp59 | c2_1(a1105) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1105)) | (~c3_1(a1105)))),
% 2.16/1.67 inference(rewrite,[status(thm)],[])).
% 2.16/1.67 tff(1765,plain,
% 2.16/1.67 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | (~c3_1(a1080)) | c2_1(a1105) | (~c1_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | c2_1(a1105) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1105)) | (~c3_1(a1105))))),
% 2.16/1.67 inference(monotonicity,[status(thm)],[1764])).
% 2.16/1.67 tff(1766,plain,
% 2.16/1.67 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | (~c3_1(a1080)) | c2_1(a1105) | (~c1_1(a1105)) | (~c3_1(a1105)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c2_1(a1105) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1105)) | (~c3_1(a1105)))),
% 2.16/1.67 inference(transitivity,[status(thm)],[1765, 1763])).
% 2.16/1.67 tff(1767,plain,
% 2.16/1.67 ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1080) | c2_1(a1080) | (~c3_1(a1080)) | c2_1(a1105) | (~c1_1(a1105)) | (~c3_1(a1105)))),
% 2.16/1.67 inference(quant_inst,[status(thm)],[])).
% 2.16/1.67 tff(1768,plain,
% 2.16/1.67 ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c2_1(a1105) | c0_1(a1080) | c2_1(a1080) | (~ndr1_0) | (~c3_1(a1080)) | (~c1_1(a1105)) | (~c3_1(a1105))),
% 2.16/1.67 inference(modus_ponens,[status(thm)],[1767, 1766])).
% 2.16/1.67 tff(1769,plain,
% 2.16/1.67 (hskp59),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1768, 126, 1516, 1505, 1494, 1761, 1760, 143, 1762])).
% 2.16/1.67 tff(1770,plain,
% 2.16/1.67 (~c0_1(a1095)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[173, 1769])).
% 2.16/1.67 tff(1771,plain,
% 2.16/1.67 (c1_1(a1095)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[191, 1769])).
% 2.16/1.67 tff(1772,plain,
% 2.16/1.67 (~c2_1(a1095)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[198, 126, 1291, 53, 1771, 1770, 63])).
% 2.16/1.67 tff(1773,plain,
% 2.16/1.67 (~c3_1(a1095)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[167, 1769])).
% 2.16/1.67 tff(1774,plain,
% 2.16/1.67 ($false),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[180, 126, 53, 1770, 1773, 73, 1772])).
% 2.16/1.67 tff(1775,plain,(hskp43 | hskp10), inference(lemma,lemma(discharge,[]))).
% 2.16/1.67 tff(1776,plain,
% 2.16/1.67 (hskp43),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1775, 53])).
% 2.16/1.67 tff(1777,plain,
% 2.16/1.67 (c1_1(a1049)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[209, 1776])).
% 2.16/1.67 tff(1778,plain,
% 2.16/1.67 (c2_1(a1049)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[220, 1776])).
% 2.16/1.67 tff(1779,plain,
% 2.16/1.67 (c0_1(a1049)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[231, 1776])).
% 2.16/1.67 tff(1780,plain,
% 2.16/1.67 (~c1_1(a1080)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[727, 1759])).
% 2.16/1.67 tff(1781,plain,
% 2.16/1.67 (~c0_1(a1031)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[860, 126, 1545, 1544, 1543, 322, 299, 10])).
% 2.16/1.67 tff(1782,plain,
% 2.16/1.67 (~c3_1(a1049)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1553, 1543, 1544, 1545])).
% 2.16/1.67 tff(1783,plain,
% 2.16/1.67 (hskp12 | hskp7),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1603, 126, 1544, 1543, 1564, 1782])).
% 2.16/1.67 tff(1784,plain,
% 2.16/1.67 (hskp7),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1783, 1718])).
% 2.16/1.67 tff(1785,plain,
% 2.16/1.67 (~c2_1(a1035)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1609, 1784])).
% 2.16/1.67 tff(1786,plain,
% 2.16/1.67 (c0_1(a1035)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1620, 1784])).
% 2.16/1.67 tff(1787,plain,
% 2.16/1.67 (~c3_1(a1035)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1627, 126, 1718, 1545, 1544, 1543, 1786, 1785, 1288])).
% 2.16/1.67 tff(1788,plain,
% 2.16/1.67 (~c0_1(a1031)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[860, 126, 1545, 1544, 1543, 863, 302, 10])).
% 2.16/1.67 tff(1789,plain,
% 2.16/1.67 (c1_1(a1035)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1653, 1784])).
% 2.16/1.67 tff(1790,plain,
% 2.16/1.67 ($false),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1756, 126, 1240, 863, 302, 1789, 1785, 1001, 1788, 1787])).
% 2.16/1.67 tff(1791,plain,(hskp12 | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049))), inference(lemma,lemma(discharge,[]))).
% 2.16/1.67 tff(1792,plain,
% 2.16/1.67 (hskp12),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1791, 322, 299, 1545, 1544, 1543])).
% 2.16/1.67 tff(1793,plain,
% 2.16/1.67 (~c3_1(a1043)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1570, 1792])).
% 2.16/1.67 tff(1794,plain,
% 2.16/1.67 (~c1_1(a1043)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1576, 1792])).
% 2.16/1.67 tff(1795,assumption,(~c1_1(a1080)), introduced(assumption)).
% 2.16/1.67 tff(1796,assumption,(~c2_1(a1080)), introduced(assumption)).
% 2.16/1.67 tff(1797,assumption,(~c0_1(a1080)), introduced(assumption)).
% 2.16/1.67 tff(1798,plain,
% 2.16/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031))),
% 2.16/1.67 inference(rewrite,[status(thm)],[])).
% 2.16/1.67 tff(1799,plain,
% 2.16/1.67 (((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c2_1(a1043)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080)) <=> (c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031))),
% 2.16/1.67 inference(rewrite,[status(thm)],[])).
% 2.16/1.67 tff(1800,plain,
% 2.16/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c2_1(a1043)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031)))),
% 2.16/1.67 inference(monotonicity,[status(thm)],[1799])).
% 2.16/1.67 tff(1801,plain,
% 2.16/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c2_1(a1043)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031))),
% 2.16/1.67 inference(transitivity,[status(thm)],[1800, 1798])).
% 2.16/1.67 tff(1802,plain,
% 2.16/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c2_1(a1043)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))),
% 2.16/1.67 inference(quant_inst,[status(thm)],[])).
% 2.16/1.67 tff(1803,plain,
% 2.16/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031)),
% 2.16/1.67 inference(modus_ponens,[status(thm)],[1802, 1801])).
% 2.16/1.67 tff(1804,plain,
% 2.16/1.67 (~c2_1(a1043)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1803, 126, 322, 299, 1797, 1796, 1795, 1794, 1793, 538, 1781])).
% 2.16/1.67 tff(1805,plain,
% 2.16/1.67 (c0_1(a1043)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1587, 1792])).
% 2.16/1.67 tff(1806,plain,
% 2.16/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1031) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1031)) | c0_1(a1031))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1031) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1031)) | c0_1(a1031))),
% 2.16/1.67 inference(rewrite,[status(thm)],[])).
% 2.16/1.67 tff(1807,plain,
% 2.16/1.67 (((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043)) <=> (c1_1(a1031) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1031)) | c0_1(a1031))),
% 2.16/1.67 inference(rewrite,[status(thm)],[])).
% 2.16/1.67 tff(1808,plain,
% 2.16/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1031) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1031)) | c0_1(a1031)))),
% 2.16/1.67 inference(monotonicity,[status(thm)],[1807])).
% 2.16/1.67 tff(1809,plain,
% 2.16/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1031) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1031)) | c0_1(a1031))),
% 2.16/1.67 inference(transitivity,[status(thm)],[1808, 1806])).
% 2.16/1.67 tff(1810,plain,
% 2.16/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043))),
% 2.16/1.67 inference(quant_inst,[status(thm)],[])).
% 2.16/1.67 tff(1811,plain,
% 2.16/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1031) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1031)) | c0_1(a1031)),
% 2.16/1.67 inference(modus_ponens,[status(thm)],[1810, 1809])).
% 2.16/1.67 tff(1812,plain,
% 2.16/1.67 ($false),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1811, 126, 299, 1805, 288, 1794, 1793, 242, 1781, 1804])).
% 2.16/1.67 tff(1813,plain,((~hskp33) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049))), inference(lemma,lemma(discharge,[]))).
% 2.16/1.67 tff(1814,plain,
% 2.16/1.67 (~hskp33),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1813, 1761, 1760, 1780, 1779, 1778, 1777])).
% 2.16/1.67 tff(1815,plain,
% 2.16/1.67 (hskp20),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1745, 42, 21, 53])).
% 2.16/1.67 tff(1816,plain,
% 2.16/1.67 (~c2_1(a1080)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[699, 1815])).
% 2.16/1.67 tff(1817,plain,
% 2.16/1.67 (~c0_1(a1080)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[705, 1815])).
% 2.16/1.67 tff(1818,plain,
% 2.16/1.67 (~c3_1(a1080)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[719, 126, 21, 42, 1817, 1816, 52])).
% 2.16/1.67 tff(1819,plain,
% 2.16/1.67 ($false),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[743, 126, 53, 1817, 1816, 73, 1818])).
% 2.16/1.67 tff(1820,plain,(hskp15 | hskp10 | hskp33), inference(lemma,lemma(discharge,[]))).
% 2.16/1.67 tff(1821,plain,
% 2.16/1.67 (hskp15),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1820, 1814, 53])).
% 2.16/1.67 tff(1822,plain,
% 2.16/1.67 (c2_1(a1059)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[389, 1821])).
% 2.16/1.67 tff(1823,plain,
% 2.16/1.67 (c3_1(a1059)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[412, 1821])).
% 2.16/1.67 tff(1824,plain,
% 2.16/1.67 (~c0_1(a1059)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1639, 126, 1779, 1778, 1777, 1823, 1822, 10])).
% 2.16/1.67 tff(1825,plain,
% 2.16/1.67 (~c0_1(a1059)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1639, 126, 1545, 1544, 1543, 1629, 393, 10])).
% 2.16/1.67 tff(1826,plain,
% 2.16/1.67 ($false),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1660, 126, 1240, 1629, 393, 1789, 1785, 1001, 1825, 1787])).
% 2.16/1.67 tff(1827,plain,(hskp12 | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1049)) | (~c2_1(a1049)) | (~c1_1(a1049))), inference(lemma,lemma(discharge,[]))).
% 2.16/1.67 tff(1828,plain,
% 2.16/1.67 (hskp12),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1827, 1823, 1822, 1779, 1778, 1777])).
% 2.16/1.67 tff(1829,plain,
% 2.16/1.67 (~c3_1(a1043)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1570, 1828])).
% 2.16/1.67 tff(1830,plain,
% 2.16/1.67 (~c1_1(a1043)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1576, 1828])).
% 2.16/1.67 tff(1831,plain,
% 2.16/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))),
% 2.16/1.67 inference(rewrite,[status(thm)],[])).
% 2.16/1.67 tff(1832,plain,
% 2.16/1.67 (((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c2_1(a1043)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080)) <=> (c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))),
% 2.16/1.67 inference(rewrite,[status(thm)],[])).
% 2.16/1.67 tff(1833,plain,
% 2.16/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c2_1(a1043)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | (c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059)))),
% 2.16/1.67 inference(monotonicity,[status(thm)],[1832])).
% 2.16/1.67 tff(1834,plain,
% 2.16/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c2_1(a1043)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))),
% 2.16/1.67 inference(transitivity,[status(thm)],[1833, 1831])).
% 2.16/1.67 tff(1835,plain,
% 2.16/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c2_1(a1043)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1080) | c1_1(a1080) | c2_1(a1080))),
% 2.16/1.67 inference(quant_inst,[status(thm)],[])).
% 2.16/1.67 tff(1836,plain,
% 2.16/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | c2_1(W))) | c0_1(a1080) | c2_1(a1080) | c1_1(a1080) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059)),
% 2.16/1.67 inference(modus_ponens,[status(thm)],[1835, 1834])).
% 2.16/1.67 tff(1837,plain,
% 2.16/1.67 (~c2_1(a1043)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1836, 126, 1823, 1822, 1761, 1760, 1780, 1830, 1829, 538, 1824])).
% 2.16/1.67 tff(1838,plain,
% 2.16/1.67 (~c1_1(a1059)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[378, 1821])).
% 2.16/1.67 tff(1839,plain,
% 2.16/1.67 (c0_1(a1043)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1587, 1828])).
% 2.16/1.67 tff(1840,plain,
% 2.16/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1059) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1059)) | c0_1(a1059))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1059) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1059)) | c0_1(a1059))),
% 2.16/1.67 inference(rewrite,[status(thm)],[])).
% 2.16/1.67 tff(1841,plain,
% 2.16/1.67 (((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)) | c0_1(a1059) | c1_1(a1059) | (~c2_1(a1059)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043)) <=> (c1_1(a1059) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1059)) | c0_1(a1059))),
% 2.16/1.67 inference(rewrite,[status(thm)],[])).
% 2.16/1.67 tff(1842,plain,
% 2.16/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)) | c0_1(a1059) | c1_1(a1059) | (~c2_1(a1059)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a1059) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1059)) | c0_1(a1059)))),
% 2.16/1.67 inference(monotonicity,[status(thm)],[1841])).
% 2.16/1.67 tff(1843,plain,
% 2.16/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)) | c0_1(a1059) | c1_1(a1059) | (~c2_1(a1059)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1059) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1059)) | c0_1(a1059))),
% 2.16/1.67 inference(transitivity,[status(thm)],[1842, 1840])).
% 2.16/1.67 tff(1844,plain,
% 2.16/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a1043) | c1_1(a1043) | (~c0_1(a1043)) | c0_1(a1059) | c1_1(a1059) | (~c2_1(a1059)) | c3_1(a1043) | c1_1(a1043) | c2_1(a1043))),
% 2.16/1.67 inference(quant_inst,[status(thm)],[])).
% 2.16/1.67 tff(1845,plain,
% 2.16/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a1059) | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | c2_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1059)) | c0_1(a1059)),
% 2.16/1.67 inference(modus_ponens,[status(thm)],[1844, 1843])).
% 2.16/1.67 tff(1846,plain,
% 2.16/1.67 ($false),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1845, 126, 1822, 1839, 1838, 1830, 1829, 242, 1824, 1837])).
% 2.16/1.67 tff(1847,plain,(hskp10), inference(lemma,lemma(discharge,[]))).
% 2.16/1.67 tff(1848,plain,
% 2.16/1.67 (~c0_1(a1039)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[455, 1847])).
% 2.16/1.67 tff(1849,plain,
% 2.16/1.67 (~c2_1(a1039)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[438, 1847])).
% 2.16/1.67 tff(1850,plain,
% 2.16/1.67 (hskp33 | hskp15 | (~c3_1(a1039))),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[643, 126, 1849, 1848, 52])).
% 2.16/1.67 tff(1851,plain,
% 2.16/1.67 (~c3_1(a1039)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1850, 42, 21])).
% 2.16/1.67 tff(1852,assumption,(hskp36), introduced(assumption)).
% 2.16/1.67 tff(1853,plain,
% 2.16/1.67 (~c0_1(a1034)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[780, 1852])).
% 2.16/1.67 tff(1854,plain,
% 2.16/1.67 (c3_1(a1034)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[826, 1852])).
% 2.16/1.67 tff(1855,plain,
% 2.16/1.67 (c2_1(a1034)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1713, 126, 21, 42, 1854, 1853, 52])).
% 2.16/1.67 tff(1856,plain,
% 2.16/1.67 (c1_1(a1039)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[449, 1847])).
% 2.16/1.67 tff(1857,plain,
% 2.16/1.67 (c1_1(a1034)),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[791, 1852])).
% 2.16/1.67 tff(1858,plain,
% 2.16/1.67 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c1_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp33 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c1_1(a1034)))),
% 2.16/1.67 inference(rewrite,[status(thm)],[])).
% 2.16/1.67 tff(1859,plain,
% 2.16/1.67 ((hskp33 | (~ndr1_0) | (~c1_1(a1034)) | (~c3_1(a1034)) | (~c2_1(a1034)) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039))) <=> (hskp33 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c1_1(a1034)))),
% 2.16/1.67 inference(rewrite,[status(thm)],[])).
% 2.16/1.67 tff(1860,plain,
% 2.16/1.67 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | (~c1_1(a1034)) | (~c3_1(a1034)) | (~c2_1(a1034)) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c1_1(a1034))))),
% 2.16/1.67 inference(monotonicity,[status(thm)],[1859])).
% 2.16/1.67 tff(1861,plain,
% 2.16/1.67 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | (~c1_1(a1034)) | (~c3_1(a1034)) | (~c2_1(a1034)) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp33 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c1_1(a1034)))),
% 2.16/1.67 inference(transitivity,[status(thm)],[1860, 1858])).
% 2.16/1.67 tff(1862,plain,
% 2.16/1.67 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | (~c1_1(a1034)) | (~c3_1(a1034)) | (~c2_1(a1034)) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039)))),
% 2.16/1.67 inference(quant_inst,[status(thm)],[])).
% 2.16/1.67 tff(1863,plain,
% 2.16/1.67 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp33 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)) | (~c1_1(a1034))),
% 2.16/1.67 inference(modus_ponens,[status(thm)],[1862, 1861])).
% 2.16/1.67 tff(1864,plain,
% 2.16/1.67 ($false),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1863, 126, 21, 1854, 1857, 1856, 1849, 1848, 758, 1855])).
% 2.16/1.67 tff(1865,plain,((~hskp36) | hskp33 | hskp15), inference(lemma,lemma(discharge,[]))).
% 2.16/1.67 tff(1866,plain,
% 2.16/1.67 (~hskp36),
% 2.16/1.67 inference(unit_resolution,[status(thm)],[1865, 42, 21])).
% 2.16/1.67 tff(1867,plain,
% 2.16/1.67 (^[U: $i] : refl((hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 2.16/1.67 inference(bind,[status(th)],[])).
% 2.16/1.67 tff(1868,plain,
% 2.16/1.67 (![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.16/1.67 inference(quant_intro,[status(thm)],[1867])).
% 2.16/1.67 tff(1869,plain,
% 2.16/1.67 (![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.16/1.68 inference(rewrite,[status(thm)],[])).
% 2.16/1.68 tff(1870,plain,
% 2.16/1.68 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp36) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp36))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp36) <=> (hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp36) <=> (hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp36) | hskp48) <=> ((hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp48))), rewrite(((hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp48) <=> (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp36) | hskp48) <=> (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 2.16/1.68 inference(bind,[status(th)],[])).
% 2.16/1.68 tff(1871,plain,
% 2.16/1.68 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp36) | hskp48) <=> ![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.16/1.68 inference(quant_intro,[status(thm)],[1870])).
% 2.16/1.68 tff(1872,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp36) | hskp48)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause267')).
% 2.16/1.68 tff(1873,plain,
% 2.16/1.68 (![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1872, 1871])).
% 2.16/1.68 tff(1874,plain,
% 2.16/1.68 (![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1873, 1869])).
% 2.16/1.68 tff(1875,plain,(
% 2.16/1.68 ![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.16/1.68 inference(skolemize,[status(sab)],[1874])).
% 2.16/1.68 tff(1876,plain,
% 2.16/1.68 (![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1875, 1868])).
% 2.16/1.68 tff(1877,plain,
% 2.16/1.68 (((~![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp48 | hskp36 | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)))) <=> ((~![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp48 | hskp36 | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)))),
% 2.16/1.68 inference(rewrite,[status(thm)],[])).
% 2.16/1.68 tff(1878,plain,
% 2.16/1.68 ((hskp48 | hskp36 | (~ndr1_0) | c0_1(a1039) | c3_1(a1039) | (~c1_1(a1039))) <=> (hskp48 | hskp36 | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)))),
% 2.16/1.68 inference(rewrite,[status(thm)],[])).
% 2.16/1.68 tff(1879,plain,
% 2.16/1.68 (((~![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp48 | hskp36 | (~ndr1_0) | c0_1(a1039) | c3_1(a1039) | (~c1_1(a1039)))) <=> ((~![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp48 | hskp36 | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039))))),
% 2.16/1.68 inference(monotonicity,[status(thm)],[1878])).
% 2.16/1.68 tff(1880,plain,
% 2.16/1.68 (((~![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp48 | hskp36 | (~ndr1_0) | c0_1(a1039) | c3_1(a1039) | (~c1_1(a1039)))) <=> ((~![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp48 | hskp36 | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)))),
% 2.16/1.68 inference(transitivity,[status(thm)],[1879, 1877])).
% 2.16/1.68 tff(1881,plain,
% 2.16/1.68 ((~![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp48 | hskp36 | (~ndr1_0) | c0_1(a1039) | c3_1(a1039) | (~c1_1(a1039)))),
% 2.16/1.68 inference(quant_inst,[status(thm)],[])).
% 2.16/1.68 tff(1882,plain,
% 2.16/1.68 ((~![U: $i] : (hskp48 | hskp36 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp48 | hskp36 | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039))),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1881, 1880])).
% 2.16/1.68 tff(1883,plain,
% 2.16/1.68 (hskp48 | hskp36 | c3_1(a1039)),
% 2.16/1.68 inference(unit_resolution,[status(thm)],[1882, 126, 1856, 1848, 1876])).
% 2.16/1.68 tff(1884,plain,
% 2.16/1.68 (hskp48),
% 2.16/1.68 inference(unit_resolution,[status(thm)],[1883, 1866, 1851])).
% 2.16/1.68 tff(1885,plain,
% 2.16/1.68 (((~hskp48) | c0_1(a1062)) <=> ((~hskp48) | c0_1(a1062))),
% 2.16/1.68 inference(rewrite,[status(thm)],[])).
% 2.16/1.68 tff(1886,axiom,((~hskp48) | c0_1(a1062)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 2.16/1.68 tff(1887,plain,
% 2.16/1.68 ((~hskp48) | c0_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 2.16/1.68 tff(1888,plain,
% 2.16/1.68 ((~hskp48) | c0_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1887, 1885])).
% 2.16/1.68 tff(1889,plain,
% 2.16/1.68 ((~hskp48) | c0_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1888, 1885])).
% 2.16/1.68 tff(1890,plain,
% 2.16/1.68 ((~hskp48) | c0_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1889, 1885])).
% 2.16/1.68 tff(1891,plain,
% 2.16/1.68 ((~hskp48) | c0_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1890, 1885])).
% 2.16/1.68 tff(1892,plain,
% 2.16/1.68 ((~hskp48) | c0_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1891, 1885])).
% 2.16/1.68 tff(1893,plain,
% 2.16/1.68 ((~hskp48) | c0_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1892, 1885])).
% 2.16/1.68 tff(1894,plain,
% 2.16/1.68 ((~hskp48) | c0_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1893, 1885])).
% 2.16/1.68 tff(1895,plain,
% 2.16/1.68 (c0_1(a1062)),
% 2.16/1.68 inference(unit_resolution,[status(thm)],[1894, 1884])).
% 2.16/1.68 tff(1896,plain,
% 2.16/1.68 (((~hskp48) | c2_1(a1062)) <=> ((~hskp48) | c2_1(a1062))),
% 2.16/1.68 inference(rewrite,[status(thm)],[])).
% 2.16/1.68 tff(1897,axiom,((~hskp48) | c2_1(a1062)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 2.16/1.68 tff(1898,plain,
% 2.16/1.68 ((~hskp48) | c2_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1897, 1896])).
% 2.16/1.68 tff(1899,plain,
% 2.16/1.68 ((~hskp48) | c2_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1898, 1896])).
% 2.16/1.68 tff(1900,plain,
% 2.16/1.68 ((~hskp48) | c2_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1899, 1896])).
% 2.16/1.68 tff(1901,plain,
% 2.16/1.68 ((~hskp48) | c2_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1900, 1896])).
% 2.16/1.68 tff(1902,plain,
% 2.16/1.68 ((~hskp48) | c2_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1901, 1896])).
% 2.16/1.68 tff(1903,plain,
% 2.16/1.68 ((~hskp48) | c2_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1902, 1896])).
% 2.16/1.68 tff(1904,plain,
% 2.16/1.68 ((~hskp48) | c2_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1903, 1896])).
% 2.16/1.68 tff(1905,plain,
% 2.16/1.68 ((~hskp48) | c2_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1904, 1896])).
% 2.16/1.68 tff(1906,plain,
% 2.16/1.68 (c2_1(a1062)),
% 2.16/1.68 inference(unit_resolution,[status(thm)],[1905, 1884])).
% 2.16/1.68 tff(1907,plain,
% 2.16/1.68 (((~hskp48) | c3_1(a1062)) <=> ((~hskp48) | c3_1(a1062))),
% 2.16/1.68 inference(rewrite,[status(thm)],[])).
% 2.16/1.68 tff(1908,axiom,((~hskp48) | c3_1(a1062)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 2.16/1.68 tff(1909,plain,
% 2.16/1.68 ((~hskp48) | c3_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1908, 1907])).
% 2.16/1.68 tff(1910,plain,
% 2.16/1.68 ((~hskp48) | c3_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1909, 1907])).
% 2.16/1.68 tff(1911,plain,
% 2.16/1.68 ((~hskp48) | c3_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1910, 1907])).
% 2.16/1.68 tff(1912,plain,
% 2.16/1.68 ((~hskp48) | c3_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1911, 1907])).
% 2.16/1.68 tff(1913,plain,
% 2.16/1.68 ((~hskp48) | c3_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1912, 1907])).
% 2.16/1.68 tff(1914,plain,
% 2.16/1.68 ((~hskp48) | c3_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1913, 1907])).
% 2.16/1.68 tff(1915,plain,
% 2.16/1.68 ((~hskp48) | c3_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1914, 1907])).
% 2.16/1.68 tff(1916,plain,
% 2.16/1.68 ((~hskp48) | c3_1(a1062)),
% 2.16/1.68 inference(modus_ponens,[status(thm)],[1915, 1907])).
% 2.16/1.68 tff(1917,plain,
% 2.16/1.68 (c3_1(a1062)),
% 2.16/1.68 inference(unit_resolution,[status(thm)],[1916, 1884])).
% 2.22/1.68 tff(1918,plain,
% 2.22/1.68 (((~![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp33 | hskp23 | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)))) <=> ((~![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp33 | hskp23 | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(1919,plain,
% 2.22/1.68 ((hskp33 | hskp23 | (~ndr1_0) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062))) <=> (hskp33 | hskp23 | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(1920,plain,
% 2.22/1.68 (((~![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))) <=> ((~![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp33 | hskp23 | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062))))),
% 2.22/1.68 inference(monotonicity,[status(thm)],[1919])).
% 2.22/1.68 tff(1921,plain,
% 2.22/1.68 (((~![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))) <=> ((~![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp33 | hskp23 | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)))),
% 2.22/1.68 inference(transitivity,[status(thm)],[1920, 1918])).
% 2.22/1.68 tff(1922,plain,
% 2.22/1.68 ((~![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))),
% 2.22/1.68 inference(quant_inst,[status(thm)],[])).
% 2.22/1.68 tff(1923,plain,
% 2.22/1.68 ((~![U: $i] : (hskp33 | hskp23 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp33 | hskp23 | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062))),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1922, 1921])).
% 2.22/1.68 tff(1924,plain,
% 2.22/1.68 (hskp23),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1923, 126, 21, 1917, 1906, 1895, 41])).
% 2.22/1.68 tff(1925,plain,
% 2.22/1.68 (((~hskp23) | (~c2_1(a1088))) <=> ((~hskp23) | (~c2_1(a1088)))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(1926,plain,
% 2.22/1.68 (((~c2_1(a1088)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a1088)))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(1927,axiom,((~c2_1(a1088)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause218')).
% 2.22/1.68 tff(1928,plain,
% 2.22/1.68 ((~hskp23) | (~c2_1(a1088))),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1927, 1926])).
% 2.22/1.68 tff(1929,plain,
% 2.22/1.68 ((~hskp23) | (~c2_1(a1088))),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1928, 1925])).
% 2.22/1.68 tff(1930,plain,
% 2.22/1.68 (~c2_1(a1088)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1929, 1924])).
% 2.22/1.68 tff(1931,plain,
% 2.22/1.68 (((~hskp23) | c3_1(a1088)) <=> ((~hskp23) | c3_1(a1088))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(1932,axiom,((~hskp23) | c3_1(a1088)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 2.22/1.68 tff(1933,plain,
% 2.22/1.68 ((~hskp23) | c3_1(a1088)),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 2.22/1.68 tff(1934,plain,
% 2.22/1.68 ((~hskp23) | c3_1(a1088)),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1933, 1931])).
% 2.22/1.68 tff(1935,plain,
% 2.22/1.68 ((~hskp23) | c3_1(a1088)),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1934, 1931])).
% 2.22/1.68 tff(1936,plain,
% 2.22/1.68 ((~hskp23) | c3_1(a1088)),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1935, 1931])).
% 2.22/1.68 tff(1937,plain,
% 2.22/1.68 ((~hskp23) | c3_1(a1088)),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1936, 1931])).
% 2.22/1.68 tff(1938,plain,
% 2.22/1.68 ((~hskp23) | c3_1(a1088)),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1937, 1931])).
% 2.22/1.68 tff(1939,plain,
% 2.22/1.68 ((~hskp23) | c3_1(a1088)),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1938, 1931])).
% 2.22/1.68 tff(1940,plain,
% 2.22/1.68 ((~hskp23) | c3_1(a1088)),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1939, 1931])).
% 2.22/1.68 tff(1941,plain,
% 2.22/1.68 (c3_1(a1088)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1940, 1924])).
% 2.22/1.68 tff(1942,plain,
% 2.22/1.68 (((~hskp23) | c1_1(a1088)) <=> ((~hskp23) | c1_1(a1088))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(1943,axiom,((~hskp23) | c1_1(a1088)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 2.22/1.68 tff(1944,plain,
% 2.22/1.68 ((~hskp23) | c1_1(a1088)),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1943, 1942])).
% 2.22/1.68 tff(1945,plain,
% 2.22/1.68 ((~hskp23) | c1_1(a1088)),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1944, 1942])).
% 2.22/1.68 tff(1946,plain,
% 2.22/1.68 ((~hskp23) | c1_1(a1088)),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1945, 1942])).
% 2.22/1.68 tff(1947,plain,
% 2.22/1.68 ((~hskp23) | c1_1(a1088)),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1946, 1942])).
% 2.22/1.68 tff(1948,plain,
% 2.22/1.68 ((~hskp23) | c1_1(a1088)),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1947, 1942])).
% 2.22/1.68 tff(1949,plain,
% 2.22/1.68 ((~hskp23) | c1_1(a1088)),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1948, 1942])).
% 2.22/1.68 tff(1950,plain,
% 2.22/1.68 ((~hskp23) | c1_1(a1088)),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1949, 1942])).
% 2.22/1.68 tff(1951,plain,
% 2.22/1.68 ((~hskp23) | c1_1(a1088)),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1950, 1942])).
% 2.22/1.68 tff(1952,plain,
% 2.22/1.68 (c1_1(a1088)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1951, 1924])).
% 2.22/1.68 tff(1953,plain,
% 2.22/1.68 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | c2_1(a1088) | (~ndr1_0) | (~c1_1(a1088)) | (~c3_1(a1088)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | c2_1(a1088) | (~ndr1_0) | (~c1_1(a1088)) | (~c3_1(a1088)))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(1954,plain,
% 2.22/1.68 ((hskp56 | hskp22 | (~ndr1_0) | c2_1(a1088) | (~c1_1(a1088)) | (~c3_1(a1088))) <=> (hskp56 | hskp22 | c2_1(a1088) | (~ndr1_0) | (~c1_1(a1088)) | (~c3_1(a1088)))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(1955,plain,
% 2.22/1.68 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1088) | (~c1_1(a1088)) | (~c3_1(a1088)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | c2_1(a1088) | (~ndr1_0) | (~c1_1(a1088)) | (~c3_1(a1088))))),
% 2.22/1.68 inference(monotonicity,[status(thm)],[1954])).
% 2.22/1.68 tff(1956,plain,
% 2.22/1.68 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1088) | (~c1_1(a1088)) | (~c3_1(a1088)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | c2_1(a1088) | (~ndr1_0) | (~c1_1(a1088)) | (~c3_1(a1088)))),
% 2.22/1.68 inference(transitivity,[status(thm)],[1955, 1953])).
% 2.22/1.68 tff(1957,plain,
% 2.22/1.68 ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1088) | (~c1_1(a1088)) | (~c3_1(a1088)))),
% 2.22/1.68 inference(quant_inst,[status(thm)],[])).
% 2.22/1.68 tff(1958,plain,
% 2.22/1.68 ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | c2_1(a1088) | (~ndr1_0) | (~c1_1(a1088)) | (~c3_1(a1088))),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1957, 1956])).
% 2.22/1.68 tff(1959,plain,
% 2.22/1.68 (hskp22),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1958, 126, 1126, 1952, 1941, 1930, 31])).
% 2.22/1.68 tff(1960,plain,
% 2.22/1.68 (~c1_1(a1083)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1178, 1959])).
% 2.22/1.68 tff(1961,plain,
% 2.22/1.68 (c3_1(a1083)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1144, 1959])).
% 2.22/1.68 tff(1962,plain,
% 2.22/1.68 (c2_1(a1083)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1155, 1959])).
% 2.22/1.68 tff(1963,plain,
% 2.22/1.68 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1083) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1083)) | (~c2_1(a1083)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1083) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(1964,plain,
% 2.22/1.68 ((hskp53 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062))) <=> (hskp53 | c1_1(a1083) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(1965,plain,
% 2.22/1.68 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1083) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1083)) | (~c2_1(a1083))))),
% 2.22/1.68 inference(monotonicity,[status(thm)],[1964])).
% 2.22/1.68 tff(1966,plain,
% 2.22/1.68 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1083) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1083)) | (~c2_1(a1083)))),
% 2.22/1.68 inference(transitivity,[status(thm)],[1965, 1963])).
% 2.22/1.68 tff(1967,plain,
% 2.22/1.68 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))),
% 2.22/1.68 inference(quant_inst,[status(thm)],[])).
% 2.22/1.68 tff(1968,plain,
% 2.22/1.68 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1083) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1083)) | (~c2_1(a1083))),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1967, 1966])).
% 2.22/1.68 tff(1969,plain,
% 2.22/1.68 (hskp53),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1968, 126, 1917, 1906, 1895, 1962, 1961, 1960, 20])).
% 2.22/1.68 tff(1970,plain,
% 2.22/1.68 (c0_1(a1073)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[340, 1969])).
% 2.22/1.68 tff(1971,plain,
% 2.22/1.68 (c2_1(a1073)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[351, 1969])).
% 2.22/1.68 tff(1972,plain,
% 2.22/1.68 (c1_1(a1073)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[362, 1969])).
% 2.22/1.68 tff(1973,plain,
% 2.22/1.68 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c2_1(a1088) | (~ndr1_0) | (~c3_1(a1088)) | c0_1(a1088))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c2_1(a1088) | (~ndr1_0) | (~c3_1(a1088)) | c0_1(a1088))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(1974,plain,
% 2.22/1.68 ((hskp33 | hskp15 | (~ndr1_0) | c0_1(a1088) | c2_1(a1088) | (~c3_1(a1088))) <=> (hskp33 | hskp15 | c2_1(a1088) | (~ndr1_0) | (~c3_1(a1088)) | c0_1(a1088))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(1975,plain,
% 2.22/1.68 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1088) | c2_1(a1088) | (~c3_1(a1088)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | c2_1(a1088) | (~ndr1_0) | (~c3_1(a1088)) | c0_1(a1088)))),
% 2.22/1.68 inference(monotonicity,[status(thm)],[1974])).
% 2.22/1.68 tff(1976,plain,
% 2.22/1.68 (((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1088) | c2_1(a1088) | (~c3_1(a1088)))) <=> ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c2_1(a1088) | (~ndr1_0) | (~c3_1(a1088)) | c0_1(a1088))),
% 2.22/1.68 inference(transitivity,[status(thm)],[1975, 1973])).
% 2.22/1.68 tff(1977,plain,
% 2.22/1.68 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp33 | hskp15 | (~ndr1_0) | c0_1(a1088) | c2_1(a1088) | (~c3_1(a1088)))),
% 2.22/1.68 inference(quant_inst,[status(thm)],[])).
% 2.22/1.68 tff(1978,plain,
% 2.22/1.68 ((~![U: $i] : (hskp33 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp33 | hskp15 | c2_1(a1088) | (~ndr1_0) | (~c3_1(a1088)) | c0_1(a1088)),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1977, 1976])).
% 2.22/1.68 tff(1979,plain,
% 2.22/1.68 (c0_1(a1088)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1978, 126, 21, 42, 1941, 1930, 52])).
% 2.22/1.68 tff(1980,plain,
% 2.22/1.68 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c2_1(a1088) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1088)) | (~c0_1(a1088)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c2_1(a1088) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1088)) | (~c0_1(a1088)))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(1981,plain,
% 2.22/1.68 ((hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1088) | (~c3_1(a1088)) | (~c0_1(a1088))) <=> (hskp57 | c2_1(a1088) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1088)) | (~c0_1(a1088)))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(1982,plain,
% 2.22/1.68 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1088) | (~c3_1(a1088)) | (~c0_1(a1088)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c2_1(a1088) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1088)) | (~c0_1(a1088))))),
% 2.22/1.68 inference(monotonicity,[status(thm)],[1981])).
% 2.22/1.68 tff(1983,plain,
% 2.22/1.68 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1088) | (~c3_1(a1088)) | (~c0_1(a1088)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c2_1(a1088) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1088)) | (~c0_1(a1088)))),
% 2.22/1.68 inference(transitivity,[status(thm)],[1982, 1980])).
% 2.22/1.68 tff(1984,plain,
% 2.22/1.68 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1083) | (~c3_1(a1083)) | (~c2_1(a1083)) | c2_1(a1088) | (~c3_1(a1088)) | (~c0_1(a1088)))),
% 2.22/1.68 inference(quant_inst,[status(thm)],[])).
% 2.22/1.68 tff(1985,plain,
% 2.22/1.68 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c2_1(a1088) | c1_1(a1083) | (~ndr1_0) | (~c3_1(a1083)) | (~c2_1(a1083)) | (~c3_1(a1088)) | (~c0_1(a1088))),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1984, 1983])).
% 2.22/1.68 tff(1986,plain,
% 2.22/1.68 (hskp57),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1985, 126, 1941, 1962, 1961, 1930, 1960, 1058, 1979])).
% 2.22/1.68 tff(1987,plain,
% 2.22/1.68 (c3_1(a1085)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1076, 1986])).
% 2.22/1.68 tff(1988,plain,
% 2.22/1.68 (c0_1(a1085)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1087, 1986])).
% 2.22/1.68 tff(1989,plain,
% 2.22/1.68 (c2_1(a1085)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1098, 1986])).
% 2.22/1.68 tff(1990,plain,
% 2.22/1.68 ($false),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1115, 126, 1989, 1988, 1987, 1972, 1971, 1970, 10])).
% 2.22/1.68 tff(1991,plain,(hskp15 | hskp33), inference(lemma,lemma(discharge,[]))).
% 2.22/1.68 tff(1992,plain,
% 2.22/1.68 (hskp15),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1991, 21])).
% 2.22/1.68 tff(1993,plain,
% 2.22/1.68 (c2_1(a1059)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[389, 1992])).
% 2.22/1.68 tff(1994,plain,
% 2.22/1.68 (~c1_1(a1059)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[378, 1992])).
% 2.22/1.68 tff(1995,plain,
% 2.22/1.68 (c3_1(a1059)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[412, 1992])).
% 2.22/1.68 tff(1996,assumption,(c0_1(a1059)), introduced(assumption)).
% 2.22/1.68 tff(1997,plain,
% 2.22/1.68 (hskp53 | (~c0_1(a1059))),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[419, 126, 1629, 393, 392, 20])).
% 2.22/1.68 tff(1998,plain,
% 2.22/1.68 (hskp53),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1997, 1996])).
% 2.22/1.68 tff(1999,plain,
% 2.22/1.68 (c0_1(a1073)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[340, 1998])).
% 2.22/1.68 tff(2000,plain,
% 2.22/1.68 (c2_1(a1073)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[351, 1998])).
% 2.22/1.68 tff(2001,plain,
% 2.22/1.68 (c1_1(a1073)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[362, 1998])).
% 2.22/1.68 tff(2002,plain,
% 2.22/1.68 ($false),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[429, 126, 2001, 2000, 1999, 1629, 393, 10, 1996])).
% 2.22/1.68 tff(2003,plain,((~c0_1(a1059)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c1_1(a1059)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.68 tff(2004,plain,
% 2.22/1.68 (~c0_1(a1059)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[2003, 1995, 1993, 1994])).
% 2.22/1.68 tff(2005,assumption,(~c2_1(a1043)), introduced(assumption)).
% 2.22/1.68 tff(2006,assumption,(~hskp7), introduced(assumption)).
% 2.22/1.68 tff(2007,assumption,(c3_1(a1039)), introduced(assumption)).
% 2.22/1.68 tff(2008,plain,
% 2.22/1.68 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(2009,plain,
% 2.22/1.68 ((hskp59 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039))) <=> (hskp59 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(2010,plain,
% 2.22/1.68 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039))))),
% 2.22/1.68 inference(monotonicity,[status(thm)],[2009])).
% 2.22/1.68 tff(2011,plain,
% 2.22/1.68 (((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)))) <=> ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)))),
% 2.22/1.68 inference(transitivity,[status(thm)],[2010, 2008])).
% 2.22/1.68 tff(2012,plain,
% 2.22/1.68 ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp59 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)))),
% 2.22/1.68 inference(quant_inst,[status(thm)],[])).
% 2.22/1.68 tff(2013,plain,
% 2.22/1.68 ((~![V: $i, U: $i] : (hskp59 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp59 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039))),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[2012, 2011])).
% 2.22/1.68 tff(2014,plain,
% 2.22/1.68 (hskp59 | (~c3_1(a1039))),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[2013, 126, 1856, 1849, 1848, 143])).
% 2.22/1.68 tff(2015,plain,
% 2.22/1.68 (hskp59),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[2014, 2007])).
% 2.22/1.68 tff(2016,plain,
% 2.22/1.68 (~c3_1(a1095)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[167, 2015])).
% 2.22/1.68 tff(2017,plain,
% 2.22/1.68 (c1_1(a1095)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[191, 2015])).
% 2.22/1.68 tff(2018,plain,
% 2.22/1.68 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | c3_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp12 | hskp7 | c3_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095)))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(2019,plain,
% 2.22/1.68 ((hskp12 | hskp7 | (~ndr1_0) | c3_1(a1095) | (~c1_1(a1095)) | (~c2_1(a1095))) <=> (hskp12 | hskp7 | c3_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095)))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(2020,plain,
% 2.22/1.68 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c3_1(a1095) | (~c1_1(a1095)) | (~c2_1(a1095)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | c3_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095))))),
% 2.22/1.69 inference(monotonicity,[status(thm)],[2019])).
% 2.22/1.69 tff(2021,plain,
% 2.22/1.69 (((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c3_1(a1095) | (~c1_1(a1095)) | (~c2_1(a1095)))) <=> ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp12 | hskp7 | c3_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095)))),
% 2.22/1.69 inference(transitivity,[status(thm)],[2020, 2018])).
% 2.22/1.69 tff(2022,plain,
% 2.22/1.69 ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp12 | hskp7 | (~ndr1_0) | c3_1(a1095) | (~c1_1(a1095)) | (~c2_1(a1095)))),
% 2.22/1.69 inference(quant_inst,[status(thm)],[])).
% 2.22/1.69 tff(2023,plain,
% 2.22/1.69 ((~![U: $i] : (hskp12 | hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp12 | hskp7 | c3_1(a1095) | (~ndr1_0) | (~c2_1(a1095)) | (~c1_1(a1095))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[2022, 2021])).
% 2.22/1.69 tff(2024,plain,
% 2.22/1.69 (~c2_1(a1095)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2023, 126, 1718, 2006, 2017, 2016, 1564])).
% 2.22/1.69 tff(2025,plain,
% 2.22/1.69 (~c0_1(a1095)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[173, 2015])).
% 2.22/1.69 tff(2026,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | c0_1(a1095) | c3_1(a1095) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | c2_1(a1095))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1095) | c3_1(a1095) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | c2_1(a1095))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(2027,plain,
% 2.22/1.69 ((hskp35 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095)) <=> (hskp35 | c0_1(a1095) | c3_1(a1095) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | c2_1(a1095))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(2028,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | c0_1(a1095) | c3_1(a1095) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | c2_1(a1095)))),
% 2.22/1.69 inference(monotonicity,[status(thm)],[2027])).
% 2.22/1.69 tff(2029,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1095) | c3_1(a1095) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | c2_1(a1095))),
% 2.22/1.69 inference(transitivity,[status(thm)],[2028, 2026])).
% 2.22/1.69 tff(2030,plain,
% 2.22/1.69 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c3_1(a1039)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095))),
% 2.22/1.69 inference(quant_inst,[status(thm)],[])).
% 2.22/1.69 tff(2031,plain,
% 2.22/1.69 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1095) | c3_1(a1095) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | c2_1(a1095)),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[2030, 2029])).
% 2.22/1.69 tff(2032,plain,
% 2.22/1.69 ($false),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2031, 126, 1240, 2025, 2016, 1849, 1848, 1436, 2007, 2024])).
% 2.22/1.69 tff(2033,plain,((~c3_1(a1039)) | hskp12 | hskp7), inference(lemma,lemma(discharge,[]))).
% 2.22/1.69 tff(2034,plain,
% 2.22/1.69 (~c3_1(a1039)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2033, 2006, 1718])).
% 2.22/1.69 tff(2035,plain,
% 2.22/1.69 (^[U: $i] : refl((hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))),
% 2.22/1.69 inference(bind,[status(th)],[])).
% 2.22/1.69 tff(2036,plain,
% 2.22/1.69 (![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.22/1.69 inference(quant_intro,[status(thm)],[2035])).
% 2.22/1.69 tff(2037,plain,
% 2.22/1.69 (![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(2038,plain,
% 2.22/1.69 (^[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)) | c0_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp36))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp36) <=> (hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) <=> (hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) | hskp7) <=> ((hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp7))), rewrite(((hskp36 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp7) <=> (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) | hskp7) <=> (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))))),
% 2.22/1.69 inference(bind,[status(th)],[])).
% 2.22/1.69 tff(2039,plain,
% 2.22/1.69 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) | hskp7) <=> ![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.22/1.69 inference(quant_intro,[status(thm)],[2038])).
% 2.22/1.69 tff(2040,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c0_1(U)) | hskp36) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause265')).
% 2.22/1.69 tff(2041,plain,
% 2.22/1.69 (![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[2040, 2039])).
% 2.22/1.69 tff(2042,plain,
% 2.22/1.69 (![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[2041, 2037])).
% 2.22/1.69 tff(2043,plain,(
% 2.22/1.69 ![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.22/1.69 inference(skolemize,[status(sab)],[2042])).
% 2.22/1.69 tff(2044,plain,
% 2.22/1.69 (![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[2043, 2036])).
% 2.22/1.69 tff(2045,plain,
% 2.22/1.69 (((~![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp36 | hskp7 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)))) <=> ((~![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp36 | hskp7 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(2046,plain,
% 2.22/1.69 ((hskp36 | hskp7 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039))) <=> (hskp36 | hskp7 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(2047,plain,
% 2.22/1.69 (((~![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp36 | hskp7 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039)))) <=> ((~![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp36 | hskp7 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039))))),
% 2.22/1.69 inference(monotonicity,[status(thm)],[2046])).
% 2.22/1.69 tff(2048,plain,
% 2.22/1.69 (((~![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp36 | hskp7 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039)))) <=> ((~![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp36 | hskp7 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039)))),
% 2.22/1.69 inference(transitivity,[status(thm)],[2047, 2045])).
% 2.22/1.69 tff(2049,plain,
% 2.22/1.69 ((~![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp36 | hskp7 | (~ndr1_0) | c0_1(a1039) | c2_1(a1039) | (~c1_1(a1039)))),
% 2.22/1.69 inference(quant_inst,[status(thm)],[])).
% 2.22/1.69 tff(2050,plain,
% 2.22/1.69 ((~![U: $i] : (hskp36 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp36 | hskp7 | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | (~c1_1(a1039))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[2049, 2048])).
% 2.22/1.69 tff(2051,plain,
% 2.22/1.69 (hskp36 | hskp7),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2050, 126, 1856, 1849, 1848, 2044])).
% 2.22/1.69 tff(2052,plain,
% 2.22/1.69 (hskp36),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2051, 2006])).
% 2.22/1.69 tff(2053,plain,
% 2.22/1.69 (~c0_1(a1034)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[780, 2052])).
% 2.22/1.69 tff(2054,plain,
% 2.22/1.69 (c3_1(a1034)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[826, 2052])).
% 2.22/1.69 tff(2055,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c0_1(a1034) | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c0_1(a1034) | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(2056,plain,
% 2.22/1.69 ((hskp35 | (~ndr1_0) | c2_1(a1039) | c3_1(a1039) | (~c1_1(a1039)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034))) <=> (hskp35 | c0_1(a1034) | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(2057,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1039) | c3_1(a1039) | (~c1_1(a1039)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c0_1(a1034) | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034))))),
% 2.22/1.69 inference(monotonicity,[status(thm)],[2056])).
% 2.22/1.69 tff(2058,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1039) | c3_1(a1039) | (~c1_1(a1039)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c0_1(a1034) | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034)))),
% 2.22/1.69 inference(transitivity,[status(thm)],[2057, 2055])).
% 2.22/1.69 tff(2059,plain,
% 2.22/1.69 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1039) | c3_1(a1039) | (~c1_1(a1039)) | c0_1(a1034) | (~c3_1(a1034)) | (~c2_1(a1034)))),
% 2.22/1.69 inference(quant_inst,[status(thm)],[])).
% 2.22/1.69 tff(2060,plain,
% 2.22/1.69 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c0_1(a1034) | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1034)) | (~c2_1(a1034))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[2059, 2058])).
% 2.22/1.69 tff(2061,plain,
% 2.22/1.69 (c3_1(a1039) | (~c2_1(a1034))),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2060, 126, 1240, 2054, 1856, 2053, 1849, 1001])).
% 2.22/1.69 tff(2062,plain,
% 2.22/1.69 (~c2_1(a1034)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2061, 2034])).
% 2.22/1.69 tff(2063,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | c0_1(a1034) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c3_1(a1034)) | c2_1(a1034))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1034) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c3_1(a1034)) | c2_1(a1034))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(2064,plain,
% 2.22/1.69 ((hskp35 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)) | c0_1(a1039) | c3_1(a1039) | c2_1(a1039)) <=> (hskp35 | c0_1(a1034) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c3_1(a1034)) | c2_1(a1034))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(2065,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)) | c0_1(a1039) | c3_1(a1039) | c2_1(a1039))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | c0_1(a1034) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c3_1(a1034)) | c2_1(a1034)))),
% 2.22/1.69 inference(monotonicity,[status(thm)],[2064])).
% 2.22/1.69 tff(2066,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)) | c0_1(a1039) | c3_1(a1039) | c2_1(a1039))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1034) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c3_1(a1034)) | c2_1(a1034))),
% 2.22/1.69 inference(transitivity,[status(thm)],[2065, 2063])).
% 2.22/1.69 tff(2067,plain,
% 2.22/1.69 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)) | c0_1(a1039) | c3_1(a1039) | c2_1(a1039))),
% 2.22/1.69 inference(quant_inst,[status(thm)],[])).
% 2.22/1.69 tff(2068,plain,
% 2.22/1.69 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1034) | c2_1(a1039) | c0_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c3_1(a1034)) | c2_1(a1034)),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[2067, 2066])).
% 2.22/1.69 tff(2069,plain,
% 2.22/1.69 (c3_1(a1039) | c2_1(a1034)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2068, 126, 1240, 2054, 2053, 1849, 1848, 1436])).
% 2.22/1.69 tff(2070,plain,
% 2.22/1.69 ($false),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2069, 2062, 2034])).
% 2.22/1.69 tff(2071,plain,(hskp7 | hskp12), inference(lemma,lemma(discharge,[]))).
% 2.22/1.69 tff(2072,plain,
% 2.22/1.69 (hskp7),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2071, 1718])).
% 2.22/1.69 tff(2073,plain,
% 2.22/1.69 (~c2_1(a1035)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1609, 2072])).
% 2.22/1.69 tff(2074,plain,
% 2.22/1.69 (c0_1(a1035)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1620, 2072])).
% 2.22/1.69 tff(2075,plain,
% 2.22/1.69 (c1_1(a1035)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1653, 2072])).
% 2.22/1.69 tff(2076,plain,
% 2.22/1.69 (c1_1(a1034)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[791, 2052])).
% 2.22/1.69 tff(2077,plain,
% 2.22/1.69 (~c2_1(a1034)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1863, 126, 21, 2054, 2076, 1856, 1849, 1848, 758])).
% 2.22/1.69 tff(2078,plain,
% 2.22/1.69 (c3_1(a1039)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2068, 126, 1240, 2054, 2053, 1849, 1848, 1436, 2077])).
% 2.22/1.69 tff(2079,plain,
% 2.22/1.69 (hskp59),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2014, 2078])).
% 2.22/1.69 tff(2080,plain,
% 2.22/1.69 (~c3_1(a1095)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[167, 2079])).
% 2.22/1.69 tff(2081,plain,
% 2.22/1.69 (c1_1(a1095)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[191, 2079])).
% 2.22/1.69 tff(2082,plain,
% 2.22/1.69 (~c2_1(a1095)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2023, 126, 1718, 2006, 2081, 2080, 1564])).
% 2.22/1.69 tff(2083,plain,
% 2.22/1.69 (~c0_1(a1095)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[173, 2079])).
% 2.22/1.69 tff(2084,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034) | c2_1(a1095))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034) | c2_1(a1095))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(2085,plain,
% 2.22/1.69 ((hskp35 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095)) <=> (hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034) | c2_1(a1095))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(2086,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034) | c2_1(a1095)))),
% 2.22/1.69 inference(monotonicity,[status(thm)],[2085])).
% 2.22/1.69 tff(2087,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034) | c2_1(a1095))),
% 2.22/1.69 inference(transitivity,[status(thm)],[2086, 2084])).
% 2.22/1.69 tff(2088,plain,
% 2.22/1.69 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | (hskp35 | (~ndr1_0) | c0_1(a1034) | c2_1(a1034) | (~c3_1(a1034)) | c0_1(a1095) | c3_1(a1095) | c2_1(a1095))),
% 2.22/1.69 inference(quant_inst,[status(thm)],[])).
% 2.22/1.69 tff(2089,plain,
% 2.22/1.69 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c3_1(V) | c2_1(V))) | hskp35 | c0_1(a1095) | c3_1(a1095) | c0_1(a1034) | (~ndr1_0) | (~c3_1(a1034)) | c2_1(a1034) | c2_1(a1095)),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[2088, 2087])).
% 2.22/1.69 tff(2090,plain,
% 2.22/1.69 ($false),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2089, 126, 1240, 2054, 2083, 2080, 2053, 1436, 2077, 2082])).
% 2.22/1.69 tff(2091,plain,(hskp7 | hskp12 | hskp33), inference(lemma,lemma(discharge,[]))).
% 2.22/1.69 tff(2092,plain,
% 2.22/1.69 (hskp7),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2091, 21, 1718])).
% 2.22/1.69 tff(2093,plain,
% 2.22/1.69 (c1_1(a1035)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1653, 2092])).
% 2.22/1.69 tff(2094,plain,
% 2.22/1.69 (~c2_1(a1035)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1609, 2092])).
% 2.22/1.69 tff(2095,plain,
% 2.22/1.69 (c0_1(a1035)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1620, 2092])).
% 2.22/1.69 tff(2096,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(2097,plain,
% 2.22/1.69 ((hskp35 | (~ndr1_0) | c2_1(a1039) | c3_1(a1039) | (~c1_1(a1039)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059))) <=> (hskp35 | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(2098,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1039) | c3_1(a1039) | (~c1_1(a1039)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059)))),
% 2.22/1.69 inference(monotonicity,[status(thm)],[2097])).
% 2.22/1.69 tff(2099,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1039) | c3_1(a1039) | (~c1_1(a1039)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059))),
% 2.22/1.69 inference(transitivity,[status(thm)],[2098, 2096])).
% 2.22/1.69 tff(2100,plain,
% 2.22/1.69 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1039) | c3_1(a1039) | (~c1_1(a1039)) | c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)))),
% 2.22/1.69 inference(quant_inst,[status(thm)],[])).
% 2.22/1.69 tff(2101,plain,
% 2.22/1.69 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1039) | (~ndr1_0) | c3_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1059)) | (~c2_1(a1059)) | c0_1(a1059)),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[2100, 2099])).
% 2.22/1.69 tff(2102,plain,
% 2.22/1.69 (c3_1(a1039)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2101, 126, 1240, 1629, 393, 1856, 1849, 1001, 391])).
% 2.22/1.69 tff(2103,plain,
% 2.22/1.69 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(2104,plain,
% 2.22/1.69 ((hskp56 | hskp22 | (~ndr1_0) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039))) <=> (hskp56 | hskp22 | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(2105,plain,
% 2.22/1.69 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039))))),
% 2.22/1.69 inference(monotonicity,[status(thm)],[2104])).
% 2.22/1.69 tff(2106,plain,
% 2.22/1.69 (((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)))) <=> ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)))),
% 2.22/1.69 inference(transitivity,[status(thm)],[2105, 2103])).
% 2.22/1.69 tff(2107,plain,
% 2.22/1.69 ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp56 | hskp22 | (~ndr1_0) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)))),
% 2.22/1.69 inference(quant_inst,[status(thm)],[])).
% 2.22/1.69 tff(2108,plain,
% 2.22/1.69 ((~![U: $i] : (hskp56 | hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp56 | hskp22 | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[2107, 2106])).
% 2.22/1.69 tff(2109,plain,
% 2.22/1.69 (hskp22 | (~c3_1(a1039))),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2108, 126, 1126, 1856, 1849, 31])).
% 2.22/1.69 tff(2110,plain,
% 2.22/1.69 (hskp22),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2109, 2102])).
% 2.22/1.69 tff(2111,plain,
% 2.22/1.69 (~c1_1(a1083)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1178, 2110])).
% 2.22/1.69 tff(2112,plain,
% 2.22/1.69 (c3_1(a1083)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1144, 2110])).
% 2.22/1.69 tff(2113,plain,
% 2.22/1.69 (c2_1(a1083)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1155, 2110])).
% 2.22/1.69 tff(2114,assumption,(~c2_1(a1035)), introduced(assumption)).
% 2.22/1.69 tff(2115,assumption,(c1_1(a1035)), introduced(assumption)).
% 2.22/1.69 tff(2116,plain,
% 2.22/1.69 (c3_1(a1035)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1660, 126, 1240, 1629, 393, 2115, 2114, 1001, 391])).
% 2.22/1.69 tff(2117,assumption,(c0_1(a1035)), introduced(assumption)).
% 2.22/1.69 tff(2118,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a1059) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1059) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(2119,plain,
% 2.22/1.69 ((hskp57 | (~ndr1_0) | c1_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035))) <=> (hskp57 | c1_1(a1059) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(2120,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a1059) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059))))),
% 2.22/1.69 inference(monotonicity,[status(thm)],[2119])).
% 2.22/1.69 tff(2121,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1059) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059)))),
% 2.22/1.69 inference(transitivity,[status(thm)],[2120, 2118])).
% 2.22/1.69 tff(2122,plain,
% 2.22/1.69 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)))),
% 2.22/1.69 inference(quant_inst,[status(thm)],[])).
% 2.22/1.69 tff(2123,plain,
% 2.22/1.69 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1059) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1059)) | (~c2_1(a1059))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[2122, 2121])).
% 2.22/1.69 tff(2124,plain,
% 2.22/1.69 (hskp57 | (~c3_1(a1035))),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2123, 126, 1629, 393, 2117, 392, 2114, 1058])).
% 2.22/1.69 tff(2125,plain,
% 2.22/1.69 (hskp57),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2124, 2116])).
% 2.22/1.69 tff(2126,plain,
% 2.22/1.69 (c3_1(a1085)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1076, 2125])).
% 2.22/1.69 tff(2127,plain,
% 2.22/1.69 (c0_1(a1085)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1087, 2125])).
% 2.22/1.69 tff(2128,plain,
% 2.22/1.69 (c2_1(a1085)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1098, 2125])).
% 2.22/1.69 tff(2129,plain,
% 2.22/1.69 (hskp53),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1234, 126, 2128, 2127, 2126, 2113, 2112, 2111, 20])).
% 2.22/1.69 tff(2130,plain,
% 2.22/1.69 (c0_1(a1073)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[340, 2129])).
% 2.22/1.69 tff(2131,plain,
% 2.22/1.69 (c2_1(a1073)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[351, 2129])).
% 2.22/1.69 tff(2132,plain,
% 2.22/1.69 (c1_1(a1073)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[362, 2129])).
% 2.22/1.69 tff(2133,plain,
% 2.22/1.69 ($false),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1115, 126, 2128, 2127, 2126, 2132, 2131, 2130, 10])).
% 2.22/1.69 tff(2134,plain,(c0_1(a1059) | (~c3_1(a1059)) | (~c2_1(a1059)) | (~c0_1(a1035)) | c1_1(a1059) | c2_1(a1035) | (~c1_1(a1035))), inference(lemma,lemma(discharge,[]))).
% 2.22/1.69 tff(2135,plain,
% 2.22/1.69 (c0_1(a1059)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2134, 1995, 1993, 2095, 1994, 2094, 2093])).
% 2.22/1.69 tff(2136,plain,
% 2.22/1.69 (hskp53 | (~c0_1(a1059))),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[419, 126, 1995, 1993, 1994, 20])).
% 2.22/1.69 tff(2137,plain,
% 2.22/1.69 (hskp53),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2136, 2135])).
% 2.22/1.69 tff(2138,plain,
% 2.22/1.69 (c0_1(a1073)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[340, 2137])).
% 2.22/1.69 tff(2139,plain,
% 2.22/1.69 (c2_1(a1073)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[351, 2137])).
% 2.22/1.69 tff(2140,plain,
% 2.22/1.69 (c1_1(a1073)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[362, 2137])).
% 2.22/1.69 tff(2141,plain,
% 2.22/1.69 ($false),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[429, 126, 2140, 2139, 2138, 1995, 1993, 10, 2135])).
% 2.22/1.69 tff(2142,plain,(hskp33 | hskp12), inference(lemma,lemma(discharge,[]))).
% 2.22/1.69 tff(2143,plain,
% 2.22/1.69 (hskp33),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2142, 1718])).
% 2.22/1.69 tff(2144,plain,
% 2.22/1.69 (~c1_1(a1031)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[287, 2143])).
% 2.22/1.69 tff(2145,plain,
% 2.22/1.69 (c2_1(a1031)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[298, 2143])).
% 2.22/1.69 tff(2146,plain,
% 2.22/1.69 (c3_1(a1031)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[321, 2143])).
% 2.22/1.69 tff(2147,assumption,(~hskp53), introduced(assumption)).
% 2.22/1.69 tff(2148,plain,
% 2.22/1.69 (hskp53 | (~c0_1(a1031))),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[328, 126, 863, 302, 301, 20])).
% 2.22/1.69 tff(2149,plain,
% 2.22/1.69 (~c0_1(a1031)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[2148, 2147])).
% 2.22/1.69 tff(2150,plain,
% 2.22/1.70 (c3_1(a1035)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1756, 126, 1240, 863, 302, 2115, 2114, 1001, 2149])).
% 2.22/1.70 tff(2151,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a1031) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1031) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(2152,plain,
% 2.22/1.70 ((hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035))) <=> (hskp57 | c1_1(a1031) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(2153,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a1031) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031))))),
% 2.22/1.70 inference(monotonicity,[status(thm)],[2152])).
% 2.22/1.70 tff(2154,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1031) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 2.22/1.70 inference(transitivity,[status(thm)],[2153, 2151])).
% 2.22/1.70 tff(2155,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)))),
% 2.22/1.70 inference(quant_inst,[status(thm)],[])).
% 2.22/1.70 tff(2156,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a1031) | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c3_1(a1031)) | (~c2_1(a1031))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[2155, 2154])).
% 2.22/1.70 tff(2157,plain,
% 2.22/1.70 (hskp57 | (~c3_1(a1035))),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2156, 126, 863, 302, 2117, 301, 2114, 1058])).
% 2.22/1.70 tff(2158,plain,
% 2.22/1.70 (hskp57),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2157, 2150])).
% 2.22/1.70 tff(2159,plain,
% 2.22/1.70 (c3_1(a1085)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1076, 2158])).
% 2.22/1.70 tff(2160,plain,
% 2.22/1.70 (c0_1(a1085)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1087, 2158])).
% 2.22/1.70 tff(2161,plain,
% 2.22/1.70 (c2_1(a1085)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1098, 2158])).
% 2.22/1.70 tff(2162,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(2163,plain,
% 2.22/1.70 ((hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085))) <=> (hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(2164,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1031)) | (~c2_1(a1031))))),
% 2.22/1.70 inference(monotonicity,[status(thm)],[2163])).
% 2.22/1.70 tff(2165,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 2.22/1.70 inference(transitivity,[status(thm)],[2164, 2162])).
% 2.22/1.70 tff(2166,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1085)) | (~c0_1(a1085)) | (~c2_1(a1085)))),
% 2.22/1.70 inference(quant_inst,[status(thm)],[])).
% 2.22/1.70 tff(2167,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1085)) | (~c2_1(a1085)) | (~c0_1(a1085)) | (~c3_1(a1031)) | (~c2_1(a1031))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[2166, 2165])).
% 2.22/1.70 tff(2168,plain,
% 2.22/1.70 ($false),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2167, 126, 2147, 2161, 2160, 2159, 863, 302, 301, 20])).
% 2.22/1.70 tff(2169,plain,(hskp53 | (~c3_1(a1031)) | (~c2_1(a1031)) | c1_1(a1031) | (~c0_1(a1035)) | c2_1(a1035) | (~c1_1(a1035))), inference(lemma,lemma(discharge,[]))).
% 2.22/1.70 tff(2170,plain,
% 2.22/1.70 (hskp53),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2169, 2146, 2145, 2144, 2074, 2073, 2075])).
% 2.22/1.70 tff(2171,plain,
% 2.22/1.70 (c0_1(a1073)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[340, 2170])).
% 2.22/1.70 tff(2172,plain,
% 2.22/1.70 (c2_1(a1073)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[351, 2170])).
% 2.22/1.70 tff(2173,plain,
% 2.22/1.70 (c1_1(a1073)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[362, 2170])).
% 2.22/1.70 tff(2174,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(2175,plain,
% 2.22/1.70 ((hskp12 | (~ndr1_0) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073))) <=> (hskp12 | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(2176,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073))))),
% 2.22/1.70 inference(monotonicity,[status(thm)],[2175])).
% 2.22/1.70 tff(2177,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 2.22/1.70 inference(transitivity,[status(thm)],[2176, 2174])).
% 2.22/1.70 tff(2178,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a1035) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 2.22/1.70 inference(quant_inst,[status(thm)],[])).
% 2.22/1.70 tff(2179,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp12 | c2_1(a1035) | (~ndr1_0) | (~c3_1(a1035)) | (~c0_1(a1035)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[2178, 2177])).
% 2.22/1.70 tff(2180,plain,
% 2.22/1.70 (~c3_1(a1035)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2179, 126, 1718, 2173, 2172, 2171, 2074, 2073, 1288])).
% 2.22/1.70 tff(2181,plain,
% 2.22/1.70 (~c0_1(a1031)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[369, 126, 2173, 2172, 2171, 2146, 2145, 10])).
% 2.22/1.70 tff(2182,plain,
% 2.22/1.70 ($false),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1756, 126, 1240, 2146, 2145, 2075, 2073, 1001, 2181, 2180])).
% 2.22/1.70 tff(2183,plain,(hskp12), inference(lemma,lemma(discharge,[]))).
% 2.22/1.70 tff(2184,plain,
% 2.22/1.70 (~c3_1(a1043)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1570, 2183])).
% 2.22/1.70 tff(2185,plain,
% 2.22/1.70 (~c1_1(a1043)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1576, 2183])).
% 2.22/1.70 tff(2186,plain,
% 2.22/1.70 (c0_1(a1043)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1587, 2183])).
% 2.22/1.70 tff(2187,plain,
% 2.22/1.70 ($false),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1845, 126, 393, 2186, 392, 2185, 2184, 242, 391, 2005])).
% 2.22/1.70 tff(2188,plain,(c0_1(a1059) | (~c2_1(a1059)) | c1_1(a1059) | c2_1(a1043)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.70 tff(2189,plain,
% 2.22/1.70 (c2_1(a1043)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2188, 2004, 1994, 1993])).
% 2.22/1.70 tff(2190,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c0_1(a1043)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp47 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c0_1(a1043)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(2191,plain,
% 2.22/1.70 ((hskp47 | (~ndr1_0) | c3_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1043)) | c1_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1043))) <=> (hskp47 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c0_1(a1043)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(2192,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1043)) | c1_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1043)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c0_1(a1043))))),
% 2.22/1.70 inference(monotonicity,[status(thm)],[2191])).
% 2.22/1.70 tff(2193,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1043)) | c1_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1043)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp47 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c0_1(a1043)))),
% 2.22/1.70 inference(transitivity,[status(thm)],[2192, 2190])).
% 2.22/1.70 tff(2194,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp47 | (~ndr1_0) | c3_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1043)) | c1_1(a1043) | (~c0_1(a1043)) | (~c2_1(a1043)))),
% 2.22/1.70 inference(quant_inst,[status(thm)],[])).
% 2.22/1.70 tff(2195,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp47 | c1_1(a1043) | c3_1(a1043) | (~ndr1_0) | (~c2_1(a1043)) | (~c0_1(a1043))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[2194, 2193])).
% 2.22/1.70 tff(2196,plain,
% 2.22/1.70 (hskp47 | (~c2_1(a1043))),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2195, 126, 2186, 2185, 2184, 480])).
% 2.22/1.70 tff(2197,plain,
% 2.22/1.70 (hskp47),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2196, 2189])).
% 2.22/1.70 tff(2198,plain,
% 2.22/1.70 (c3_1(a1056)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[498, 2197])).
% 2.22/1.70 tff(2199,plain,
% 2.22/1.70 (c1_1(a1056)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[509, 2197])).
% 2.22/1.70 tff(2200,plain,
% 2.22/1.70 (c2_1(a1056)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[520, 2197])).
% 2.22/1.70 tff(2201,plain,
% 2.22/1.70 (~hskp19),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[811, 2200, 21, 2199, 2198])).
% 2.22/1.70 tff(2202,plain,
% 2.22/1.70 (hskp20),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1596, 2201, 2183])).
% 2.22/1.70 tff(2203,plain,
% 2.22/1.70 (~c1_1(a1080)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[727, 2202])).
% 2.22/1.70 tff(2204,plain,
% 2.22/1.70 (~c2_1(a1080)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[699, 2202])).
% 2.22/1.70 tff(2205,plain,
% 2.22/1.70 (~c0_1(a1080)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[705, 2202])).
% 2.22/1.70 tff(2206,plain,
% 2.22/1.70 ($false),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1836, 126, 1995, 1993, 2205, 2204, 2203, 2185, 2184, 538, 2004, 2189])).
% 2.22/1.70 tff(2207,plain,(hskp33), inference(lemma,lemma(discharge,[]))).
% 2.22/1.70 tff(2208,plain,
% 2.22/1.70 (~c1_1(a1031)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[287, 2207])).
% 2.22/1.70 tff(2209,plain,
% 2.22/1.70 (c2_1(a1031)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[298, 2207])).
% 2.22/1.70 tff(2210,plain,
% 2.22/1.70 (c3_1(a1031)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[321, 2207])).
% 2.22/1.70 tff(2211,plain,
% 2.22/1.70 (hskp53 | (~c0_1(a1031))),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[328, 126, 2210, 2209, 2208, 20])).
% 2.22/1.70 tff(2212,plain,
% 2.22/1.70 (~c0_1(a1031)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2211, 2147])).
% 2.22/1.70 tff(2213,assumption,(hskp48), introduced(assumption)).
% 2.22/1.70 tff(2214,plain,
% 2.22/1.70 (c0_1(a1062)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1894, 2213])).
% 2.22/1.70 tff(2215,plain,
% 2.22/1.70 (c2_1(a1062)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1905, 2213])).
% 2.22/1.70 tff(2216,plain,
% 2.22/1.70 (c3_1(a1062)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1916, 2213])).
% 2.22/1.70 tff(2217,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1031) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1031) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(2218,plain,
% 2.22/1.70 ((hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062))) <=> (hskp53 | c1_1(a1031) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(2219,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | c1_1(a1031) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1031)) | (~c2_1(a1031))))),
% 2.22/1.70 inference(monotonicity,[status(thm)],[2218])).
% 2.22/1.70 tff(2220,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1031) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 2.22/1.70 inference(transitivity,[status(thm)],[2219, 2217])).
% 2.22/1.70 tff(2221,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (hskp53 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))),
% 2.22/1.70 inference(quant_inst,[status(thm)],[])).
% 2.22/1.70 tff(2222,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | hskp53 | c1_1(a1031) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c3_1(a1031)) | (~c2_1(a1031))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[2221, 2220])).
% 2.22/1.70 tff(2223,plain,
% 2.22/1.70 (hskp53),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2222, 126, 2216, 2215, 2214, 863, 302, 301, 20])).
% 2.22/1.70 tff(2224,plain,
% 2.22/1.70 (c0_1(a1073)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[340, 2223])).
% 2.22/1.70 tff(2225,plain,
% 2.22/1.70 (c2_1(a1073)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[351, 2223])).
% 2.22/1.70 tff(2226,plain,
% 2.22/1.70 (c1_1(a1073)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[362, 2223])).
% 2.22/1.70 tff(2227,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(2228,plain,
% 2.22/1.70 (((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062))) <=> ((~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(2229,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073))))),
% 2.22/1.70 inference(monotonicity,[status(thm)],[2228])).
% 2.22/1.70 tff(2230,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)))),
% 2.22/1.70 inference(transitivity,[status(thm)],[2229, 2227])).
% 2.22/1.70 tff(2231,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | ((~ndr1_0) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073)) | (~c3_1(a1062)) | (~c0_1(a1062)) | (~c2_1(a1062)))),
% 2.22/1.70 inference(quant_inst,[status(thm)],[])).
% 2.22/1.70 tff(2232,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))) | (~ndr1_0) | (~c0_1(a1062)) | (~c2_1(a1062)) | (~c3_1(a1062)) | (~c1_1(a1073)) | (~c0_1(a1073)) | (~c2_1(a1073))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[2231, 2230])).
% 2.22/1.70 tff(2233,plain,
% 2.22/1.70 ($false),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2232, 126, 2226, 2225, 2224, 2216, 2215, 2214, 10])).
% 2.22/1.70 tff(2234,plain,((~hskp48) | (~c3_1(a1031)) | (~c2_1(a1031)) | c1_1(a1031)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.70 tff(2235,plain,
% 2.22/1.70 (~hskp48),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2234, 2210, 2209, 2208])).
% 2.22/1.70 tff(2236,assumption,(~c3_1(a1039)), introduced(assumption)).
% 2.22/1.70 tff(2237,assumption,(~hskp48), introduced(assumption)).
% 2.22/1.70 tff(2238,plain,
% 2.22/1.70 (hskp36),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1883, 2236, 2237])).
% 2.22/1.70 tff(2239,plain,
% 2.22/1.70 (~c0_1(a1034)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[780, 2238])).
% 2.22/1.70 tff(2240,plain,
% 2.22/1.70 (c3_1(a1034)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[826, 2238])).
% 2.22/1.70 tff(2241,plain,
% 2.22/1.70 (~c2_1(a1034)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2060, 126, 1240, 2240, 1856, 2239, 1849, 1001, 2236])).
% 2.22/1.70 tff(2242,plain,
% 2.22/1.70 ($false),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2068, 126, 1240, 2240, 2239, 1849, 1848, 1436, 2236, 2241])).
% 2.22/1.70 tff(2243,plain,(c3_1(a1039) | hskp48), inference(lemma,lemma(discharge,[]))).
% 2.22/1.70 tff(2244,plain,
% 2.22/1.70 (c3_1(a1039)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2243, 2235])).
% 2.22/1.70 tff(2245,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | c1_1(a1031) | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)) | (~c2_1(a1031)) | c0_1(a1031))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp42 | c1_1(a1031) | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)) | (~c2_1(a1031)) | c0_1(a1031))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(2246,plain,
% 2.22/1.70 ((hskp42 | (~ndr1_0) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031))) <=> (hskp42 | c1_1(a1031) | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)) | (~c2_1(a1031)) | c0_1(a1031))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(2247,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | c1_1(a1031) | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)) | (~c2_1(a1031)) | c0_1(a1031)))),
% 2.22/1.70 inference(monotonicity,[status(thm)],[2246])).
% 2.22/1.70 tff(2248,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp42 | c1_1(a1031) | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)) | (~c2_1(a1031)) | c0_1(a1031))),
% 2.22/1.70 inference(transitivity,[status(thm)],[2247, 2245])).
% 2.22/1.70 tff(2249,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp42 | (~ndr1_0) | c2_1(a1039) | (~c1_1(a1039)) | (~c3_1(a1039)) | c0_1(a1031) | c1_1(a1031) | (~c2_1(a1031)))),
% 2.22/1.70 inference(quant_inst,[status(thm)],[])).
% 2.22/1.70 tff(2250,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp42 | c1_1(a1031) | c2_1(a1039) | (~ndr1_0) | (~c3_1(a1039)) | (~c1_1(a1039)) | (~c2_1(a1031)) | c0_1(a1031)),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[2249, 2248])).
% 2.22/1.70 tff(2251,plain,
% 2.22/1.70 (hskp42),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2250, 126, 2209, 1856, 2208, 1849, 1173, 2244, 2212])).
% 2.22/1.70 tff(2252,plain,
% 2.22/1.70 (~c2_1(a1046)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1191, 2251])).
% 2.22/1.70 tff(2253,plain,
% 2.22/1.70 (c1_1(a1046)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1202, 2251])).
% 2.22/1.70 tff(2254,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | c3_1(a1046) | (~c1_1(a1046)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | c3_1(a1046) | (~c1_1(a1046)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(2255,plain,
% 2.22/1.70 ((hskp35 | (~ndr1_0) | c2_1(a1046) | c3_1(a1046) | (~c1_1(a1046)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031))) <=> (hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | c3_1(a1046) | (~c1_1(a1046)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(2256,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1046) | c3_1(a1046) | (~c1_1(a1046)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | c3_1(a1046) | (~c1_1(a1046))))),
% 2.22/1.70 inference(monotonicity,[status(thm)],[2255])).
% 2.22/1.70 tff(2257,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1046) | c3_1(a1046) | (~c1_1(a1046)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)))) <=> ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | c3_1(a1046) | (~c1_1(a1046)))),
% 2.22/1.70 inference(transitivity,[status(thm)],[2256, 2254])).
% 2.22/1.70 tff(2258,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp35 | (~ndr1_0) | c2_1(a1046) | c3_1(a1046) | (~c1_1(a1046)) | c0_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)))),
% 2.22/1.70 inference(quant_inst,[status(thm)],[])).
% 2.22/1.70 tff(2259,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp35 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp35 | c2_1(a1046) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | c0_1(a1031) | c3_1(a1046) | (~c1_1(a1046))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[2258, 2257])).
% 2.22/1.70 tff(2260,plain,
% 2.22/1.70 (c3_1(a1046)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2259, 126, 1240, 2253, 2210, 2209, 2252, 1001, 2212])).
% 2.22/1.70 tff(2261,plain,
% 2.22/1.70 (c0_1(a1046)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1257, 2251])).
% 2.22/1.70 tff(2262,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c2_1(a1046) | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1046)) | (~c0_1(a1046)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c2_1(a1046) | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1046)) | (~c0_1(a1046)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(2263,plain,
% 2.22/1.70 ((hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1046) | (~c3_1(a1046)) | (~c0_1(a1046))) <=> (hskp57 | c2_1(a1046) | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1046)) | (~c0_1(a1046)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(2264,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1046) | (~c3_1(a1046)) | (~c0_1(a1046)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c2_1(a1046) | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1046)) | (~c0_1(a1046))))),
% 2.22/1.70 inference(monotonicity,[status(thm)],[2263])).
% 2.22/1.70 tff(2265,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1046) | (~c3_1(a1046)) | (~c0_1(a1046)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c2_1(a1046) | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1046)) | (~c0_1(a1046)))),
% 2.22/1.70 inference(transitivity,[status(thm)],[2264, 2262])).
% 2.22/1.70 tff(2266,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | c1_1(a1031) | (~c3_1(a1031)) | (~c2_1(a1031)) | c2_1(a1046) | (~c3_1(a1046)) | (~c0_1(a1046)))),
% 2.22/1.70 inference(quant_inst,[status(thm)],[])).
% 2.22/1.70 tff(2267,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c2_1(a1046) | c1_1(a1031) | (~ndr1_0) | (~c3_1(a1031)) | (~c2_1(a1031)) | (~c3_1(a1046)) | (~c0_1(a1046))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[2266, 2265])).
% 2.22/1.70 tff(2268,plain,
% 2.22/1.70 (hskp57 | (~c3_1(a1046))),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2267, 126, 2261, 2210, 2209, 2252, 2208, 1058])).
% 2.22/1.70 tff(2269,plain,
% 2.22/1.70 (hskp57),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2268, 2260])).
% 2.22/1.70 tff(2270,plain,
% 2.22/1.70 (c3_1(a1085)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1076, 2269])).
% 2.22/1.70 tff(2271,plain,
% 2.22/1.70 (c0_1(a1085)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1087, 2269])).
% 2.22/1.70 tff(2272,plain,
% 2.22/1.70 (c2_1(a1085)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1098, 2269])).
% 2.22/1.70 tff(2273,plain,
% 2.22/1.70 ($false),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2167, 126, 2147, 2272, 2271, 2270, 2210, 2209, 2208, 20])).
% 2.22/1.70 tff(2274,plain,(hskp53), inference(lemma,lemma(discharge,[]))).
% 2.22/1.70 tff(2275,plain,
% 2.22/1.70 (c0_1(a1073)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[340, 2274])).
% 2.22/1.70 tff(2276,plain,
% 2.22/1.70 (c2_1(a1073)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[351, 2274])).
% 2.22/1.70 tff(2277,plain,
% 2.22/1.70 (c1_1(a1073)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[362, 2274])).
% 2.22/1.70 tff(2278,plain,
% 2.22/1.70 (~c0_1(a1031)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[369, 126, 2277, 2276, 2275, 2210, 2209, 10])).
% 2.22/1.70 tff(2279,plain,
% 2.22/1.70 (hskp42),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2250, 126, 2209, 1856, 2208, 1849, 1173, 2244, 2278])).
% 2.22/1.70 tff(2280,plain,
% 2.22/1.70 (~c2_1(a1046)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1191, 2279])).
% 2.22/1.70 tff(2281,plain,
% 2.22/1.70 (c1_1(a1046)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1202, 2279])).
% 2.22/1.70 tff(2282,plain,
% 2.22/1.70 (c3_1(a1046)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2259, 126, 1240, 2281, 2210, 2209, 2280, 1001, 2278])).
% 2.22/1.70 tff(2283,plain,
% 2.22/1.70 (c0_1(a1046)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1257, 2279])).
% 2.22/1.70 tff(2284,plain,
% 2.22/1.70 (hskp57 | (~c3_1(a1046))),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2267, 126, 2283, 2210, 2209, 2280, 2208, 1058])).
% 2.22/1.70 tff(2285,plain,
% 2.22/1.70 (hskp57),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[2284, 2282])).
% 2.22/1.70 tff(2286,plain,
% 2.22/1.70 (c3_1(a1085)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1076, 2285])).
% 2.22/1.70 tff(2287,plain,
% 2.22/1.70 (c0_1(a1085)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1087, 2285])).
% 2.22/1.70 tff(2288,plain,
% 2.22/1.70 (c2_1(a1085)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1098, 2285])).
% 2.22/1.70 tff(2289,plain,
% 2.22/1.70 ($false),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1115, 126, 2288, 2287, 2286, 2277, 2276, 2275, 10])).
% 2.22/1.70 % SZS output end Proof
%------------------------------------------------------------------------------